Autonomous trajectory method for strict-feedback nonlinear systems with Prescribed performance and Optimization Framework

For the high-precision control problem of strict-feedback nonlinear systems in the presence of model uncertainties and external disturbances, this paper proposes an autonomous trajectory control method with prescribed performance. Traditional Prescribed Performance Control (PPC) methods often employ fixed-shape performance functions, which lack the flexibility to accurately describe performance boundaries. Furthermore, significant initial errors can easily lead to severe overshoot, oscillations, or even instability when tracking the original reference signal. To address these issues, this paper constructs an ”autonomous trajectory” connecting the initial state and the predefined time point of reference signal by using piecewise Bezier curves. This ensures a smooth and stable transition to the reference signal within a predefined time, while simultaneously enforcing precise constraints on both the transient and steady-state performance. Additionally, a disturbance observer based on performance constraints is designed to estimate and compensate for disturbances. The Fata Morgana Algorithm (FATA) is introduced to establish a systematic controller parameter optimization framework, which utilizes a standardized optimization test set for automatic tuning of key parameters, minimizing control energy while guaranteeing the prescribed tracking performance. Lyapunov stability analysis proves the uniformly ultimate boundedness of all closed-loop system signals and their convergence within the predefined time. Simulation results validate the effectiveness of the proposed method in enhancing system transient performance, robustness, and control efficiency.