Infinite-Horizon Optimal Wireless Control Over Shared State-Dependent Fading Channels for IIoT Systems

Abstract

Heterogeneous systems consisting of a multiloop wireless control system (WCS) and a mobile agent system (MAS) are ubiquitous in Industrial Internet of Things systems. Within these systems, the positions of mobile agents may lead to shadow fading on the wireless channel that the WCS is controlled over and can significantly compromise its performance, requiring joint coordination between the WCS and MAS. Such coordination introduces different time steps and hybrid state spaces consisting of logical components and continuous components. This paper focuses on the infinite-horizon optimal control of MAS to ensure the performance of WCS while minimizing an average cost for the heterogeneous system subject to safety constraints. A state-dependent fading channel is modeled to capture interference among transmission links, as well as the effects of mobile agents' movements on successful wireless transmission. In order to address the heterogeneous system dynamics, the optimal control problem is formulated as the optimal constrained set stabilization of the MAS by establishing a necessary and sufficient condition for the Lyapunov-like performance of WCS with the expected decay rates. Using the semi-tensor product of matrices, a constrained optimal state transition graph is constructed to encode the constrained system dynamics as well as objective function, which further reduces the problem into a minimum-mean cycle problem for the graph. By studying the properties of the graph, the feasibility is proven, and an effective algorithm is proposed for the construction of optimal input sequences. An illustrative example is provided to demonstrate effectiveness of the proposed method.