Abstract
We present a semantic framework for the deductive verification of hybrid systems with Isabelle/HOL. It supports reasoning about the temporal evolutions of hybrid programs in the style of differential dynamic logic modelled by flows or invariant sets for vector fields. We introduce the semantic foundations of this framework and summarise their Isabelle formalisation as well as the resulting verification components. A series of simple examples shows our approach at work.
Highlights
Hybrid systems combine continuous dynamics with discrete control
Before developing relational and state transformer models for the basic evolution commands of hybrid programs we briefly review some basic facts about continuous dynamical systems and ordinary differential equations
We have presented a new semantic framework for the deductive verification of hybrid systems with the Isabelle/HOL proof assistant
Summary
Hybrid systems combine continuous dynamics with discrete control. Their verification is receiving increasing attention as the number of computing systems controlling real-world physical systems is growing. Hybrid system verification requires integrating continuous system dynamics, often modelled by systems of differential equations, and discrete control components into hybrid automata, hybrid programs or similar domain-specific modelling formalisms, and into analysis techniques for these. After certifying the flow conditions and checking Lipschitz continuity of the vector field, as dictated by the Picard–Lindelöf theorem, the orbit for the flow can be used to compute the weakest liberal preconditions for the evolution command This workflow deviates from dL in allowing users to supply an interval of interest as domain of the flow. – The third workflow uses flows ab initio in the specification and semantic analysis of evolution commands This circumvents checking any continuity, existence, uniqueness or invariant conditions of vector fields mentioned. A glossary of cross-references between theorems in the text and the Isabelle theories is presented in Appendix A
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