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

Abstract

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. Note to Practitioners—The singularity issue caused by tracking error hitting performance boundary is addressed by adjusting performance boundary to balance input saturation and performance constraint in the existing PPC methods considering input saturation. However, practical systems such as autonomous vehicles, aircrafts, spacecrafts, and robots often impose state constraints for safety. Experience is relied upon in the aforementioned methods for adjusting performance boundary, which can easily lead to violation of state constraint and cause safety risks, or only provide limited improvements in addressing singularity issue. To address this issue, the EAPPCC strategy with the SDE is proposed. The maximum safe adjustable range of the dynamic envelope is calculated in real-time by this strategy, and the performance boundary is adjusted within the safety range based on the SDS. Additionally, a hybrid observer framework combined with the FSOB and DOBs is designed to address unmodeled dynamics and disturbances. Finally, the STCC based on dynamic surface control (DSC) method is designed to ensure performance constraint can be met. This method maximizes the improvement in addressing singularity issue within the PPC while ensuring system safety, thereby satisfying critical safety requirements in practical applications.