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564 Forest St
Beds: 2
Baths: 1
Sq. Ft.: 1,306
Listing #40788021
Exquisite 1916 Rockridge Craftsman home combines traditional character with tasteful updates. Chefs kitchen for the most discerning cook. Ideally situated in a coveted neighborhood. Lovely tree lined streets that are a short stroll to gourmet dining, vibrant cafe culture and specialty shops. Close to nearby commuter transportation (Buses and BART). Near the University and zoned for the highly regarded Peralta Elementary School (enrollment prioritized but not guaranteed).
Property Features
Location Information
County: Alameda
Neighborhood: ROCKRIDGE
Area: Oakland Zip Code 94618
Cross Street: Alcatraz
Interior Features
Rooms: Office, Sun Porch
Other Bathrooms Description: Tile, Tub, Updated Baths
Kitchen Description: Counter - Solid Surface, Dishwasher, Garbage Disposal, Range/Oven Built-in, Refrigerator
Has Fireplace: yes
Number of Fireplaces: 1
Fireplace Description: Decorative Only
Heating: Forced Air 1 Zone
Cooling: None
Floors: Hardwood Floors, Linoleum
Laundry: In Unit
Additional Equipment: None
Exterior Features
Style: Craftsman
Stories: Other
Exterior: Other
Foundation: Crawl Space, Partial Basement
Roof: Composition Shingles
Possession: COE
Water / Sewer: Sewer System - Public
Parking Description: Detached Garage, Space Per Unit - 2
Has Garage: yes
Garage Spaces: 0
Yard: Deck(s)
Has a Pool: No
Pool Description: None
Lot Description: Regular
Lot Size in Acres: 0.05
Lot Size in Sq. Ft.: 1, 960
Additional Information
Property Type: SFR
Property SubType: Detached
Year Built: 1913
Status: Active
Home Owners Association: N
On The Market Since: 07/05/2017
$ per month
Year Fixed. % Interest Rate.
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Listing Agent: CARLA J. HIGGINS
Bay East ©2017. CCAR ©2017. BridgeMLS ©2017. Information Deemed Reliable But Not Guaranteed. This information is being provided by the Bay East MLS, or CCAR MLS, or BridgeMLS. The listings presented here may or may not be listed by the Broker/Agent operating this website. This information is intended for the personal use of consumers, and may not be used for any purpose other than to identify prospective properties consumers may be interested in purchasing.
Bridge-CCAR-Bay East data last updated at July 27, 2017 5:13 PM PT
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text:
|First appearance
|"The Locket" (mentioned)
Delik was a scientist who studied time and temporal anomalies.
Stark mentioned Delik when he and Zhaan were trying to determine the reason why John Crichton and Aeryn Sun disappeared while investigating a planet in a dense cloud of stellar mist.
After discovering that Aeryn had apparently aged over 160 cycles in what would seem to be only a few arns, Stark suggested that perhaps it was Moya who was trapped in some sort of temporal anomaly once described by a scientist named Delik. Stark stated that Delik "theorized about what he called 'center halos.' He believed that scattered throughout the universe were mists where all dimensions met and time ceased to exist." ("The Locket")

subset: commoncrawl


text:
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Robust output feedbackstabilization via risk-sensitive control
- Wilfrid Holmes
- 2 years ago
- Views:
1 Automatica 38 22) Robust output feedbackstabilization via risk-sensitive control Valery A. Ugrinovskii, Ian R. Petersen School of Electrical Engineering, Australian Defence Force Academy, Canberra AC 26, Australia Received 2 February 2; received in revised form 24 October 2; accepted 2 November 2 Abstract We consider a problem of robust linear quadratic Gaussian LQG) control for discrete-time stochastic uncertain systems with partial state measurements. For a nite-horizon case, the problem was recently introduced by Petersen et al. IEEE rans. Automat. Control 45 2) 398). In this paper, an innite horizon extension of the results of Petersen et al. IEEE rans. Automat. Control 45 2) 398) is discussed. We show that for a broad class of uncertain systems under consideration, a controller constructed in terms of the solution to a specially parameterized risk-sensitive stochastic control problem absolutely stabilizes the stochastic uncertain system.? 22 Elsevier Science Ltd. All rights reserved. Keywords: Robust control; LQG control; Stochastic control; Stochastic risk-sensitive control. Introduction For systems with partial state measurements, the linear quadratic Gaussian LQG) methodology has proved to be a useful technique for designing output feedbackcontrollers. However, the development of a robust version of the LQG technique has been a challenging problem. It is known that LQG controllers may lead to very poor robustness in terms of gain and phase robustness margins Doyle, 978). herefore, considerable eorts have recently been undertaken to develop a robust version of the LQG control synthesis methodology. For dierent uncertainty models, this problem has been attacked using the H and mixed H 2 =H control approach e.g., see Mustafa & Bernstein, 99; Haddad et al., 99; Basar & Bernhard, 995), the guaranteed cost and quadratic stabilization approach Fu, de Souza, & Xie, 99), the minimax optimization approach based on sum quadratic constraints Moheimani, Savkin, & Petersen, 995). It has recently been demonstrated in Petersen, James, and Dupuis 2a) that one possibility to enhance the his workwas ported by he Australian Research Council and he Defence Science and echnology Organization. his paper was not presented at any IFAC meeting. Corresponding author. el.: ; fax: addresses: V.A. Ugrinovskii), I.R. Petersen). robustness of an LQG controller is to use a risk-sensitive control approach to the controller synthesis. he risksensitive control approach has a number of attractive features. Apart from the enhanced robustness of a controller, this approach leads to a tractable minimax design procedure which can be viewed as a direct extension of the existing LQG control technique, see Petersen, Ugrinovskii, and Savkin 2b). Note that the results in Petersen et al. 2a) which concern the output feedbackrobust control of linear systems, are incomplete in that they address the nite-horizon control problem and lead to time-varying controllers, whereas in practical robust controller design problems, time-invariant controllers are most useful. he derivation of time-invariant output feedbackrobust controllers requires that an innite-horizon version of the partial information minimax optimal control problem of Petersen et al. 2a) be considered. Although a steady-state version of the minimax optimal controller was discussed by Petersen et al. 2a), the stabilizing properties of this controller were not addressed. In this paper, we rigorously address an innite-horizon robust control problem which can be regarded as an extension of the problems considered by Petersen et al. 2a) to the innite time horizon case. he contribution of this paper is to show that the resulting optimal control schemes guarantee the absolute stability of the closed loop system against the class of admissible uncertainty perturbations under consideration; see also Ugrinovskii and Petersen 2a), Petersen et al. 2b) and Dupuis et al. 998) in the continuous-time case. 5-98/2/$ - see front matter? 22 Elsevier Science Ltd. All rights reserved. PII: S 5-98)288-6
