Practical prescribed-time command-filtered resilient fuzzy learning control for cyber–physical systems: A shaping-modulated Lyapunov function approach

In cyber–physical systems (CPSs), implementing rapid and resilient control is essential to prevent physical failures and ensure operational safety. However, existing prescribed-time control methods often suffer from potentially unbounded gains, reducing the reliability of the algorithm. To address this bottleneck, this paper proposes a novel shaping-modulated practical prescribed-time command-filtered resilient fuzzy learning control framework for nonlinear CPSs under simultaneous dual-channel deception attacks and unknown disturbances. By integrating fuzzy logic systems with a bounded smooth time-shaping function, a shaping-modulated Lyapunov mechanism is constructed to eliminate unbounded gains, thereby avoiding potential control singularities. Furthermore, an integral Lyapunov function-based command-filtered backstepping approach is developed. It not only removes conventional error compensation filters, but also enables the system stability and tracking accuracy to be explicitly analyzed based on the direct state tracking error rather than the compensated one. Theoretical analysis guarantees that the actual output tracking error converges to an adjustable neighborhood of zero within a prescribed time. Finally, comparative simulations validate the effectiveness and reliability of the proposed scheme.