Secure Control of Markovian Jumping Systems Under Deception Attacks: An Attack-Probability-Dependent Adaptive Event-Triggered Mechanism

Abstract

This article considers the secure control of Markovian jumping systems (MJSs) under stochastic deception attacks that occurred in the communication network. Therein, the stochastic deception attack is described by a Bernoulli random variable. Considering the limited network bandwidth and the impact of deception attacks simultaneously, we propose an attack-probability-dependent adaptive event-trigger mechanism (AETM). It can not only reduce the number of the controller updates, but also adapt to the variation of the system dynamics subject to deception attacks. A mathematical model is established for the closed-loop system under stochastic deception attacks. Then, a time-dependent looped-functional is constructed to reduce the conservatism of stability results. The norm of the system state is estimated, and based on the discrete-time Lyapunov theory, a less conservative stability criterion is derived. Then, an easy-to-implement design algorithm for the controller gain is given so that the exponential stabilization in mean square sense can be realized for Markovian jumping system subject to stochastic deception attacks. Finally, an electrical circuit example is provided to validate the feasibility and superiority of the presented method.