Predictor control for nonlinear systems actuated via transport PDEs with time/space varying propagation speeds

Abstract

We consider predictor controls for two kinds of cascaded systems of nonlinear ordinary differential equations (ODEs) and transport partial differential equations (PDEs) with time/space varying propagation speeds. Since the propagation speeds depend on time/space variables, how to get the prediction states of PDEs is a key challenge. We solve this challenge in this paper. We construct two infinite backstepping transformations to transform the original systems into target systems and design predictor controls for these two kinds of cascaded systems, respectively. We prove stability of the closed‐loop systems using Lyapunov‐like arguments and derive alternative representations of cascaded systems as nonlinear systems with time/space varying input delays and also establish equivalent predictor feedbacks for the delay systems.