Passivation and Cooperative Control of Equilibrium-Independent Passivity-Short Systems.
Anoop Jain, Miel Sharf, Daniel Zelazo · arXiv (Cornell University) · 2019
Maximal equilibrium-independent passivity (MEIP) is a recently introduced system property which has acquired special attention in the study of networked dynamical systems. MEIP requires a system to be passive with respect to any forced equilibrium configuration and the associated steady-state input-output map must be maximally monotone. In practice, however, most of the systems are not well behaved and possess shortage of passivity or non-passiveness in their operation. In this paper, we consider a class of passivity-short systems, namely equilibrium-independent passivity-short (EIPS) systems, and presents an input-output transformation based generalized passivation approach to ensure their MEIP properties. We characterize the steady-state input-output relations of the EIPS systems and establish their connection with that of the transformed MEIP systems. We further study the diffusively-coupled networked interactions of such EIPS systems and explore their connection to a pair of dual network optimization problems, under the proposed matrix transformation. A simulation example is given to illustrate the theoretical results.