Projection-based Controllers with Inherent Dissipativity Properties

TL;DR

This paper demonstrates how projection-based controllers can induce passivity and dissipativity properties in nonlinear control systems, ensuring stability and broad applicability through theoretical analysis and numerical examples.

Contribution

It introduces a method to induce dissipativity in nonlinear controllers using projections, enabling stability guarantees for passive nonlinear systems.

Findings

Projection operations can induce passivity in nonlinear controllers

Dissipativity properties lead to stability of feedback interconnections

Numerical examples validate the control design approach

Abstract

Projection-based Controllers (PBCs) are currently gaining traction in both scientific and engineering communities. In PBCs, the input-output signals of the controller are kept in sector-bounded sets by means of projection. In this paper, we will show how this projection operation can be used to induce useful passivity or general dissipativity properties on broad classes of (unprojected) nonlinear controllers that otherwise would not have these properties. The induced dissipativity properties of PBC will be exploited to guarantee asymptotic stability of negative feedback interconnections of passive nonlinear plants and suitably designed PBC, under mild conditions. Proper generalizations to so-called $(q,s,r)$-dissipativity will be presented as well. For illustrating the effectiveness of PBC control design via these passivity-based techniques, two numerical examples are provided.