On the Uniformness of Full-State Error Prescribed Performance for Strict-Feedback Systems

Most existing results on full-state error prescribed performance control for multiple-input multiple-output (MIMO) strict-feedback nonlinear systems typically impose demanding constraining conditions on the initial full-state errors, rendering the performance boundary nonuniform with respective to initial conditions, and consequently tedious offline computations for initial error (especially the initial virtual error) constraint verification is inevitable, which is highly undesirable or even impractical for the design and implementation of the corresponding controls. In this article, we present a novel adaptive control solution that allows the performance uniformness (with respect to the initial condition) and the transient behavior (with respect to error overshoot) to be addressed simultaneously under a unified framework. The key design steps and features include: 1) by constructing a nonlinear transformation based on the time-varying scaling function, the developed performance boundary is uniform to any initial condition; 2) the demanding condition on the initial values of full-state errors in the existing prescribed performance works is removed, allowing the designer more freedom to select design parameters and rendering the solution more user-friendly and less demanding in design and implementation; and 3) by making use of the minimum eigenvalues of the resultant diagonal matrix and imposing a critical negative feedback term in the control design, the stability of closed-loop system is ensured by the developed uniform control strategy. The effectiveness of the proposed approach is verified by simulations.