differential equations

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Visible to the public Sound Invariant Generation for Continuous and Hybrid Systems

Invariant generation is crucial to the success of rigorous deductive verification tools for cyber-physical system. We develop a dedicated invariant generation toolbox for the KeYmaera X theorem prover which combines many custom invariant generation methods under a unified framework. Additionally, we develop a generalization of the method of barrier certificates (vector barrier certificates), building on R. Bellman's work on vector Lyapunov functions.

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Visible to the public Differential Radical Invariants: Safety Verification and Design of Correct Hybrid Systems

Abstract:

The verification of hybrid systems requires ways of handling both the discrete and continuous dynamics, e.g., by proofs, abstraction, or approximation. Fundamentally, however, the study of the safety of hybrid systems can be shown to reduce constructively to the problem of generating invariants for their differ- ential equations. We recently focused on this core problem. We study the case of algebraic invariant equation, i.e. invariants described by a polynomial equation of the form p = 0 for a polynomial p.