 Optimizing Resource Allocation in URLLC for Real-Time Wireless Control Systems in Figures 14.1 and 14.2. In the rest of this section, we first illustrate the control performance and then discuss the optimal resource allocation to maximize the communication SE. 14.5.1 Control Performance From the perspective of real-time wireless control, since M plants are independent in communication-control co-design, we assume that only two plants, i.e. M = 2 plants, are considered in the simulations. For simplicity, we assume that both plants have identical dynamics, where we assume that deo = 1.5 and de = 0.5. We further assume that the given positive definite weight matrix is Qm = 1, the variance of the disturbance matrix nm(t) is 1, i.e. R m = 1, and the sample period is Sm,n = 100 ms. In addition, we adopt the average control cost to evaluate the control performance [36], which can be expressed as (14.39) where N = T/Sm.n is adopted, and T is the total time of the control process. Figure 14.3 shows the average control cost Jave with control time increasing, where we consider three different decreasing rates Pm' i.e. 0.01, 0.25, and 0.9. In the figure, all the curves increase at the initial time. This is because the control process is performed before the state returns to the preset point, where the plant state update leads to increasing Jave Furthermore, as the control time increases, when Pm is small, i.e. Pm = 0.01, the curve has little drop and reaches a low approximative horizontal line smoothly. However, when Pm is large, i.e. Pm = 0.9, the curves have a little drop and reach a high approximative horizontal line roughly. This is reasonable since the plant state update is smaller when the plant turns more stable than that at the start phase, which leads to the average control cost Jave having little drop and reaching an approximative horizontal line. These phenomena indicate that small decreasing rate Pm leads to smooth state updating, where we can obtain small average Pm=0.01 Pm=0.25 Pm=0.9 Time (s) Figure 14.3 Aver