Pareto optimization for multi-controller cyber-physical systems

This paper delves into the Pareto optimal control of multi-controller cyber-physical systems (MCPSs), characterized by cooperative game interactions among multiple controllers within the cyber-physical systems (CPSs). Distinct from previous research, the multi-controller framework is more susceptible to Denial-of-Service (DoS) attacks when transmitting control signals, which increases the risk of packet loss and the control cost of the systems. To overcome this challenge, we introduce the Pareto optimal control for MCPSs, aimed at deriving the Pareto optimal strategies for each controller to minimize their respective cost functions. This article underscores the pivotal role of the generalized difference Riccati equations (GDREs) in solving the Pareto optimal strategy. This methodology utilizes the equivalence between the Pareto optimal strategy and the optimal strategy of the weighted sum cost functions to derive the corresponding minimum input costs. Ultimately, the efficacy of the proposed approach is validated through a numerical simulation.