On IDA-PBC with Maximum Energy Shapeability

Abstract

Interconnection and Damping Assignment Passivity-Based Control (IDA-PBC) is a well-established stabilization technique for affine nonlinear systems. However, its application is generally hindered by the requirement of solving a set of partial differential equations (PDEs), i.e., the so-called matching equation. This paper explores the notion of maximum energy shapeability which describes the scenario that the homogeneous part of the matching equation admits $m$ independent solutions with $m$ the dimension of the control input. We show that the maximum energy shapeability enables a systematic procedure for the IDA-PBC design by transforming the matching equation into a set of new PDEs. Specifically, the transformed matching equation admits an explicit solution in the single input case. Sufficient conditions for maximum energy shapeability are also provided. It is shown that some existing constructive IDA-PBC designs actually implicitly exploit the maximum energy shapeability. The proposed procedure for the IDA-PBC design is demonstrated with two practical examples.

arXiv comment8 pages, 4 figures