Passivity Measures in Cyberphysical Systems Design: An Overview of Recent Results and Applications

Abstract

Dissipativity theory is an important energy-based framework for the analysis and design of control systems using an input–output approach. Quadratic supply rate functions in particular have been of great interest since their introduction by Jan Willems. Quadratic supply rate dissipativity exhibits many interesting properties, including a tighter relation to stability. Q-dissipativity and its most prominent special case, passivity, are classical tools. However, their relevance to cyberphysical system (CPS) design stems from the fact that these concepts can be extended to more general hybrid/ switched and networked systems. Dissipative and passive systems exhibit a compositional property for parallel and negative feedback interconnections. Thus, by ensuring that each subsystem is passive, a complex system can be constructed to satisfy specific properties by design and avoid undesirable emergent behaviors. Passivity indices also stem from Q-dissipativity. They are measures of passivity margins and further extend the applicability of passivity-based tools to nonpassive systems as well. The indices have been used in designing secure and stable interconnected systems, hybrid systems, and data-driven analysis and control design. Because of these facts, measures of passivity have been further developed for systems with significant cybercomponents. This short article provides a brief overview of of these new findings in the context of CPSs and presents directions for future work.