Stabilization of monotone control systems with input constraints

TL;DR

This paper develops a stabilizing output-feedback controller for monotone control systems that respects input constraints, ensuring stabilization under certain detectability conditions, with applications to PDEs and port-Hamiltonian systems.

Contribution

It introduces a novel control design that guarantees stabilization of monotone systems with input constraints using a saturated passivity-based approach.

Findings

Controller achieves stabilization respecting input constraints.

Applicable to PDEs like heat and wave equations.

Validated on finite-dimensional nonlinear port-Hamiltonian systems.

Abstract

We present a stabilizing output-feedback controller for nonlinear finite and infinite-dimensional control systems governed by monotone operators that respects given input constraints. In particular, we show under a detectability-like assumption that a saturated version of the classical output feedback controller in passivity-based control achieves control-constrained stabilization as long as the control corresponding to the desired equilibrium is in the interior of the control constraint set. We illustrate our findings using a heat equation, a wave equation, and a finite-dimensional nonlinear port-Hamiltonian system.