Robustness Analysis of Stochastic Jumps and Design of Resource-Optimal Switching Policies for Cyber-Physical Systems

This paper focuses on the robustness analysis of real-time embedded control systems that are common in many cyber-physical systems. Uncertainty in any of them induces asynchrony in the system such as communication delays or packet losses and its effects are commonly analysed in the framework of Markov jump linear systems. In this paper, we present new results that enable uncertainty quantification for general stochastic jump linear systems, not necessarily Markov process. Robustness is quantified via Wasserstein distance that assesses robustness based on shapes of state probability density functions. We show that convergence in this metric is equivalent to mean square stability. Both the transient and steady-state performance of the systems with given initial state uncertainties can be analysed in this framework. Finally, we also present new algorithms with stability guarantees that can be used to synthesize a switching policy for resource-optimal implementation of control algorithms, without significant degradation in performance. The proposed methods are also verified through numerical examples relevant to cyber-physical systems.

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