Continuity and Invariance in Hybrid Automata
نویسندگان
چکیده
Hybrid automata have been proposed as a language for modelling and analysing the interaction of digital and analogue dynamics in embedded computer systems. In this paper, hybrid automata are studied from a dynamical systems perspective. Extending earlier work on conditions for local existence and uniqueness of executions of hybrid automata, we characterise a class of hybrid automata whose executions depend continuously on the initial state. The continuity conditions are subsequently used to derive an extension of LaSalle’s principle for studying the stability of invariant sets of states of hybrid automata.
منابع مشابه
Continuity and Invariance of Hybrid Automata
Hybrid automata have been proposed as a language for modelling and analysing the interaction of digital and analogue dynamics in embedded computation systems. In this paper, hybrid automata are studied from a dynamical systems perspective. Extending earlier work on conditions for local existence and uniqueness of executions of hybrid automata, we characterise a class of hybrid automata whose ex...
متن کاملDynamical properties of hybrid automata
Hybrid automata provide a language for modeling and analyzing digital and analogue computations in real-time systems. Hybrid automata are studied here from a dynamical systems perspective. Necessary and sufficient conditions for existence and uniqueness of solutions are derived and a class of hybrid automata whose solutions depend continuously on the initial state is characterized. The results ...
متن کاملGenerating Discrete Trace Transition System of a Polyhe-dral Invariant Hybrid Automaton
Supervisory control and fault diagnosis of hybrid systems need to have complete information about the discrete states transitions of the underling system. From this point of view, the hybrid system should be abstracted to a Discrete Trace Transition System (DTTS) and represented by a discrete mode transition graph. In this paper an effective method is proposed for generating discrete mode trans...
متن کاملAsymptotic convergence of constrained primal-dual dynamics
This paper studies the asymptotic convergence properties of the primal-dual dynamics designed for solving constrained concave optimization problems using classical notions from stability analysis. We motivate the need for this study by providing an example that rules out the possibility of employing the invariance principle for hybrid automata to study asymptotic convergence. We understand the ...
متن کاملConvergence of Caratheodory solutions for primal-dual dynamics in constrained concave optimization
This paper characterizes the asymptotic convergence properties of the primal-dual dynamics to the solutions of a constrained concave optimization problem using classical notions from stability analysis. We motivate our study by providing an example which rules out the possibility of employing the invariance principle for hybrid automata to analyze the asymptotic convergence. We understand the s...
متن کامل