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

TL;DR

This work tackles the problem of maintaining Lyapunov-like performance for a multiloop WCS in IIoT environments where mobile agents induce state-dependent shadow fading on shared wireless channels. It models the coupled WCS and MAS as a hybrid system with different time scales and uses the semi-tensor product to convert the MAS into a linear representation, enabling a constrained state-transition graph construction. The infinite-horizon control objective is transformed into a minimum-mean cycle problem on this graph, yielding a principled algorithm to design optimal MAS input sequences that guarantee WCS performance while respecting MAS safety constraints. The approach is demonstrated through an illustrative example, showing that the resulting input sequences achieve energy-efficient control and robust operation under state-dependent channel fading, with potential impact on co-design of scheduling and motion planning in 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.

Figures (9)

• Figure 1: Framework of a heterogeneous IIoT consisting of a multiloop WCS and an MAS in a factory floor. 'S' and 'A' respectively represent sensing and actuation capabilities. The workspace is partitioned into $\kappa$ cells $\{0,1,\cdots, \kappa-1\}$, and each cell is abstracted as a logical state indicating a level of shadowing effects. Each mobile agent $j$ moves within its task area, leading to logical state transitions among cells in the state constraint set $\mathcal{C}_{\alpha_j}$.
• Figure 2: State-dependent fading channel (\ref{['eq011']}).
• Figure 3: Constrained optimal state transition graph $G=(\mathcal{V},\mathcal{E},w)$.
• Figure 4: Weighted state transition graph $G[\Phi]$.
• Figure 5: Input sequences and steered state trajectories for AGVs in logical forms in the time interval $0\!-\!30$ s, where (a), (b) are obtained by Algorithm \ref{['al04']}, (c), (d) are obtained by the method proposed in hu2022hu2019, states and control inputs violating safety constraints are depicted with red circles.