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. The generalization allows us to use tractable optimization algorithms to search for broader classes of invariants than was previously possible.