Secure optimal control of Itô stochastic Markov jump systems subject to DoS attacks: A hybrid learning algorithm - Wang, Xin; Kong, Linghuan; Zhu, Quanxin; Niu, Ben (Automatica (Oxford), 2026)
This paper investigates the secure optimal control problem (SOCP) for Itô stochastic Markov jump system (ISMJS) in the presence of unknown system dynamics, dynamic uncertainty, and denial-of-service (DoS) attacks. Initially, by utilizing the Lyapunov theorem, some sufficient conditions for achieving input-to-state stability (ISS) of the ISMJS are established. Subsequently, to overcome the inherent limitations of existing methods for solving the OCP, specifically, the requirement for both an initially stable control in policy iteration (PI) and the slow convergence rate of value iteration (VI), a model-based robust hybrid learning (HI) algorithm is first proposed. Although the algorithm effectively integrates PI and VI techniques to obtain optimal policies, the system dynamics are required during the learning process. Then, a model-free robust HI scheme without the system dynamics is developed to overcome the aforementioned challenges. Meanwhile, the stability and convergence of the proposed mechanisms are analyzed. Finally, the effectiveness and applicability of the proposed algorithms are validated through a simulation example involving a single-link robot arm.