ource allocation. Case C: When C* < 1 - - Eth' the actual resource consumption is lower than the bound in the traditional URLLC resource allocation. In the rest of this section, we solve the optimal problem in (14.29). First, we obtain the optimal communication resource allocation with constraint on control convergence rate. Then, the optimal control convergence rate can be obtained. 14.4.2 Optimal Resource Allocation In this section, we first convert the optimal problem into a solvable problem. Then, we develop an algorithm to obtain the solution for optimal resource allocation. 14.4.2.1 Problem Conversion Though the state update of the control is relevant in different time index n, the wireless resource allocation to guarantee the control requirement is independent. In addition, the available resource, i.e. the transmission power and bandwidth, is independent among different sensors. Thus, we can drop the time indices n and decompose Problem (14.29) into M subproblems. Furthermore, the constraint on communication reliability in (14.29b) should be replaced by the relationship in Theorem 14.1. Thus, (14.29) can be rewritten as (14.34a) (14.34b) (14.34c) (14.34d) Tm T th, (14.34e) 14 Optimizing Resource Allocation in URLLC for Real-Time Wireless Control Systems where the control convergence rate Pm is omitted in the optimal variables since the expres- sion (14.32) and the constraint in (14.34b) indicate that Pm can be obtained by Em=1-cm. The optimal control convergence rate Pm will be discussed later in the Section 14.4.3. Our goal is to maximize the wireless SE by optimal resource allocation, and meanwhile cause less resource consumption. To achieve this goal in solving (14.34), the time delay should be long enough, i.e. Tm=Tth, (14.35) which is because large time domain resource can reduce other resource consumption. Then, we have (14.36) 1 - cm. Then, (14.34) can be rewritten as r (14.37a) NmPm , (14.37b) Bm 3 Bmax, (14.37c) Em<1-cm. (14.37d) This is the final expression of the problem formulation. Next, we fo