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.

中文翻译：

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对遭受恶意攻击的马尔可夫跳转网络物理系统进行安全控制：一种弹性混合学习方案


本文重点介绍通过为具有恶意攻击的离散时间马尔可夫跳跃网络物理系统开发一种新颖的弹性混合学习方案来解决安全控制问题。在零和博弈框架中，安全控制问题被转化为求解一组博弈耦合代数 Riccati 方程。但是，它包含马尔可夫跳跃参数产生的耦合项，这些项很难求解。为了解决这个问题，我们提出了一个并行强化学习框架。此后，首先设计基于模型的弹性混合学习方案以获得最佳策略，其中学习过程中需要系统动力学。此外，该文提出了一种新颖的在线无模型弹性混合学习方案，该方案结合了价值迭代和策略迭代的优点，无需使用系统动力学。此外，还讨论了所提出的混合学习方案的收敛性。最终，通过倒摆模型证明了所设计算法的有效性。