Forwarding design for stabilization of a coupled transport equation-ODE with a cone-bounded input nonlinearity

TL;DR

This paper introduces a novel forwarding-based control design to stabilize a coupled transport equation and ODE system with cone-bounded nonlinear input, ensuring well-posedness and asymptotic stability.

Contribution

It presents a new stabilization method for coupled ODE-PDE systems with cone-bounded nonlinearities, extending forwarding techniques to this class of systems.

Findings

The proposed control guarantees asymptotic stability of the coupled system.

The method ensures well-posedness of the closed-loop system.

The transport equation remains conservative without stabilization without control.

Abstract

We propose a new design technique for the stabilization of coupled ODE-PDE systems in feedforward form. In particular, we address the stabilization problem of a one-dimensional transport equation driven by a scalar ODE which is controlled via a cone-bounded nonlinearity. The unforced transport equation is conservative but not asymptotically stable. The proposed technique is inspired by the forwarding approach early introduced in the 90's. Well-posedness and asymptotic stability of the closed-loop system are discussed.