Security-Based Resilient Robust Model Predictive Control for Polytopic Uncertain Systems Subject to Deception Attacks and RR Protocol
Jianhua Wang, Yan Song, Guoliang Wei
Abstract
This article is concerned with the security-based resilient robust model predictive control (RMPC) problem for a class of discrete-time polytopic uncertain systems with deception attacks and the round-robin (RR) protocol. The well-known RR protocol is adopted with the hope to reduce the communication burden, where the control signal is transmitted only at the given transmission instant. By means of the concept of bounded energy and the independent Bernoulli-distributed (BD) white sequences, a representative attack model is given. A definition of mean-square (MS) security in <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> -sense is employed to reasonably explain the dynamics process of the controlled systems. We aim at designing a set of resilient RMPC controllers so as to make the closed-loop system state under consideration of deception attacks and the RR protocol enter and stay in a certain bounded region. Furthermore, with the aid of stochastic analysis methods and inequality analysis techniques, sufficient conditions are obtained to satisfy the desirable security requirements. To tackle the nonconvex obstacles resulting from attacks and the RR protocol, the cone complementary linearization (CCL) method is exploited to cast them into a convex optimization problem (OP) for its solvability. Then, an online OP regarding a certain upper bound of the concerned objective is provided for the solvability and resilient RMPC-based controller gains are obtained. Finally, two examples, including a high-purity distillation one and a numerical one, are used to demonstrate the effectiveness and the validity of the proposed techniques.