A New Implementation Pathway: Self-Adjusting Performance Function-Based Control for Strict-Feedback Systems Under Input Saturation

A novel approach is proposed for flexible performance-based control of strict-feedback systems subject to input saturation. The core design consists of three key components. First, the regulation of the performance function (PF) is achieved by reformulating it as an adaptive modification of its exponential index, exploiting its inherent structural properties. Second, a performance indicator function (PIF) is constructed based on output-side information by analyzing the system behavior in the absence of saturation, thereby avoiding the reliance on input-side compensation signals with limited differentiability. Third, a first-order auxiliary system is designed to adaptively adjust the exponential index in real time, driving the PIF to closely track the upper envelope of the actual tracking error. As a result, the proposed self-adjusting PF (SAPF) is able to maintain a dynamic balance between input and output behaviors by relaxing performance boundaries when constraint violations are imminent while actively accelerating PF contraction to enhance transient performance under saturation constraints. Building on this framework, an SAPF-based control algorithm is developed with rigorous closed-loop stability guarantees. Finally, the effectiveness and superiority of the proposed method are demonstrated through quantitative simulation comparisons with two advanced algorithms in a vehicle lane-keeping task.