2 946 V.A. Ugrinovskii, I.R. Petersen / Automatica 38 22) he main result of the paper is a robust LQG control synthesis procedure based on a pair of discrete-time algebraic Riccati equations arising in a risk-sensitive optimal control; see Glover and Doyle 988). We show that solutions to a certain specially parameterized risk-sensitive control problem provide us with a controller which guarantees an optimal upper bound on the time-averaged performance of the closed-loop system in the presence of admissible uncertainties. his result is analogous to the corresponding continuous-time result of Ugrinovskii and Petersen 2a). 2. Denitions We adopt the stochastic uncertain system model introduced in Petersen et al. 2a). his model includes a nominal system model and also a description of a class of admissible uncertain perturbations. In this section, we present a modication of the model of Petersen et al. 2a) which is required in order to obtain an innite-horizon minimax LQG control result. he nominal system and measurement dynamics are described by the following equation: x t+ = Ax t + B u t + B 2 w t+ ; z t = C x t + D u t ; y t+ = C 2 x t + v t+ : ) In the above equations x t R n is the state, z t R p is the uncertainty output, and y t R q is the measured output. Also, w := {w t } t= ;v := {v t } t= are two sequences of i.i.d. Gaussian variables with zero mean and covariance matrices W ;, respectively. It is assumed that w t R r ;v t R q ;t=; 2;:::.WeletP w ;P v denote marginal probability measures of w t ;v t. he sequence w corresponds to the system noise, while the sequence v is referred to as the measurement noise. For simplicity, we pose that the reference system noise and the reference measurement noise are independent. All coecients in Eqs. ) are assumed to be constant matrices of corresponding dimensions. Also for the sake of simplicity, we assume that C D =. he initial state of system ) is a Gaussian random vector x R n with mean x and non-singular covariance matrix Y. he corresponding Gaussian probability measure associated with x is denoted P x. he random variable x is assumed to be independent of the reference noise sequences w ;v. he joint probability measure on the initial condition vector x and the reference noise sequences w and v is hroughout the paper, t ; t will denote sequences of random variables as follows t := { t; t+ ;:::; }; t := { t; t+ ;:::}. denoted by P : P dx dw dv ) = P x dx ) P w dw t ) P v dv t ): t= his probability measure is dened on measurable sets of the ltration {F ;=; ;:::}. For each =; ;:::;the -algebra F is generated by the initial condition x of system ) and the noise sequences w, v and is completed by including all sets of P -probability zero. he sets of the -algebra F are subsets of the noise space W, W = {x ;w ;v )}: From Kolmogorov s theorem, the family of probability measures P gives rise to a probability measure P dened on measurable space W; F); F = {F ;=; ;:::}. 2.. Stochastic uncertain system We now introduce an uncertainty model. he uncertainty will be modeled in terms of perturbations of corresponding joint probability distributions of the noise inputs w, v and the initial condition of the system. It is demonstrated in Section 2.3 that such a model provides a meaningful description of stochastic uncertain systems modeled using a linear fractional transformation LF); also, see Petersen et al. 2a,b) and Ugrinovskii and Petersen 999). he rigorous denition of our uncertainty model is the following. Let Q := {Q ;Q 2 ;:::} be a collection of conditional probability measures referred to as an uncertainty; i.e., for each t =; 2;:::; Q t dw t dv t x ;w t ;v t ) is a probability measure dened on measurable subsets of R r R q.itisassumed that Q t dw t dv t x ;w t ;v t ) Pdw t dv t x ;w t ;v t ); t =; 2;::: 2) Here, the notation means that the probability measure is absolutely continuous with respect to the reference probability measure. Using the collection Q, the joint probability measure of the initial condition vector x and the perturbed noise sequences w and v is dened by Q dx dw dv ) = P x dx ) t= Q t dw t dv t x ;w t ;v t ): t= It follows from Eq. 2) that Q P. Also, for any F -measurable set W; Q )=Q ). As in Petersen et al. 2a), we will require that each uncertainty Q = {Q ;Q 2 ;:::} has the property hq P ) for all :
3 Here, hq P ) is the relative entropy functional; e.g., see Dupuis and Ellis 997). his requirement will allow us to rule out the possibility of singular uncertain probability measure perturbations. he class of uncertain systems considered in this paper comprises the systems of the form ) in which the marginal conditional probability measures of the noise inputs w, v are required to satisfy the above requirements. he set of such uncertainties Q will be denoted as Q. From the denition and properties of the relative entropy functional, it follows that the set Q is convex. V.A. Ugrinovskii, I.R. Petersen / Automatica 38 22) Relative entropy constraint on stochastic uncertainty LF uncertainty models require that a magnitude constraint be imposed on the uncertainty. For example, it is often required that the unmodeled dynamics transfer function has a bounded H norm. As shown in Ugrinovskii and Petersen 999, 2a) and Petersen et al. 2b), for stochastic LF systems with additive noise, the constraint on the H norm of the uncertainty transfer function can be replaced by a constraint on the relative entropy of the associated perturbation probability measure. For discrete time systems, this leads to an extension of the sum quadratic constraint uncertainty description Moheimani et al., 995); see Section 2.3. Let E Q denote the expectation with respect to the probability measure Q. Denition. Let d be a given positive constant. A collection of conditional probability measures Q Q is said to dene an admissible uncertainty if the following stochastic uncertainty constraint is satised: hq P ) 6 d + 2 EQ z s 2 + ) 3) for all =; 2;:::.In3);z t is the uncertainty output dened by Eq. ). Also; ) as. We denote the set of uncertainties Q Q satisfying condition 3) by. he corresponding probability measures Q are also called admissible probability measures. Observe that the set is not empty. Indeed, consider the reference probability measure P. Since the Gaussian random variables w t, v t are independent, the corresponding reference conditional probability measures are simply the marginal probability measures: P t dw t dv t x ;w t ;v t )=P w dw t ) P v dv t ): Also, the fact that hp P ) = and the condition d imply that the corresponding collection of conditional probabilities P := {P ;P 2 ;:::} is admissible, P. Note that in this case, constraint 3) is satised strictly. Hence, P is an interior point of the set. Fig.. An uncertain control system A connection between uncertainty input signals and uncertain probability measures In order to give a further insight into Denition, we show that the uncertainty class introduced in Section 2.2 includes uncertainty models which often arise in control systems such as H norm-bounded uncertainty and bounded exogenous uncertainty. Consider an uncertain system shown in Fig.. he system is described by the equations x t+ = Ax t + B u t + B 2 t z t = C x t + D u t ; y t+ = C 2 x t + t + ex t + w t+ ); + ex t +ṽ t+ ); 4) and is driven by the system and measurement noises w t, ṽ t, exogenous disturbance processes ex t, ex t and uncertainty inputs t, t which are generated by a stable linear time-invariant uncertainty. he latter is due to the presence of unmodeled dynamics which are described by a stable transfer function z). It is assumed that! ; W =2 e j! ) =2 6 2 : 5) Condition 5) constitutes a H type norm bound on the size of unmodeled dynamics in system 4). System 4) is considered in a complete probability space W; F; Q); w,ṽ are Gaussian white noise processes in this probability space, E Q w t w t =W, E Qṽ t ṽ t =. It follows from 5) that the processes, are adapted to the ltration {F ;=; ;:::;} generated by the noise inputs
