Fuzzy Adaptive Quantized Tracking Control of Switched High-Order Nonlinear Systems: A New Fixed-Time Prescribed Performance Method

Abstract

This brief addresses the fixed-time adaptive tracking control problem for a class of switched high-order nonlinear systems (powers are positive odd integers) subject to input quantization and guaranteed performances. The most advanced peculiarity of this design lies in that some transient-state and steady-state metrics (e.g., maximum overshoot and convergence rate) can be preselected <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> within fixed time, and in considering non-smooth behaviors (e.g., switching dynamics and input quantization). More precisely, different from conventional fixed-time control schemes that typically contain some exponential terms in their designs, this brief removes the dependence on the need of above-mentioned exponential terms. As opposed to the state-of-the-art prescribed performance control methods, a new error transformation is designed to get rid of the non-differentiability issue and to alleviate computation burden. Meanwhile, a newly proposed fixed-time performance function (FTPF) is utilized to guarantee fixed-time convergence and remove the reliance on precise initial error values. A numerical example is provided to illustrate the effectiveness of the proposed control scheme.