Secure Control for Markov Jump Cyber-Physical Systems Subject to Malicious Attacks: A Resilient Hybrid Learning Scheme
针对受恶意攻击的离散时间马尔可夫跳变信息物理系统，提出一种弹性混合学习方案，将安全控制问题转化为求解博弈耦合代数Riccati方程，并设计了基于模型和无模型的在线学习算法，用倒立摆模型验证了有效性。
This article focuses on solving the secure control problem by developing a novel resilient hybrid learning scheme for discrete-time Markov jump cyber-physical systems with malicious attacks. Within the zero-sum game framework, the secure control problem is converted into solving a set of game coupled algebraic Riccati equations. However, it contains the coupling terms arising from the Markov jump parameters, which are difficult to solve. To address this issue, we propose a framework for parallel reinforcement learning. Thereafter, a model-based resilient hybrid learning scheme is first designed to obtain the optimal policies, where the system dynamics are required during the learning process. Furthermore, a novel online model-free resilient hybrid learning scheme combining the advantages of value iteration and policy iteration is proposed without using the system dynamics. Besides, the convergence of the proposed hybrid learning schemes is discussed. Eventually, the effectiveness of the designed algorithms is demonstrated with the inverted pendulum model.