Projected integral control of impedance passive nonlinear systems

TL;DR

This paper introduces a projected integral control framework for impedance passive nonlinear systems, ensuring constraint satisfaction and stability in infinite-dimensional settings, demonstrated through three case studies.

Contribution

It develops a novel projected integral controller for constrained set-point tracking in impedance passive nonlinear systems governed by monotone differential inclusions.

Findings

Controller guarantees constraint satisfaction

Framework applicable to infinite-dimensional systems

Validated through three case studies

Abstract

We propose an abstract framework for solving the constrained set-point tracking problem for impedance passive infinite-dimensional nonlinear systems. The class of systems considered is governed by monotone differential inclusions and allows us to exploit the theory of contraction semigroups. To account for possible operational constraints, e.g., bounds on the input, we replace a classical integral controller with a projected integral controller. This guarantees that the integrator state remains in a given closed convex set, where said constraints are satisfied. We showcase our results through three case studies.