4 948 V.A. Ugrinovskii, I.R. Petersen / Automatica 38 22) and W =2 t 2 + =2 t 2 ) 6 2 E Q z t 2 : E Q Also, it is assumed that the exogenous disturbances ex, ex are adapted to the ltration {F ;=; ;:::;} and E Q W =2 ex t 2 + =2 ex t 2 ) 6 d + ); 6) where d is a given constant, and ) as. Condition 6) imposes a bound on the size of uncertain exogenous perturbations in system 4). In particular, one can see the role of the constant d from Denition in this example. he introduction of this constant reects the fact that the power seminorm of the input disturbances does not exceed d. he above constraints on the exogenous disturbance and unmodeled dynamics lead to an uncertainty constraint which can be represented in the form of the relative entropy uncertainty constraint 3). Indeed, the above assumptions imply that the processes ex, ex t := t + ex t ; t := t + ex t satisfy the condition 2 E Q W =2 t 2 + =2 t 2 ) 6 d + 2 E Q z t 2 + ): 7) In order to express constraint 7) in the form of condition 3), we introduce the probability measure transformation dp = exp { d Q tw w t+ 2 } F tw t exp { t ṽ t+ 2 } t t : 8) Using the discrete-time version of the Girsanov s theorem Elliott, Aggoun, & Moore, 994) we conclude that under the probability measure P the sequences w ;v dened by the equations w t+ = w t+ + t ; v t+ =ṽ t+ + t ; t =; ; 2;::: : 9) are the sequences of i.i.d. Gaussian random variables. Furthermore, when considered with respect to the probability measure P, system 4) becomes a system of the form ) driven by the i.i.d. Gaussian white noises w t ;v t. Finally, using the chain rule Dupuis & Ellis, 997), we obtain h Q P )= 2 E Q W =2 t 2 + =2 t 2) : Here, Q and P denote the restrictions of the probability measures Q and P to W; F ). hus, from 7), condition 3) of Denition 2 follows. herefore, the uncertain system considered in this section belongs to the class of uncertain systems dened in Denition. It can be shown in a similar fashion that Denition encompasses some other important classes of uncertainty arising in control systems such as, for example, the cone-bounded uncertainty Absolutely stabilizing control In this paper, our attention will be restricted to linear output-feedbackcontrollers of the form ˆx t+ = A c ˆx t + B c y t+ ; u t = C c ˆx t ; ) where ˆx R ˆn is the state of the controller, A c R ˆn ˆn, B c R ˆn q, and C c R m ˆn. Let U denote this class of linear controllers. Note that controller ) is adapted to the ltration {Y t ;t } generated by the observation process y; Y t = {y s ;s=;:::;t}. he closed-loop system corresponding to system ) and controller ) is described by a linear dierence equation of the form x t+ = A x t + B w t+ ; z t = C x t ; u t = C c x t : ) In Eq. ), x =x ˆx R n+ˆn and w t =w t v t are the state and the noise input of the closed loop system. Also, the following notation is used: A B C c B2 A = ; B = ; B c C 2 A c B c C =C D C c : 2) In the sequel, we will consider a subclass of controllers ) which satisfy some additional stabilizability and observability requirements. We say that a controller K belongs to the class U U if for this controller, the corresponding matrix pair A; B) is stabilizable 2 and the pair A c ;C c )is observable. It was shown in Petersen et al. 2a) that in the steady-state case, the minimax optimal LQG controller has the structure given in equation ). As mentioned above, we wish to investigate the stabilizing properties of this optimal controller as. First, we introduce a denition 2 For example, this condition holds if the matrix pairs A; B 2 ) and A c;b c) are stabilizable.
5 V.A. Ugrinovskii, I.R. Petersen / Automatica 38 22) of stabilizability which allows for uncertain control systems driven by additive noise whose solutions are not square summable. Denition 2. A controller K of the form ) is said to be an absolutely stabilizing controller for the uncertain system ) with uncertainty satisfying the relative entropy constraint 3); if the system state process x ; the controller state process ˆx and the control process u dened by the closed-loop system ) corresponding to this controller satisfy the following condition. here exist constants c ; c 2 such that for any admissible uncertainty Q ; x t 2 + ˆx t 2 + u t 2 ) E Q +hq P ) 6 c + c 2 d: 3) In particular, for the uncertain system shown in Fig. above property means that in a stable closed-loop system, time-average norms of the system state, controller state as well as control input and uncertainty inputs are bounded regardless the value of the transfer function z) and disturbances ex, ex. In the special case of the uncontrolled uncertain system ), 3), the above denition reduces to the property of absolute stability the system. hat is, the uncertain system ), 3) with u t = is absolutely stable if for any admissible uncertainty Q, x t 2 + hq P ) 6 c + c 2 d: E Q 4) Lemma. Suppose the stochastic nominal closed-loop system ) is mean square stable; i.e. E x t 2 : 5) Also; pose the pair A; B) is stabilizable. hen; the matrix A must be stable. he proof of this lemma is identical to the proof of the corresponding continuous-time result in Ugrinovskii and Petersen 2a,b) and Petersen et al. 2b). 3. he main results he steady-state minimax LQG control problem considered in Petersen et al. 2a) was to nd a controller which attained an upper value inf J K; Q) 6) K Q of the cost functional J K; Q) = 2 EQ Fx t ;u t ); Fx; u):=x Rx + u Gu; 7) R and G are symmetric positive denite matrices, R R n n, G R m m. Here, x t denotes the solution to system ) corresponding to a given controller K and an admissible uncertainty Q. he minimax optimal controller for problem ), 3), 7) proposed in Petersen et al. 2a) was constructed using a pair of parameter dependent algebraic Riccati equations X = A X + B G + D D ) B B 2WB 2) A + R + C C ; 8) Y = A Y + C 2 C 2 ) R C C A + B 2 WB 2: 9) Here, is a positive constant which was chosen as follows. For each such that the Riccati equations 8), 9) admit positive denite stabilizing solutions satisfying the conditions Y + C 2 C 2 R C C ; X B 2WB 2 ; X Y 2) dene the quantity V = det 2 log I ) Y R + C C ) det 2 log I X I ) ) Y X ; 2) where := K + C 2 I ) ) Y R + C C ) Y C K ; K := A Y + C 2 C 2 ) R C C C 2 : 22) he set of the parameters satisfying the above requirement is denoted. In order to obtain the minimax optimal LQG controller, the parameter is chosen to achieve the inmum in inf V + d): 23) Using this optimal value of, the corresponding minimax optimal steady-state controller K is dened by the
6 95 V.A. Ugrinovskii, I.R. Petersen / Automatica 38 22) equations u t = L ˆx t ; 24) L := G + D D ) B X + B G + D D ) B B 2WB 2 A I ) Y X ; where ˆx t was generated by the lter ˆx t+ = A ˆx t + B u t + Ky t+ C 2 ˆx t ) + A Y + C 2 C 2 ) R C C R + C C )ˆx t ; ) ˆx =x : 25) he above solution to the minimax optimal LQG control problem was obtained in Petersen et al. 2a) by letting in the corresponding nite horizon problem. However, as we let approach, two important issues arise which were not addressed in Petersen et al. 2a). ) he ability of an optimal controller to stabilize the system is an important issue in optimal control on an in- nite time interval. In our case, it is desired that the resulting minimax optimal controller stabilizes the system ) for all admissible uncertainties Q. 2) It was shown in Petersen et al. 2a) that on a nite interval, the minimax optimal LQG controller exists if and only if associated parameter dependent dierence Riccati equations have positive denite solutions. In the innite horizon case, the design methodology outlined in Petersen et al. 2a) provides only a sucient condition for the minimax optimal controller to exist. However, it is often useful to know that the only if claim holds as well. Necessary conditions usually give a good indication as to how conservative the proposed controller is. hese issues are addressed in the statements given below. heorem shows that the existence of stabilizing solutions to the algebraic Riccati equations 8) and 9) is a sucient as well as a necessary condition for the innite-horizon minimax optimal LQG control problem 26) to have a solution. Furthermore, heorem 2 shows that the minimax LQG controller proposed in Petersen et al. 2a) is an absolutely stabilizing controller. heorem. i) If the set is non-empty, then the minimax optimal control problem inf J K; Q) 26) K U Q has a nite value. ii) Conversely, if there exists an absolutely stabilizing controller K U which attains the inmum in 26); then the set is not empty. he innite-horizon version of the minimax optimal LQG control result of Petersen et al. 2a) now follows from heorem. heorem 2. Suppose that and attains the inmum in 23). hen; the corresponding controller K = K dened by 24); 25); guarantees that the worst case of the cost functional 7) does not exceed the value 23). Furthermore; this controller is an absolutely stabilizing controller