This dissertation provides new results for energy-based analysis of systems modeled by switched or hybrid system models. This work is motivated by applications in cyber physical systems where systems evolve according to a combination of physical dynamics and cyber, event-driven dynamics. Having a combination of physical and logical dynamics, cyber physical systems are best modeled using switched or hybrid models.
The original energy-based results presented here are based on the notions of passivity and dissipativity from classical nonlinear control theory. Existing theory provides valuable results for analyzing stability for interconnected systems. These methods are well established for nonlinear dynamical systems but do not directly apply to more general system models. A main goal of this dissertation is to provide generalizations of these concepts for hybrid systems. This includes an original definition of passivity indices for switched systems in Chapter 4 and notions of supervisory control using passivity indices in Chapter 6. It also includes original definitions of dissipativity for discrete-event systems and hybrid systems in Chapters 7 and 8. While these properties are useful in practice, they are often difficult to show. Chapter 10 covers computational methods of demonstrating passivity for switched systems.
Often cyber physical systems are built up by connecting components over existing wired or wireless networks. The use of existing networks has advantages since they typically are lower cost and more easily reconfigured. While using existing networks has advantages, data communicated over a network may be delayed or lost entirely. Some original results, presented in Chapter 5, focuses on compensating for delays, lost data, and quantization error in networked systems. The problem of reducing communication rates by using a model based network control scheme to connect dissipative systems is studied in Chapter 9.
Overall, this dissertation provides new methods of analyzing switched and hybrid systems with regard to energy storage and dissipation. These properties provide powerful stability results for single systems and interconnections of systems. Relevant examples are provided when needed to motivate the theory or demonstrate how it can be applied in practice.