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.

During the development process of CPS, an analysis of whether the system operates safely in its target environment is of utmost importance. For many applications of CPS research such as the transportation industry, this implies interconnected research in formal verification of CPS with research on knowledge representation and reasoning in multi-agent systems. The need for such research has become tragically clear in transportation accidents, one notorious case being the Air France 447 flight incident.

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.

Abstract: Motivation and goal: The whole-system design and modeling of complex medical robotics involves analog sensors and actuators; discrete software controllers; piecewise, non-linear, discontinuous biological tissues/media; and probabilistic human administrators. In the best case, the failure of such systems risks limb. In the worst, life.

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