Adaptive fuzzy backstepping secure control for incommensurate fractional order cyber–physical power systems under intermittent denial of service attacks

This paper proposes a fuzzy adaptive control strategy, based on backstepping, for incommensurate fractional-order power systems under denial-of-service (DoS) attacks. To address a wider range of fractional-order systems, this study assumes that the agents’ dynamics where each state have non-identical fractional derivative orders. This assumption brings up additional complexity to the design of the secure control system compared to existing approaches. Our approach tackles the challenge of maintaining system stability during both normal and attack periods by integrating adaptive control technique. The method includes an attack compensator to manage unavailable output measurements during attacks and a fuzzy estimator to approximate unobservable states. It also employs a fractional-order adaptive law and a backstepping controller to ensure performance and security, maintaining bounded tracking errors. MATLAB simulations confirm the effectiveness and robustness of the proposed method, demonstrating its ability to protect power systems from cyber threats while ensuring operational integrity and stability. Compared to prior studies, the presence of an attack compensator reduces both overshoots and convergence time following each attack.