Nonlinear Predictor Feedback for Input-Affine Systems with Distributed Input Delays

TL;DR

This paper introduces a nonlinear predictor feedback method for input-affine systems with distributed delays, transforming the system to enable stabilization via Lyapunov techniques, with proven global or local stability under certain conditions.

Contribution

It develops a novel predictor feedback approach for systems with distributed delays, including stability analysis and control design examples.

Findings

Global exponential stability achieved under certain conditions.

Transforming the system simplifies stabilization analysis.

Numerical examples demonstrate effectiveness of the method.

Abstract

Prediction-based transformation is applied to control-affine systems with distributed input delays. Transformed system state is calculated as a prediction of the system's future response to the past input with future input set to zero. Stabilization of the new system leads to Lyapunov-Krasovskii proven stabilization of the original one. Conditions on the original system are: smooth linearly bounded open-loop vector field and smooth uniformly bounded input vectors. About the transformed system which turns out to be affine in the undelayed input but with input vectors dependent on the input history and system state, we assume existence of a linearly bounded stabilizing feedback and quadratically bounded control-Lyapunov function. If all assumptions hold globally, then achieved exponential stability is global, otherwise local. Analytical and numerical control design examples are provided.