for stochastic uncertain system ) satisfying relative entropy constraint 3). Remark. Note that the controller resulting from heorem 2 is the steady-state limit of the nite horizon minimax optimal controller proposed in the reference Petersen et al. 2a). Also; the worst-case performance 23) is the steady-state limit of the performance guaranteed by the nite-horizon minimax optimal controller. he proofs of the above theorems will be given in Sections 3.3 and Preliminary remarks he proof of heorem relies on a duality relationship between free energy and relative entropy established in Dupuis and Ellis 997) and Dai Pra, Meneghini and Runggaldier 996). Associated with system ), consider the parameter dependent risksensitive cost functional I ; K)= {exp log E 2 } F x t ;u t ) ; 27) where is a given constant, K is a controller dened by Eq. ). Also, F x; u):=x R + C C )x + u G + D D )u: 28) When applied to system ) and the risksensitive cost functional 27), the duality result states that for each admissible controller K, I ; K) = Q : hq P ) 2 EQ F x t ;u t ) : hq P ) 29) he use of the above duality result is a key step in this paper in that it enables us to replace a guaranteed cost control problem by the following risksensitive optimal control problem:
7 V.A. Ugrinovskii, I.R. Petersen / Automatica 38 22) Find an output feedbackcontroller of form ) which attains the inmum in inf lim I ;K): 3) K In this paper, we use the solution to this risksensitive control problem presented in Whittle 99). Note that similar results concerning problem 3) were obtained in Iglesias, Mustafa, and Glover 99) and Glover and Doyle 988) 3 where the problem was shown to be equivalent to a problem of constructing an output feedbackcontroller which maximizes the entropy functional I d K;)= log deti H e j! )H e j! )) d! 2 3) over the set of stabilizing output feedbackcontrollers satisfying the following bound: H := H e j! )H e j! ) : 32)! ; Here, H s) is the transfer function of the closed loop system dened by the equations x t+ = Ax t + B u t +B 2 W =2 t+ ; 33) R =2 z t = x t + G =2 u t; C D y t+ = C 2 x t + =2 t+ ; and a stabilizing linear controller u t =Ky t ). In particular, for a linear controller of the form ), the transfer function H s) is given by R =2 H s) := G =2 C c si A) C D C c B2 W =2 : 34) B c =2 It follows from the results of Iglesias et al. 99), Glover and Doyle 988) and Whittle 99) that the solution to the above maximum entropy problem and equivalently, the solution to the risksensitive control problem 3) is given by the central solution to the corresponding H control problem; see Basar and Bernhard 995). 4 his controller is dened by Eqs. 24) and 25) and involves positive denite solutions 3 Iglesias et al. 99), Glover and Doyle 988) consider a slightly dierent information pattern which allows the control u t to instantaneously access y t+. his leads to an optimal controller which is not strictly causal. 4 Also, the links between the problem considered in this paper and H control were discussed in Petersen et al. 2a). to the Riccati equations 8) and 9). Furthermore, the minimum risk-sensitive cost corresponding to this controller is given by Eq. 2) Absolutely stabilizing properties of risk-sensitive control In this section, we establish the absolutely stabilizing properties of the risk-sensitive controller. Lemma 2. Let K be a controller which guarantees a nite risk-sensitive cost: V K := lim I ;K) : hen; the controller K is an absolutely stabilizing controller for the stochastic uncertain system ) satisfying the relative entropy constraint 3). Furthermore; J K; Q) 6 V K + d: 35) Q Proof. We wish to prove that the controller K satises condition 3) of Denition 2. Consider an uncertain system with an admissible uncertainty Q governed by the controller K. Recall that the system is described by Eq. ) where the control process u is generated by the given controller K. Also, the joint probability distribution of the noise inputs w, v and the initial condition x is dened by the given collection of conditional probability measures Q. Note that since the uncertainty Q is admissible, then the corresponding probability measures Q have the property hq P ) for every =; 2;:::. his allows us to apply duality condition 29). From this equation, we obtain + { 2 EQ 2 EQ Fx s ;u s ) } z s 2 hq P ) 6 V K : 36) Furthermore since Q, satisfaction of Eq. 35) follows from 36) and 3). We now show that the controller K is absolutely stabilizing. Since the matrices R and G are positive denite, then inequality 35) implies EQ x s 2 + u s 2 ) 6 V K + d); 37) where is a constant which depends only on R and G. Next, we show that there exist constants c ;c 2 such that hq P ) c + c 2 d: 38)
8 952 V.A. Ugrinovskii, I.R. Petersen / Automatica 38 22) o this end, we note that for any Q, t t hqt P t ) 6 d + ˆ + t 2t EQ z s 2 : 39) t t Here, ˆ := t t) as. Inequality 39) takes into account the fact that the probability measure Q t satises the relative entropy constraint 3). herefore, inequalities 37) and 39) imply hq P ) 6 d + 6 c + c 2 d; 2 EQ z s 2 where the constants c, c 2 are dened by V K,,, C, D, and hence independent of Q. o complete the proof, it remains to prove that the process ˆx satises condition 3) of Denition 2. Indeed, consider the uncertain closed loop system ) corresponding to the controller K and an admissible uncertainty Q. Using the duality relation between free energy and relative entropy established in Dupuis and Ellis 997) and Dai Pra et al. 996), we obtain Q 2 EQ x t 2 hq P ) 6 Q :hq P ) 2 EQ x t 2 hq P ) { } =log E exp x t 2 : 2 From this equation, it follows that for any Q, 2 EQ x t 2 6 hq P ) { } + lim log E exp x t 2 : 4) 2 Note that the process x on the left-hand side of Eq. 4) corresponds to the uncertain system ) while the process x that appears in the second term on the right-hand side of Eq. 4) is generated by the nominal closed loop system ). Since this nominal system is driven by the Gaussian process w, one can choose suciently small such that the second term on the right-hand side of Eq. 4) is nite; e.g., see Glover and Doyle 988) and Whittle 99). his term is independent of Q. Since we have already proved 38), then condition 3) follows. Remark 2. It follows from Lemma 2 that the controller solving the risksensitive control problem 3) is an absolutely stabilizing controller for the uncertain system under consideration. Lemma 3. Suppose 5 that for any K U J K; Q)= : 4) Q Q If there exists an absolutely stabilizing controller K U such that J K; Q) c ; 42) Q then there exists a such that V. Proof. Since the given controller K U absolutely stabilizes the uncertain system ); 3); then condition 3) of Denition 2 is satised. Note that it follows from 3) and Lemma that the matrix A corresponding to the controller K is stable. Also; condition 3) implies that there exists a positive constants c ; such that for all Q ; lim inf 2 EQ + lim inf Fx s ;u s ) 2 EQ x s 2 + ˆx s 2 ) 6 c: 43) Consider the functionals G Q) := c lim inf lim inf G Q):= d lim inf 2 EQ 2 EQ Fx s ;u s ) x s 2 + ˆx s 2 ); 2 EQ z s 2 hq P ) : 44) It is readily proved that satisfaction of condition 43) implies that the following condition is satised: If G Q) 6 then G Q) : 45) he proof of this fact follows along the same lines as the proof of the corresponding fact in Ugrinovskii and Petersen 2a); see also Petersen et al. 2b). Furthermore; the set of uncertainties satisfying the condition G Q) 6 has an interior point; see the remarkfollowing Denition. Also; it follows from the properties of the relative entropy functional that the functionals G ) and G ) are convex. 5 Condition 4) is similar to a corresponding condition in Petersen et al. 2a). his condition was introduced in Petersen et al. 2a) to rule out the case = in the proof of heorem 3:. In the continuous-time case, this condition holds if the pair A; B) corresponding to the given controller K U is controllable; e.g., see Ugrinovskii and Petersen 2a) and Petersen et al. 2b). Obviously, in the discrete time case, condition 4) can be replaced by a similar controllability condition.
