Joint design of control policy and network scheduling policy for wireless networked control systems: Theory and application

In this paper, we study a wireless networked control system (WNCS) with N >= 2 sub-systems sharing a common wireless channel. Each sub-system consists of a plant and a controller and the control message must be delivered from the controller to the plant through the shared wireless channel. The wireless channel is unreliable due to shadowing and fading. As a result, a packet can be successfully delivered in a slot with a certain probability. A network scheduling policy determines how to transmit those control messages generated by such N sub-systems and directly influences the transmission delay of control messages. We first consider the case that all sub-systems have the same sampling period. We characterize the stability condition of such a WNCS under the joint design of the control policy and the network scheduling policy by means of 2(N) linear inequalities. For scalar systems, we further simplify the stability condition into only one linear inequality for two special cases: the perfect-channel case and the symmetric-structure case. One main technical contribution of this paper is to introduce the recent results on the network scheduling policy design for delay-constrained wireless communications into the analysis of WNCSs. In addition, we have applied our theory to a practical problem of stabilizing multiple pendulum-cart sub-systems over a shared wireless channel. Simulations show that our joint design effectively achieves better performance than existing baseline. (C) 2021 Elsevier Inc. All rights reserved.