Composite Learning Adaptive Optimized Backstepping Control for a Class of Nonlinear Strict-Feedback Systems With Prescribed Performance

Abstract

To improve the learning efficiency of control strategies in uncertain systems, this paper proposes an adaptive neural network (NN) control method that synergizes optimized backstepping (OB) with a composite learning mechanism. Under the identifier-critic-actor architecture, we refine the identifier design by embedding a composite learning structure, where a NN with local approximation properties estimates system dynamics. The composite learning rate is constructed from both tracking and prediction errors, where the prediction error is generated based on a combination of online historical data and instantaneous measurements. A dynamically adjusted identifier learning rate optimizes NN weight updates, significantly improving approximation accuracy without requiring the persistent excitation (PE) condition. To solve the control problem of achieving prescribed-time convergence with predefined precision, a time-varying switching function and quartic barrier Lyapunov functions are designed to ensure tracking errors converge to a user-specified accuracy within a predetermined time frame, while guaranteeing closed-loop stability. Theoretical analysis confirms the uniform ultimate boundedness of all signals. Comparative simulations demonstrate that, compared to reinforcement learning-based OB control methods, the proposed approach achieves faster NN parameter convergence and superior approximation performance. Additionally, it exhibits lower control resource consumption than existing composite learning strategies.