Feedback Control of Hybrid Dynamical Systems

Explore the mathematical framework and tools for analyzing and synthesizing robust hybrid feedback control systems in this 40-minute conference talk. Delve into the world of hybrid dynamical systems, which combine continuous and impulsive dynamics to describe complex systems. Learn about asymptotic stability and invariance of sets, and see how these tools are applied to real-world scenarios ranging from genetic networks to power systems. Discover the scope of hybrid systems research, recent contributions to the field, and common features in applications. Examine autonomous hybrid systems, differential equations with multistable elements, and modeling techniques for switched and impulsive systems. Gain insights into the general control problem, Lyapunov stability theorem, and hybrid basic conditions. Investigate sequential compactness theorem, invariance principle, and their consequences. Conclude with a practical application to boost converters and a comprehensive introduction to hybrid systems and modeling.

Intro
Scope of Hybrid Systems Research
Motivation and Approach Common features in applications
Recent Contributions to Hybrid Systems Theory Autonomous Hybrid Systems
Related Work A (rather incomplete) list of related contributions: Differential equations with multistable elements
A Genetic Network Consider a genetic regulatory network with two genes (A and B). each encoding for a protein
The Boost Converter
Modeling Hybrid Systems A wide range of systems can be modeled within the framework Switched systems Impulsive systems
General Control Problem Given a set A and a hybrid system H to be controlled
Lyapunov Stability Theorem Theorem
Hybrid Basic Conditions The data (C1,D, 9) of the hybrid system
Sequential Compactness Theorem Given a hybrid system satisfying the hybrid basic conditions, let
Invariance Principle Lemma Letz be a bounded and complete solution to a hybrid system H satisfying the hybrid basic conditions. Then, its w-limit set
Other Consequences of the Hybrid Basic Conditions
Back to Boost Converter
Conclusion Introduction to Hybrid Systems and Modeling Hybrid Basic Conditions and Consequences