Zero-Sum Game-Based Reinforcement Learning Tracking Control with Predefined-Time Prescribed Performance for Highly Flexible Aircraft

This paper develops a zero-sum game-based reinforcement learning tracking controller with predefined-time prescribed performance (ZG-RL-PP) for highly flexible aircraft. The disturbed tracking-error dynamics are first transformed into a min–max optimal control problem, where the control input and the disturbance are treated as two players with opposite objectives. To guarantee the prescribed transient and steady-state tracking performance, logarithmic barrier Lyapunov functions are incorporated into the value function and the Hamilton–Jacobi–Isaacs equation. For higher-relative-degree tracking-error channels, recursive auxiliary constraint variables are introduced to preserve the prescribed bounds on the original errors and enable constraint enforcement through the derivative channels in which the control inputs appear. A critic neural network is employed to approximate the value function online, and a predefined-time fractional-power learning law is adopted for critic weight updating. It is shown that the critic weight-estimation error is practically predefined-time convergent and that all closed-loop signals are uniformly ultimately bounded. Simulation results demonstrate the effectiveness and robustness of ZG-RL-PP in terms of tracking accuracy, disturbance attenuation, prescribed-performance satisfaction, and predefined-time learning.