Abstract
This paper introduces Periodically Controlled Hybrid Automata (PCHA) for describing a class of hybrid control systems. In a PCHA, control actions occur roughly periodically while internal and input actions may occur in the interim changing the discrete-state or the setpoint. Based on periodicity and subtangential conditions, a new sufficient condition for verifying invariance of PCHAs is presented. This technique is used in verifying safety of the planner-controller subsystem of an autonomous ground vehicle, and in deriving geometric properties of planner generated paths that can be followed safely by the controller under environmental uncertainties.
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References
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(1), 3–34 (1995)
Bhatia, N.P., Szegö, G.P.: Dynamical Systems: Stability Theory and Applications. Lecture notes in Mathematics, vol. 35. Springer, Heidelberg (1967)
Brown, C.W.: QEPCAD B: a program for computing with semi-algebraic sets using CADs. SIGSAM Bull. 37(4), 97–108 (2003)
Burdick, J.W., DuToit, N., Howard, A., Looman, C., Ma, J., Murray, R.M., Wongpiromsarn, T.: Sensing, navigation and reasoning technologies for the DARPA Urban Challenge. Technical report, DARPA Urban Challenge Final Report (2007)
DuToit, N.E., Wongpiromsarn, T., Burdick, J.W., Murray, R.M.: Situational reasoning for road driving in an urban environment. In: International Workshop on Intelligent Vehicle Control Systems (IVCS) (2008)
Henzinger, T.A., Kopke, P.W., Puri, A., Varaiya, P.: What’s decidable about hybrid automata? In: STOC, pp. 373–382 (1995)
Kaynar, D.K., Lynch, N., Segala, R., Vaandrager, F.: The Theory of Timed I/O Automata. Synthesis Lectures on Computer Science. Morgan Claypool (2005)
Lafferriere, G., Pappas, G.J., Yovine, S.: A new class of decidable hybrid systems. In: Vaandrager, F.W., van Schuppen, J.H. (eds.) HSCC 1999. LNCS, vol. 1569, pp. 137–151. Springer, Heidelberg (1999)
Lynch, N., Segala, R., Vaandrager, F.: Hybrid I/O automata. Information and Computation 185(1), 105–157 (2003)
Mitra, S.: A Verification Framework for Hybrid Systems. PhD thesis, Massachusetts Institute of Technology, Cambridge, MA 02139 (September 2007)
Mitra, S., Wang, Y., Lynch, N.A., Feron, E.: Safety verification of model helicopter controller using hybrid input/Output automata. In: Maler, O., Pnueli, A. (eds.) HSCC 2003. LNCS, vol. 2623, pp. 343–358. Springer, Heidelberg (2003)
Owre, S., Rajan, S., Rushby, J.M., Shankar, N., Srivas, M.K.: PVS: Combining specification, proof checking, and model checking. In: Alur, R., Henzinger, T.A. (eds.) CAV 1996. LNCS, vol. 1102, pp. 411–414. Springer, Heidelberg (1996)
Prabhakar, P., Vladimerou, V., Viswanathan, M., Dullerud, G.E.: A decidable class of planar linear hybrid systems. In: Egerstedt, M., Mishra, B. (eds.) HSCC 2008. LNCS, vol. 4981, pp. 401–414. Springer, Heidelberg (2008)
Prajna, S., Papachristodoulou, A., Parrilo, P.A.: Introducing SOSTOOLS: A general purpose sum of squares programming solver. In: CDC 2002, pp. 741–746 (2002)
Vladimerou, V., Prabhakar, P., Viswanathan, M., Dullerud, G.E.: Stormed hybrid systems. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds.) ICALP 2008, Part II. LNCS, vol. 5126, pp. 136–147. Springer, Heidelberg (2008)
Vladimerou, V., Prabhakar, P., Viswanathan, M., Dullerud, G.E.: Periodically controlled hybird systems: Verifying a controller for an autonomous vehicle. TechReport CaltechCDSTR:2008.003, California Inst. of Tech., http://resolver.caltech.edu/CaltechCDSTR:2008.003
Wongpiromsarn, T., Murray, R.M.: Distributed mission and contingency management for the DARPA urban challenge. In: International Workshop on Intelligent Vehicle Control Systems (IVCS) (2008)
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Wongpiromsarn, T., Mitra, S., Murray, R.M., Lamperski, A. (2009). Periodically Controlled Hybrid Systems. In: Majumdar, R., Tabuada, P. (eds) Hybrid Systems: Computation and Control. HSCC 2009. Lecture Notes in Computer Science, vol 5469. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00602-9_28
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DOI: https://doi.org/10.1007/978-3-642-00602-9_28
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