Abstract
A new approach based on constraint solving techniques was recently proposed for verification of hybrid systems. This approach works by searching for inductive invariants of a given form. In this paper, we extend that work to automatic synthesis of safe hybrid systems. Starting with a multi-modal dynamical system and a safety property, we present a sound technique for synthesizing a switching logic for changing modes so as to preserve the safety property. By construction, the synthesized hybrid system is well-formed and is guaranteed safe. Our approach is based on synthesizing a controlled invariant that is sufficient to prove safety. The generation of the controlled invariant is cast as a constraint solving problem. When the system, the safety property, and the controlled invariant are all expressed only using polynomials, the generated constraint is an ∃ ∀ formula in the theory of reals, which we solve using SMT solvers. The generated controlled invariant is then used to arrive at the maximally liberal switching logic.
Research supported in part by the National Science Foundation under grant CNS-0720721 and by NASA under Grant NNX08AB95A. Work done when the first author was visiting SRI International.
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Taly, A., Gulwani, S., Tiwari, A. (2008). Synthesizing Switching Logic Using Constraint Solving. In: Jones, N.D., Müller-Olm, M. (eds) Verification, Model Checking, and Abstract Interpretation. VMCAI 2009. Lecture Notes in Computer Science, vol 5403. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-93900-9_25
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DOI: https://doi.org/10.1007/978-3-540-93900-9_25
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