Algorithmic analysis of nonlinear hybrid systems

T.A. Henzinger, P. Ho, in:, Springer, 1995, pp. 225–238.

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Hybrid systems model discrete programs that are embedded in continuous environments. Model-checking tools are available for the analysis of linear hybrid systems, whose continuous variables are bounded by piecewise-linear trajectories. Most embedded programs, however, operate in nonlinear environments. We present, analyze, and apply two algorithms for translating nonlinear hybrid systems into linear hybrid systems. The clock translation replaces nonlinear variables by clock variables; the rate translation approximates nonlinear variables by piecewise-linear envelopes. Both translations are sound for reachability; that is, if we establish a safety property of the translated linear system, we may conclude that the original nonlinear system satisfies the property. The clock translation is also complete for reachability; that is, the original system and the translated system satisfy the same safety properties. The two translations apply to incomparable classes of nonlinear hybrid systems. From the clock translation we obtain a new decidability result for hybrid systems. With the help of Hytech, a symbolic model checker for linear hybrid systems, we automatically verify a nonlinear railroad gate control program using the clock translation, and a nonlinear temperature control program using the rate translation.
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This research was supported in part by the NSF grant CCR-9200794, by the AFOSR contract F49620-93-1-0056, and by the DARPA grant NAG2-892.
225 - 238
CAV: Computer Aided Verification

Cite this

Henzinger TA, Ho P. Algorithmic analysis of nonlinear hybrid systems. In: Vol 939. Springer; 1995:225-238. doi:10.1007/3-540-60045-0_53
Henzinger, T. A., & Ho, P. (1995). Algorithmic analysis of nonlinear hybrid systems (Vol. 939, pp. 225–238). Presented at the CAV: Computer Aided Verification, Springer.
Henzinger, Thomas A, and Pei Ho. “Algorithmic Analysis of Nonlinear Hybrid Systems,” 939:225–38. Springer, 1995.
T. A. Henzinger and P. Ho, “Algorithmic analysis of nonlinear hybrid systems,” presented at the CAV: Computer Aided Verification, 1995, vol. 939, pp. 225–238.
Henzinger TA, Ho P. 1995. Algorithmic analysis of nonlinear hybrid systems. CAV: Computer Aided Verification, LNCS, vol. 939, 225–238.
Henzinger, Thomas A., and Pei Ho. Algorithmic Analysis of Nonlinear Hybrid Systems. Vol. 939, Springer, 1995, pp. 225–38, doi:10.1007/3-540-60045-0_53.


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