9 V.A. Ugrinovskii, I.R. Petersen / Automatica 38 22) We have now veried all of the conditions needed to apply the Lagrange multiplier result e.g.; see Luenberger; 969). Indeed; heorem on p. 27 of Luenberger 969) implies that there exists a constant such that lim inf + EQ lim inf + lim inf 2 Fx t;u t ) 2 EQ 2 EQ x t 2 + ˆx t 2 ) z t 2 hq P ) 6 c d: 46) for all Q Q. Also; condition 4) rules out the possibility that =. hus;. Condition 46) implies the satisfaction of condition 32) for the transfer function H s) corresponding to the system 33) and the given controller K. his claim can be established using the same arguments as those used in proving the corresponding fact in Ugrinovskii and Petersen 2b) and Petersen et al. 2b). For the sake of brevity, we only outline the proof. Consider an augmented version of the closed loop system corresponding to system 33) and the given controller K: B2 x t+ = W =2 A x t + t ; 47) B c =2 R =2 G =2 C c z ;t = C D C c x t : I I his system is posed to be driven by a deterministic input disturbance which has a nite autocorrelation matrix and also has a power spectral density function Makila, Partington, & Norlander 998; Ljung, 987). We denote the set of such signals by P +. he transfer function of system 47) is denoted H ; z). We will establish condition 32) by showing that H ; 6 : 48) he proof is by establishing a contradiction. First, we observe that the failure of condition 48) to hold must lead to the existence of a sequence of deterministic inputs { N ;N =; 2;:::} P+ such that z ;t 2 t N 2 ) N 49) 2 for all ; N), where is a suciently small constant. hen, we show that the satisfaction of condition 49) must lead to a contradiction with 46). Indeed, for each input N, a collection of conditional probability measures Q N = {Q N ;QN 2 ;:::} Q can be dened using a corresponding probability measure transformation; see Section 2.3. o this end, the input N has to be partitioned as follows: N t W =2 = N =2 t : N t Also as in Section 2.3, the probability measures Q N; are dened, hq N; P )= 2 W =2 N t 2 + =2 N t 2 : 5) Next, it is shown using 49) that the closed loop system ) driven by the deterministic inputs N, N and considered on the probability space W; F ;Q N; ), satises the following condition: N; M N := lim 2 EQ Fx t;u t )+ x t 2 Q Q + z t 2 W =2 N t 2 =2 N t 2 N: 5) Letting N in Eq. 5) and using Eq. 5), we obtain the following contradiction with 46): lim inf EQ 2 Fx t;u t ) + lim inf + lim inf 2 EQ 2 EQ x t 2 z t 2 hq P ) M N = : N he above contradiction shows that condition 48) must hold. Since condition 48) implies 32), the lemma now follows from condition 32) and the results of Glover and Doyle 988) and Whittle 99) Proof of heorem Part i) of the theorem follows from Lemma 2. Indeed, if, then the corresponding Riccati equations 8) and
10 954 V.A. Ugrinovskii, I.R. Petersen / Automatica 38 22) ) have stabilizing solutions. his ensures that the corresponding controller 24) solves the maximum entropy control problem and equivalently, the risksensitive control problem 3). he corresponding value of the risk-sensitive cost in 3) is therefore nite. hus, controller 24) corresponding to also satises the conditions of Lemma 2. From this lemma, part i) of heorem follows. Part ii) follows from Lemma Proof of heorem = = = It has been observed that for each, controller 24), 25) solves the corresponding risk-sensitive optimal control problem. Hence from Lemma 2, this controller is an absolutely stabilizing controller. Also from Eq. 35) in Lemma 2, it follows that the risk-sensitive controller corresponding to guarantees that the cost is not greater than the value dened by Eq. 23). 4. Illustrative example o illustrate our theory, we consider an example discussed in Petersen et al. 2a). In this example, an uncertain system was considered which had the structure shown in Fig.. he system is dened by the equations :52 :5 :53 x t+ = :52 x t + :52 u t + :53 :52 t + w t+ ); x 4 Fig. 2. he graph of xt 2 versus. equations 8), 9) is given by the transfer function 76:85z +78:3 Hz)= z 2 53) +:48z +:386 which corresponds to =:8. o verify stabilizing properties of this controller, the closed loop system 52), 53) was simulated with dierent values of and the graphs of x t 2 ; u t 2 ; t 2 were plotted. It was observed that the above quantities showed a tendency to remain bounded over the time of simulation. One of these graphs is shown in Fig. 2. z t =:5u t ; y t+ = x t + t +ṽ t+ ): 52) he reference noise signals w t, v t are assumed to be Gaussian white noise signals with covariances W =, = 4, respectively. he uncertainty is assumed to satisfy the stochastic sum constraint 7) with d = 8. Also in Petersen et al. 2a), cost functional 7) was considered in which R = ; G = 4 : For this system, the robust LQG controller designed in Petersen et al. 2a) using the steady-state Riccati References Basar,., & Bernhard, P. 995). H -optimal control and related minimax design problems: a dynamic game approach. 2nd edition. Boston, Birkhauser. Dai Pra, P., Meneghini, L., & Runggaldier, W. 996). Connections between stochastic control and dynamic games. Mathematics of Control, Systems and Signals, 94), Doyle, J. C. 978). Guaranteed margins for LQG regulators. IEEE ransactions on Automatic Control, 23. Dupuis, P., & Ellis, R. 997). A Weak Convergence Approach to the heory of Large Deviations. New York: Wiley. Dupuis, P., James, M. R., & Petersen, I. R. 998). Robust properties of risk-sensitive control. In Proceedings of the IEEE Conference on Decision and Control, Vol. 2. pp ), ampa, FL, December. Elliott, R. J., Aggoun, L., & Moore, J. B. 994). Hidden Markov models. Estimation and Control. New York: Springer.
