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 2N 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.