Numerical Schemes for Nonlinear Predictor Feedback

TL;DR

This paper develops numerical schemes for approximating predictor mappings in nonlinear feedback control, enabling global stabilization of systems with delays using hybrid feedback laws and sampled measurements.

Contribution

It introduces a numerical approximation method for predictor mappings in nonlinear predictor feedback laws, enhancing implementation and stabilization capabilities.

Findings

Numerical schemes enable global stabilization of delayed nonlinear systems.

Hybrid feedback laws with sampled measurements achieve stabilization.

Explicit parameter estimation formulas improve control scheme design.

Abstract

Implementation is a common problem with feedback laws with distributed delays. This paper focuses on a specific aspect of the implementation problem for predictor-based feedback laws: the problem of the approximation of the predictor mapping. It is shown that the numerical approximation of the predictor mapping by means of a numerical scheme in conjunction with a hybrid feedback law that uses sampled measurements, can be used for the global stabilization of all forward complete nonlinear systems that are globally asymptotically stabilizable and locally exponentially stabilizable in the delay-free case. Special results are provided for the linear time invariant case. Explicit formulae are provided for the estimation of the parameters of the resulting hybrid control scheme.