Inexact predictor feedback for multi-input nonlinear systems with distinct input delays

Abstract

This paper presents a strategy of inexact predictor-feedback control for multi-input nonlinear systems with distinct delays. The controllers designed by an inexact predictor robustly compensate for the different delays. Different from exact predictor feedback, we propose a scheme that can achieve exponential stability of the system without accurately compensating for each delay and has the property of less complexity. For this purpose, we adopt a fixed constant as the prediction horizon, which is restricted to being within a sufficiently narrow range. Its function is to offset the partial effect of each delay. With a new Lyapunov-Krasovskii functional based on an infinite-dimensional backstepping transformation, we prove the global exponential stability of the closed-loop system. Finally, a numerical example is presented to verify the effectiveness of the theoretical results.