Enhanced Adaptive Prescribed Performance Constrained Control With Safe Dynamic Envelope for Input-Saturated Nonlinear System

When prescribed performance control (PPC) is implemented for state-constrained control, compact error boundary can easily lead to input saturation, which will trigger singularities. Existing methods for adjusting boundary through input saturation are mostly based on experience, often resulting in improper adjustments that either violate state constraints or offer limited improvement in singularity issue. To address this issue, an enhanced adaptive prescribed performance constrained control (EAPPCC) strategy with a safe dynamic envelope (SDE) is proposed. Firstly, an enhanced adaptive performance function with the SDE is designed, which offers the following advantages: (1) the safety-adjustable range of performance boundary is determined; (2) a saturation detection system (SDS) is designed to adaptively adjust the performance boundary within the adjustable safety range. A balance among performance constraint, input saturation, and safety condition is achieved by the SDE. Secondly, unknown dynamics are approximated by fuzzy logic system (FLS) independently of the control loop but integrated within a fuzzy state observer (FSOB). Then, a set of disturbance observers (DOBs) is designed to estimate the approximation errors of the FLS and unknown disturbances. Furthermore, a saturation-tolerant constrained controller (STCC) which can satisfy performance constraint is designed. Finally, the closed-loop stability is demonstrated based on the Lyapunov method, and the effectiveness and advantages of the proposed strategy are verified through simulations and experiment verifications.