11 V.A. Ugrinovskii, I.R. Petersen / Automatica 38 22) Fu, M., de Souza, C. E., & Xie, L. 99). Quadratic stabilization and H control of discrete-time uncertain systems. In Proceedings of the International Symposium on Mathematical heory of Networks and Systems, Kobe, Japan. Glover, K., & Doyle, J. C. 988). State-space formulae for all stabilizing controllers that satisfy an H -norm bound and relations to risk-sensitivity. Systems & Control Letters,, Haddad, W. H., Bernstein, D. S., & Mustafa, D. 99). Mixed-norm H 2 =H regulation and estimation: he discrete-time case. Systems & Control Letters, 64), Iglesias, P. A., Mustafa, D., & Glover, K. 99). Discrete time H controllers satisfying a minimum entropy criterion. Systems & Control Letters, 4, Ljung, L. 987). System Identication:heory for the User. Englewood-Cli, NJ: Prentice-Hall. Luenberger, D. G. 969). Optimization by Vector Space Methods. New York: Wiley. Makila, P. M., Partington, J. R., & Norlander,. 998). Bounded power signal spaces for robust control and modeling. SIAM J. Control Opt., 37), Moheimani, S. O. R., Savkin, A. V., & Petersen, I. R. 995). A connection between H control and the absolute stabilizability of discrete-time uncertain systems. Automatica, 38), Mustafa, D., & Bernstein, D. S. 99). LQG bounds in discrete-time H 2 =H control. ransactions of the Institute of Measurement and Control, 3, Petersen, I. R., James, M. R., & Dupuis, P. 2a). Minimax optimal control of stochastic uncertain systems with relative entropy constraints. IEEE ransactions on Automatic Control, 45, Petersen, I. R., Ugrinovskii, V., & Savkin, A. V. 2b). Robust Control Design using H Methods. Berlin: Springer. Ugrinovskii, V. A., & Petersen, I. A. 999). Finite horizon minimax optimal control of stochastic partially observed time varying uncertain systems. Mathematics of Control, Signals and Systems, 2), 23. Ugrinovskii, V. A., & Petersen, I. R. 2a). Minimax LQG control of stochastic partially observed uncertain systems. SIAM J. Control Optim., 44), Ugrinovskii, V. A., & Petersen, I. R. 2b). Robust stability and performance of stochastic uncertain systems on an innite time interval. Systems & Control Letters, 444), Whittle, P. 99). Risk-sensitive optimal control. Chichester, UK: Wiley. Ian R. Petersen was born in Victoria, Australia in 956. He received the Bachelor of Engineering Electrical) degree from the University of Melbourne in 979. He received a Master of Science degree in 984 and a Ph.D in Electrical Engineering in 984 both from the University of Rochester. From 983 to 985 he was a Postdoctoral Fellow in the Department of Systems Engineering, Australian National University. In 985 he was appointed as a Lecturer in the Department of Electrical Engineering, Australian Defence Force Academy and he is currently a Professor in this department. In 989, he was a visitor in the Department of Engineering, Cambridge University. He served as an Associated Editor for the IEEE ransactions on Automatic Control and Systems and Control Letters. Currently he is an Associate Editor for Automatica and SIAM Journal on Control and Optimization. His main research interests are in robust control theory, H control, robust ltering, and optimal control theory. Valery A. Ugrinovskii was born in Ukraine in 96. He received the M.Sc. degree in Applied Mathematics in 982 and a Ph.D in Physics and Mathematics in 99 both from the State University of Nizhny Novgorod, Russia. From 982 to 995 he held research positions with the Radiophysical Research Institute, Nizhny Novgorod. From 995 to 996 he was a Postdoctoral Fellow at the University of Haifa. Since 996, he has been a Research Associate and Lecturer in the School of Electrical Engineering, Australian Defence Force Academy, Canberra. He is the coauthor of the research monograph Robust Control Design using H Methods, Springer, London, 2, with Ian R. Petersen and Andrey V. Savkin. His current research interests include stochastic control theory, robust control theory and H control.
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text: TEMPE, Ariz. TheStreet) -- Before US Airways ( LCC) broke off merger talks with United ( UAUA) on Thursday, the two airlines had talked for months and had reached agreement on many key issues including the selection of Glenn Tilton as CEO of the merged company, say people familiar with the talks. But United executives were uncomfortable with the requirement that because US Airways pilots have a change of control provision in their contract, the deal would have to be structured in a way that US Airways acquired United, said the people, who could not be named because they were not authorized to speak about the negotiations. The United executives' feeling was that it would be extremely difficult for US Airways to assemble the financial resources needed to amply reward shareholders in a far larger company with three times the market capitalization. Nevertheless, the talks progressed. Eventually, the two sides "agreed the company would be named United (and) headquartered in Chicago, would have two thirds of the board from United and (would have) Tilton as CEO," a source said. US Airways CEO Doug Parker was willing to step aside, the source said, noting: "Doug was going to act in what he believed to be the best interest of his company and his employees." United's preference to merge with Continental ( CAL) was, obviously, not news to US Airways executives. But those executives believed they should go ahead and pursue a deal that would so clearly benefit the company. Parker, like predecessor Stephen Wolf, believes that US Airways is not well-positioned for long-term survival because it is neither a major global airline nor a low-cost domestic airline. Parker was also well aware that the necessity to structure a deal as a US Airways acquisition was a problem. On March 17, at the conclusion of a meeting with pilots at US Airways' Charlotte training center, he raised the topic, telling pilots that the change of control provision was a barrier to any merger the carrier might pursue. The provision snaps wages back to a pre-2000 level, far higher than today's pilot wages, if a change of control occurs.


text:
A regular client, David, climbed aboard last week for a few hours on the water. He's been wanting a tarpon so that was on the agenda. We started with absolutely slick calm conditions and a heavy haze that barely provided a few hundred yards of visibility. We didn't have to travel far though, as we found a ton of tarpon just 200 yards from the marina. The tarpon were rolling and finning right on the surface, enough to wake anyone up early in the morning.
The bite was slow though but I saw a school of something pushed towards us so I cast an artificial lure, felt a big tug and handed the rod to David. Fifteen minutes later he had a big jack on the boat. As a slight breeze kicked up and the tarpon stopped rolling we changed spots. Here David hooked into an 80-90 pound tarpon that gave us some really amazing jumps. Ten to fifteen minutes into the fight he wrapped us around a piling and broke us off. David wasn't nearly as upset as I was, as he felt the silver rage of a tarpon and enjoyed every second of it. We ended the morning with another bite, but no hook up.
Duncan from Australia was in Miami for a few days on his way down to Brazil for the World Cup. We started tarpon fishing, but the bite was slow, a roller here, another roller there but no hook ups. We switched to fishing for sea trout on a flat that has been holding both trout and tarpon.
Not long after we arrived on the flat, I saw a few big splashes and some tarpon dorsal fins coming our way. Immediately I deployed a tarpon bait and kept fishing for trout. Sure enough the tarpon rod doubles over and the line sizzles off the reel and to the left. A big 100 pound tarpon tried to jump out of the 3' deep water only 30' from the boat, but only his huge head comes out revealing an enormous mouth aimed right at Duncan. Seconds later the tarpon does what tarpon do, spits the hook and swims away leaving Duncan awe struck and me heart broken.
Capt. Mo Estevez can be reached at email@example.com
• More than 100 boats are expected to participate in the fourth annual University of Miami Sports Hall of Fame Celebrity Dolphin Fishing Tournament set for June 27-28 in Islamorada. The event is to be hosted by NFL Hall of Famer and University of Miami football great Michael Irvin. Reflective of the Hall of Fame's mission, the high- energy annual tournament allows University of Miami sports fans to celebrate the accomplishments of former student athletes as well as compete side by side with them while raising money for charitable causes. Tournament activities will take place at Founders Park at mile marker (MM) 87 and Coconut Cove Resort and Marina at MM 85. Friday evening party and mandatory anglers and captains meeting kick off the weekend from 5 to 8 p.m. Saturday's fishing begins at 8 a.m. and concludes when the weigh station closes at 4 p.m. After June 1st the entry fee for the first four anglers increases to $650. For more tournament information, visit www.canesfish.com.
• Key West Gator Club Dolphin Derby June 20th to 22nd. A grand prize of $5,000 cash is to be awarded the boat team with the largest aggregate weight in dolphin during the derby's two fishing days, with teams allowed to enter one qualifying fish each day. Second- and third-place teams will earn $2,500 and $1,000, respectively. Individual anglers can compete for trophies, prizes and cash totaling more than $15,000 in the tournament's divisions for male, female and junior participants. Contact: Greg Oropeza 305-304-1348.
• The Dolphin & Blackfin Tuna Fun Fishing Tournament in Marathon June 28th and 29th. Top prizes of $700, $350 and $200 await individual adult anglers who catch the tournament's three heaviest dolphin, with additional cash awards for the heaviest blackfin tuna and wahoo. Headquartered at Burdines Waterfront restaurant, the 14th annual challenge is open to adult and junior anglers. Contact: Brenda Duff 305-743-5317.
