age control cost as a function of time. 14.5 Simulations Results Decreasing rate of the control system, Pm Figure 14.4 Optimal Cm with different control convergence rates Pm. control cost.Jave updating. When Pm is large, the state updating is rough, which leads to large average control cost Jave updating. In addition, when Pm is small, i.e. Pm = 0.01, the smooth state updating leads to low average control cost as the time is large enough, which means that small decreasing rate has better control performance than large decreasing rate. Figure 14.4 shows the optimal CM in (14.32) when decreasing rate Pm is different. In the figure, the curve decreases monotonically with Pm from Cth = 1 to C* = 0, which means that small Pm results in high constraint on the communication reliability. This is reasonable since high reliability can guarantee smooth decrease of the plant state from control perspec- tive, which leads to small decreasing rate Pm and small average control cost in Figure 14.3. From the above control results, we can infer that Property 14.1 can be redescribed based on the different values of control decreasing rate Pm' where cm(Pth) = 1 - Eth. Then the three cases in Property 14.1 can be described as follows. Case I: Pm < Pth. In this case, Pm<Pth means that = 1 - Eth, where the allo- cated resource in traditional URLLC fails in guaranteeing the required control perfor- mance and more wireless resources are needed. Case II: Pm = Pth. In this case, Pm = Pth means that = Eth, where the allo- cated resource in traditional URLLC is just enough to guarantee the required control performance and more wireless resources are needed. Case III: Pm > Pth. In this case, Pm > Pth means that = 1 - Eth, where the allocated resource in traditional URLLC is more than that needed in guaranteeing the required control performance and wireless resource waste is presented. In the rest of this section, we discuss the communication performance of the method that was explained earlier in Section 14.4. Furthermore, we - 10-5, and cm = 