This course focuses on teaching a mathematical framework and tools for the analysis and synthesis of robust hybrid feedback control systems. The learning outcomes include understanding asymptotic stability and invariance of sets in hybrid dynamical systems. The course covers topics such as modeling hybrid systems, Lyapunov stability theorem, and invariance principle lemma. The intended audience for this course is individuals interested in studying complex systems that combine continuous and impulsive dynamics, such as researchers, engineers, and students in the field of control systems and applied mathematics. The teaching method involves theoretical presentations, examples, and applications in areas like genetic networks and power systems.
Feedback Control of Hybrid Dynamical Systems
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Overview
Syllabus
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
Taught by
Society for Industrial and Applied Mathematics
