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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Alur, R., Courcoubetis, C., Halbwachs, N., Henzinger, T.A., Ho, P.-H., Nicollin, X., Olivero, A., Sifakis, J., Yovine, S.: The algorithmic analysis of hybrid systems. Theoretical Computer Science 138(3), 3–34 (1995)
Asarin, E., Bournez, O., Dang, T., Maler, O., Pnueli, A.: Effective synthesis of switching controllers for linear systems. Proc. IEEE 88(7), 1011–1025 (2000)
Blanchini, F.: Set invariance in control. Automatica 35, 1747–1767 (1999)
Burns, K., Gidea, M.: Differential Geometry and Topology: With a view to dynamical systems. Chapman & Hall, Boca Raton (2005)
Colón, M.: Schema-guided synthesis of imperative programs by constraint solving. In: LOPSTR, pp. 166–181 (2004)
Cury, J., Brogh, B., Niinomi, T.: Supervisory controllers for hybrid systems based on approximating automata. IEEE Trans. Aut. Control 43, 564–568 (1998)
Gulwani, S., Tiwari, A.: Constraint-based approach for analysis of hybrid systems. In: Gupta, A., Malik, S. (eds.) CAV 2008. LNCS, vol. 5123, pp. 190–203. Springer, Heidelberg (2008)
Koo, T., Sastry, S.: Mode switching synthesis for reachability specification. In: Di Benedetto, M.D., Sangiovanni-Vincentelli, A.L. (eds.) HSCC 2001. LNCS, vol. 2034, pp. 333–346. Springer, Heidelberg (2001)
Manon, P., Valentin-Roubinet, C.: Controller synthesis for hybrid systems with linear vector fields. In: Proc. IEEE Symp. on Intell. Control, pp. 17–22 (1999)
Moor, T., Raisch, J.: Discrete control of switched linear systems. In: Proc. Eur. Control Conf. ECC 1999 (1999)
Prajna, S., Jadbabaie, A.: Safety verification of hybrid systems using barrier certificates. In: Alur, R., Pappas, G.J. (eds.) HSCC 2004. LNCS, vol. 2993, pp. 477–492. Springer, Heidelberg (2004)
Sankaranarayanan, S., Sipma, H., Manna, Z.: Constructing invariants for hybrid systems. In: Alur, R., Pappas, G.J. (eds.) HSCC 2004. LNCS, vol. 2993, pp. 539–554. Springer, Heidelberg (2004)
Tomlin, C., Lygeros, L., Sastry, S.: A game-theoretic approach to controller design for hybrid systems. Proc. of the IEEE 88(7), 949–970 (2000)
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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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