Conley's fundamental theorem for a class of hybrid systems
| Autor: | Paul Gustafson, Daniel E. Koditschek, Matthew D. Kvalheim |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
FOS: Computer and information sciences
Lyapunov function Class (set theory) Pure mathematics Dynamical systems theory Fundamental theorem General Topology (math.GN) Dynamical Systems (math.DS) Computer Science::Computational Geometry 01 natural sciences 010305 fluids & plasmas symbols.namesake Computer Science - Robotics Modeling and Simulation Hybrid system 0103 physical sciences FOS: Mathematics symbols 34A38 (Primary) 37B20 37B25 37C70 68T40 93C30 (Secondary) Mathematics - Dynamical Systems Robotics (cs.RO) Analysis Decomposition theorem Mathematics Mathematics - General Topology |
| Popis: | We establish versions of Conley's (i) fundamental theorem and (ii) decomposition theorem for a broad class of hybrid dynamical systems. The hybrid version of (i) asserts that a globally-defined "hybrid complete Lyapunov function" exists for every hybrid system in this class. Motivated by mechanics and control settings where physical or engineered events cause abrupt changes in a system's governing dynamics, our results apply to a large class of Lagrangian hybrid systems (with impacts) studied extensively in the robotics literature. Viewed formally, these results generalize those of Conley and Franks for continuous-time and discrete-time dynamical systems, respectively, on metric spaces. However, we furnish specific examples illustrating how our statement of sufficient conditions represents merely an early step in the longer project of establishing what formal assumptions can and cannot endow hybrid systems models with the topologically well characterized partitions of limit behavior that make Conley's theory so valuable in those classical settings. Simplified exposition in Sec. 4; minor fixes |
| Databáze: | OpenAIRE |
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