Predictor-Feedback Stabilization of Multi-Input Nonlinear Systems

TL;DR

This paper introduces a predictor-feedback control method for stabilizing multi-input nonlinear systems with different input delays, ensuring global stability and providing explicit solutions for linear cases, demonstrated on a nonholonomic unicycle.

Contribution

It develops a novel predictor-feedback control design for multi-input nonlinear systems with arbitrary input delays, including explicit solutions for linear systems and a practical example.

Findings

Global asymptotic stability achieved for nonlinear systems

Explicit predictor-feedback laws for linear systems

Successful stabilization of a nonholonomic unicycle example

Abstract

We develop a predictor-feedback control design for multi-input nonlinear systems with distinct input delays, of arbitrary length, in each individual input channel. Due to the fact that different input signals reach the plant at different time instants, the key design challenge, which we resolve, is the construction of the predictors of the plant's state over distinct prediction horizons such that the corresponding input delays are compensated. Global asymptotic stability of the closed-loop system is established by utilizing arguments based on Lyapunov functionals or estimates on solutions. We specialize our methodology to linear systems for which the predictor-feedback control laws are available explicitly and for which global exponential stability is achievable. A detailed example is provided dealing with the stabilization of the nonholonomic unicycle, subject to two different input delays affecting the speed and turning rate, for the illustration of our methodology.