• Islamorada Dolphin Tournament July 11th to 13th. Hosted by the Islamorada Charterboat Association, this annual event features $15,000 in cash and prizes up for grabs. Competition is open to all anglers and there is no limit on the number of anglers that can participate. Contact: Dianne Harbaugh 305-522-4868.
• Del Brown Permit Tournament in Key West July 13th to 16th. Anglers fly-fish on the flats in a challenge that honors the late angling pioneer Del Brown, who caught and released more than 500 permit off the Keys. Professionals and guides are allowed to compete as well. The tournament angler who catches the highest total inches of permit on fly on the flats earns the title of grand champion. Awards also await the grand champion guide, runner-up grand champion and the angler who catches the event's largest permit. Contact: Loren Rea 305-360-6969.
• Drambuie Key West Marlin Tournament, July 16th to 19th. Anglers search the waters once fished by novelist Ernest Hemingway, vying for $50,000 in guaranteed cash prizes. Held in conjunction with Key West's annual Hemingway Days, the event awards $25,000 to the first-place team. Teams can enter one fun fish (dolphin, tuna, wahoo or released sailfish) per day to add to their point total. For anglers, the Key West Marlin Tournament provides a chance to emulate Ernest's passion for deep-sea fishing. Contact: Tim Greene 305-304-0317.


text:
From Raw TV, the acclaimed creative team behind "Locked Up Abroad" and "Gold Rush Alaska", this tense, filmic and high-octane drama-documentary series brings to life the stories of people who have lived through paranormal experiences that defy explanation. Using the mixture of intimate first-hand testimony and grittily realistic drama that Raw TV is known for, "Paranormal Witness" will transport the audience into a world turned upside down by extraordinary and terrifying events. "Paranormal Witness" is produced by Raw TV. Executive producers: Dimitri Doganis and Bart Layton.
Links: Screenshot – TVDB – IMDB
Paranormal Witness S04E13 Ashes to Ashes HDTV x264-W4F
Published on: Nov 26, 2015 @ 22:55


text:
This two-day course is designed for physicians whose clinical practices include general ophthalmology, refractive surgery, pathologies of cornea, and lens. Using an interactive, case-based approach, the distinguished speakers will present a variety of vignettes and practice pearls to illustrate clinical dilemmas in the diagnosis and management of anterior segment diseases. Day 1 will focus on refractive surgery including cataract and other lens-based refractive procedures, corneal refractive surgery and alternative refractive technologies; Day 2 will focus primarily on cornea and external disease. The topics will include: cataract and refractive surgery pearls, presbyopia correction, collagen crosslinking, high-risk anterior segment surgery, management of severe ocular surface disease, and the medical and surgical techniques for management of various infectious and inflammatory conditions of the anterior segment. A case-based format will be used throughout the program to encourage a more interactive forum.Additionally, a wet lab will be available for participants to gain hands-on exposure to femtosecond laser technology, lamellar keratoplasty and a variety of other anterior segment techniques.
Friday, February 3, 2017 - Saturday, February 4, 2017
Bascom Palmer Eye Institute900 NW 17 StreetMiami, Florida 33136USA305-326-6110
Danicza Zupcic
Cvent Online Event Registration Software | Copyright © 2000-2017 Cvent, Inc. All rights reserved.


text: Christmas in July is available on selected dates from Monday - Friday in July. Bring your club or a group of friends and enjoy all the trappings of a traditional Christmas lunch just a little early. Live entertainment and trivia fun is included if the total bookings are above 60 people. (see online booking form below for the available dates) $28 per person - Main Roast turkey with roast potatoes, pumpkin, honey roasted carrots, minted peas and rich gravy served with cranberry sauce, Yorkshire pudding and stuffing Dessert Steamed Christmas pudding with brandy and vanilla custard, double cream and strawberry. 2 jugs of lemon lime & bitters on each large table; with self serve tea and filter coffee. For further information call Graham or Haylee on (03) 9751 0443. Book early to avoid disappointment &;lt;h1>Your browser cannot load the Online Booking Widget.;gt;lt;a href=&;quot;http://www.obee.com.au/skyhigh/events/index.php" _cke_saved_href=&a;quot;http://www.obee.com.au/skyhigh/events/index.php&a;amp;amp;amp;amp;gt;Click here to make a booking instead.;lt;/h1>


text:
Airstream Jewelry designed by Krista Tranquilla offered exclusively at Airstream Brands. Buy the charms individually or mix and match to build your own favorite combination. Chain is not included and is available as a separate item. All made of Silver.
Make sure to hit the back button on the shopping cart page to add more items while building your custom necklace!
Flamingo Charm - 3/4" - $34Live Riveted Tag Charm with three small rivets - $36Small Trailer Charm 5/8" - $30Logo Charm - 5/8" - $26Silver Chain - 18" - $22
$ 22.00
Copyright © 2017 Airstream Brands.


text:
Luke Baumgarten
April 27, 2011 at 3:03PM
Tons of releases this week in music, including new Times New Viking, Explosions in the Sky, Of Montreal, Prefuse 73 and the immortal Bootsy frickin Collins. The one getting the most press, though, is Poly Styrene's Generation Indigo.
April 27, 2011 at 1:37PM
The fatal shooting of an elderly pastor by a Spokane County Sheriff's deputy last summer has been determined to be reasonable and justified, according to two internal Sheriff's Office review panels. In a news release Wednesday, the Sheriff's office says that a Deadly Force Review Board and a Citizen's Advisory Board each has concluded in recent months that Deputy Brian Hirzel was justified in his use of force in a late-night encounter Aug. 25 that resulted in the shooting death of Wayne Scott Creach.
April 27, 2011 at 1:36PM
Each Wednesday on Bloglander, we give you a taste of happy
hours going on at bars around town that night. (Read previous posts.)
Daniel Walters
April 27, 2011 at 12:24PM
"Not drawing conclusions, but it's a little unpleasant to realize one of our
most popular TV genres is "hot chick getting murdered," writes Zack Handlen,
critic for the AV Club. It's true: For years, TV procedurals have revolved around murder.
April 27, 2011 at 7:34AM
Obama releases birth certificate — Critics have already started qualifying the release. Donald Trump, who has helped fuel the "birther" movement, said he was honored to have played "such a big role in hopefully, hopefully, getting rid of this issue." (NYT)
NIC considers free speech zone — A visit from Westboro Baptist Church members last fall got North Idaho College thinking about creating an area on campus where controversial events would be allowed but contained.
Amy Hunter
April 26, 2011 at 10:41AM
Generally my wanderings actively involve people; talking, listening, asking questions, and hearing stories. There's another kind of wandering, however, that requires very few words or direct interaction, but is equally engaging and, at times, provides a much-needed change of pace.
April 26, 2011 at 8:16AM
Harpham continues 'not guilty' plea — Kevin Harpham, the alleged mastermind of the failed MLK Day bombing in Spokane, had already pleaded not guilty to charges of possessing an unregistered explosive and attempting to use a weapon of mass destruction. He pleaded the same to new hate crime charges.
April 25, 2011 at 7:50AM
South Hill shooting ruled justified — Spokane Police Officer Trevor Nollmyeer's fatal shooting of Todd Ely White last year on 36th Avenue was ruled justified because White had aimed his gun at the officer first. (NWCN)
Leah Sottile
April 22, 2011 at 2:42PM
April 22, 2011 at 7:11AM
Libya chaos touches Palouse — Libyan students at WSU in tight spot as funding in doubt, worries about family back home. (SR)
Drones are NOT mission creep — U.S. Secretary of Defense Gates says armed drones are already patrolling Libya.
