Adaptive strategy optimization for cyber-physical systems under denial-of-service attacks using continuous learning automata

Cyber-physical systems (CPS) combine computational, communication, and physical components to enable real-time monitoring and control in critical infrastructures. Despite their advantages, CPS are highly susceptible to Denial-of-Service (DoS) attacks that disrupt communication and impair state estimation. This study conducted a comprehensive analysis of CPS defense under DoS attacks using learning automata (LA) within a game-theoretic framework. Sensor–attacker interactions were modeled as a two-player zero-sum game, in which the sensor sought to minimize estimation error and communication cost, while the attacker aimed to maximize disruption. Both discrete (DLA) and continuous (CLA) learning automata were employed to adaptively optimize sensor strategies and were integrated with a Kalman filter to achieve accurate state estimation. Simulations in MATLAB/Simulink, including generic CPS and microgrid systems, were performed to evaluate performance under reliable and unreliable channels, as well as under varying attack frequencies and durations. The results demonstrated that CLA achieved smooth convergence and high-accuracy state estimation under stable conditions, whereas DLA adapted more rapidly to abrupt disturbances and dynamic environments. Analyses of attack patterns confirmed the framework’s capacity to maintain system resilience through adaptive strategy allocation. Overall, the study demonstrated that learning automata provided an effective, real-time approach for optimizing CPS defense, balancing estimation accuracy, operational cost, and security, and offered a flexible solution applicable to other cyber threats.