Predictor-Based Output Feedback for Nonlinear Delay Systems

TL;DR

This paper introduces two novel predictor-based output feedback methods for stabilizing nonlinear delay systems with arbitrarily long input and output delays, applicable to sampled-data and disturbed systems, with proven global stability.

Contribution

It presents two new solutions for stabilizing nonlinear systems with long delays using output feedback, including explicit and approximate predictor constructions, addressing sampled-data and disturbance scenarios.

Findings

First approach allows finite-step state reconstruction from past data.

Second approach employs high-gain observer and predictor approximation.

Both methods demonstrated with analytical and numerical examples.

Abstract

We provide two solutions to the heretofore open problem of stabilization of systems with arbitrarily long delays at the input and output of a nonlinear system using output feedback only. Both of our solutions are global, employ the predictor approach over the period that combines the input and output delays, address nonlinear systems with sampled measurements and with control applied using a zero-order hold, and require that the sampling/holding periods be sufficiently short, though not necessarily constant. Our first approach considers general nonlinear systems for which the solution map is available explicitly and whose one-sample-period predictor-based discrete-time model allows state reconstruction, in a finite number of steps, from the past values of inputs and output measurements. Our second approach considers a class of globally Lipschitz strict-feedback systems with disturbances and employs an appropriately constructed successive approximation of the predictor map, a high-gain sampled-data observer, and a linear stabilizing feedback for the delay-free system. We specialize the second approach to linear systems, where the predictor is available explicitly. We provide two illustrative examples-one analytical for the first approach and one numerical for the second approach.