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Australia is one of the world's most urbanised countries. Outside of all urban zones lie large rural areas where fewer than 15% of Australians live. Beyond that lies the Outback a vast wilderness of desert and grasslands. The grassland areas have huge stations that engage in sheep farming, cattle, and other livestock. Herds of cattle are often spread out over wide distances that helicopters are sometimes used to round up the herd.
Sheep farming in rural areas is the traditional farming of this land. The saying 'Riding on the sheep's back' is a reference to when Australia dependence on wool in early history made the nation quite wealthy. Although not as important today, Australia still has more sheep than any other nation on Earth, with over 100 million. These days sheep farming is in decline, and the new industry boosting the economy is mining. Read more →
Australia is the world's largest exporter of beef. With over 28 million heads of cattle, it accounts for over half of all farms with agricultural activity. Beef in Australia is of good quality and reasonably priced and is a common staple of the Australian diet.
Wheat is the country's most important grain and is the fouth largest exporter of wheat in the world. Other important crops grown in Australia include barley, sugarcane, and temperate and tropical fruits.


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Phthalo Blue BR-NCF (4353-03T)
Phthalo Blue BR-NCF (4353-03T) is a dry pigment, with a color index of (PB 15:2). This product is used as a pigment in OEM and refinish automotive paint applications as well as in coil coating and powder industrial paint applications. Phthalo Blue BR-NCF (4353-03T) is also used in solvent and water based decorative paint applications.
Ggink International Limited is a supplier of colorants in the Paints and Coatings industry. The company manufactures resins, pigments and other materials for a wide range of applications.
Ggink International Limited
希望在赛百库经销商/贸易商板块进行展示推广?请立即联络我们 !
Ggink International Limited目前只在以下作出标识的区域展示其产品资料:


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as316018 Model
SmareoPhotographer Male Calgary, Alberta, Canada
Halifax, Nova Scotia, Canada
Ottawa, Ontario, Canada
My Website: YourApertureMy MM URL: http://www.modelmayhem.com/smareo
Mayhem # 2810859
About MeMy name is David, I'm a photographer operating in the Calgary Area. I have a portable studio. I specialize in promoting products, portrait shooting (Groups, Couples, and Singles) and sports. I looking to gain experience and expand my portfolio in a studio setting because I shoot mostly outdoors. Feel free to contact me for photoshoot opportunities or suggestions. My time is limited, since I do work a full time job and do photography as a hobby.
What I offer: TFCD/TFP, which will include all proof shoots chosen by you.
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It is imperative for children to have access to all the services, therapies, and academic programs that will help them develop to their full natural potential and transition to success; yet the current model does not meet this need. At The Hope Learning Center, we offer an all inclusive approach by providing a multidisciplinary team of experts that will assess and create an individualized treatment plan for every child. The Hope Learning Center allows parents the opportunity to take control of their child's future. Call today to schedule an appointment, tour our facility, and receive a free developmental screening for your child.
Make your summer plan now! Joins us at The Hope Learning Center for an individualized summer experience! Supplemental weekly camps, Six week camp program, and Extended School Year Services!
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TGS announces three new multi-client surveys; a 3D survey in the Atwater Valley area of the central Gulf of Mexico, a 3D onshore survey in Alberta, Canada and a 2D survey offshore Newfoundland.
The Francisco 3D multi-client survey in the Atwater Valley area of the central Gulf of Mexico expands upon the previously announced survey. Upon completion, the survey will total more than 6,667 km2 of seismic data in this frontier area of the Gulf of Mexico. Data processing will be performed by TGS using Clari-Fi technology, a proprietary broadband processing technique. Final data will be available to clients in Q4 2014.
Pendryl, a new 3D multi-client onshore survey covering 320 km2 in Central Deep Basin in Alberta, Canada will expand TGS' existing coverage in the emerging Duvernay play. The survey is located Southwest of Edmonton and is designed to evaluate multiple zones from Cretaceous to Devonian, including currently producing formations such as Cardium, Glauconite, Nordegg, Pekisko and Duvernay. The seismic data will be processed by TGS' Calgary-based subsidiary, Arcis Seismic Solutions, and final data will be available to clients late Q1 2014.
TGS-NOPEC Geophysical Company
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Building Hope
RestlessBeings short documentary screenings, will be followed by an informal discussion and an opportunity for you to ask any questions about the films, the projects, the communities we are working with, and make suggestions, support and help us develop our work.
If you are new to RestlessBeings, this is a great event for you to meet the team, find out more and get involved. Alongside this, there will be food, networking and positive vibes to start the weekend with...
Join us :)
This is a FREE event.
However, you must register. We have limited space on the night. Dinner will be provided & hopefully drinks and cake too :]
To book your place please email email@example.com with the following information:
- Full Name
- Email Address
- Mobile Number
- Home Address
- Profession
- Why are you interested in attending this event?
- How did you find out about RestlessBeings?
- What makes you restless about the world today?
Email the form above and wait for a confirmation email from us :)
Enjoy Pear Drops in a Can, as Drop Drinks will be available on the night to purchase (100% going to RestlessBeings)
This event is kindly supported by LBTH.
Food will also be provided by Nina Spice Rozina Iqbal.
Cakes provided by missBeesbakery.
Event summaryBuilding Hope
Short documentary screenings, informal discussion and an opportunity for you to ask any questions about the films, the projects, and our work
Event scheduled on: Saturday, 16 June 2012 at 17:00


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All Seeing Eye Titanium Steel & Micro Pavé Bracelet
All Seeing Eye Titanium Steel Bracelet
- 6mm Titanium Steel Beads
- CZ Pavé Micro Inlay All Seeing Eye
**We ship internationally! Shipping takes between two and four weeks for US.
All other countries, please understand that it can take 3 - 8 wks. Thank you!**
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Partake on an out of this world flavor experience!
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These Lifted Liquids flavors are Max VG blends, and can be found in the High-VG collection. High-VG e-liquids are crafted for use with RBA, RDA, RTA and sub-ohm tank devices.
Lifted Liquids pushes the limits in flavor to create a satisfying and smooth vape in Max VG, without ever sacrificing quality.
Every so often, a flavor comes along and changes everything. AshawnT finds its flavor through discovery of a secret hibiscus raspberry nectar that only humming birds can pull from the flowers. Delicious beyond imagination, taste the ambrosia from heaven itself. Shop now »
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The 13th District champion Lady Cougars had a great season in 2016. Coach Brandy Trimble had a very young team in her first season as coach for Logan County. In fact, six of the varsity starters were actually still in middle school this year. The starting pitcher for the majority of the season, Abby Hinton, was only in 7th grade. The age of this group speaks volumes about the amount of talent on that field. The Lady Cougars were able to put together a winning season for the first time in quite a while. They finished with a record of (18-14.) In 2015, Logan was (13-21.)
The Lady Cougars also won the District championship for the first time since 2009 after beating Franklin-Simpson 5-4.
Kennedy Nichols led the offense with a batting average just under .400. Four other players had an average of at least .300. Nichols had 41 hits, ten doubles, and the team's only home run. Jillian McLellan smacked three triples this year. Brea Croslin and Torrie Pollard each scored 25 runs in 2016.
From the circle, Abby Hinton led all pitchers. Hinton pitched in 26 games, which includes 152.2 innings. She assembled a (12-12) record. The 7th grader struck out 71 and had an ERA of 2.75. Sydney Lee struck out 21 batters in only 35 innings of work. Her ERA was 1.40.
The Lady Cougars lose only two seniors, Meagan Ferguson and Torrie Pollard. This young Logan County team will continue to improve and play together for several seasons to come. Expect the Lady Cougars to have many winning seasons.