Abstract
We investigate the behavior of a Pfaffian dynamical system with respect to viability constraints and invariants. For Pfaffian dynamical systems we construct an algorithm with an elementary (doubly-exponential) upper complexity bound for checking satisfiability of viability constraints. This algorithm also provides a useful tool for checking invariance properties of given sets.
This research was partially supported by Grant Scientific School-4413.2006.1, Deutsche Forschungsgemeinschaft Project WE 843/17-1, and Project GZ: 436 RUS 113/850/01.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Aubin, J.-P.: Viability Analysis. Birkhauser, Boston (1991)
Basu, S., Pollack, R., Roy, M.-F.: Algorithms in Real Algebraic Geometry. Springer, Heidelberg (2003)
Blum, L., et al.: Complexity and Real Computation. Springer, New York (1997)
Brihaye, T., et al.: On o-minimal hybrid systems. In: Alur, R., Pappas, G.J. (eds.) HSCC 2004. LNCS, vol. 2993, pp. 219–233. Springer, Heidelberg (2004)
Gabrielov, A., Vorobjov, N.: Complexity of computations with Pfaffian and Noetherian functions. In: Ilyashenko, Y., et al. (eds.) Normal Forms, Bifurcations and Finiteness Problems in Differential Equations. NATO Science Series, vol. II, pp. 211–250. Kluwer Academic Publishers, Dordrecht (2004)
Gabrielov, A., Vorobjov, N.: Complexity of cylindrical decompositions of sub-Pfaffian sets. J. Pure and Appl. Algebra 164(1-2), 179–197 (2001)
Gabrielov, A., Vorobjov, N.: Betti numbers of semialgebraic sets defined by quantifier-free formulae. To appear in: Discrete and Computational Geometry (2004)
Khovanskii, A.: Fewnomials. Translations of Mathematical Monographs, vol. 88. American Mathematical Society, Providence (1991)
Korovina, M., Vorobjov, N.: Pfaffian hybrid systems. In: Marcinkowski, J., Tarlecki, A. (eds.) CSL 2004. LNCS, vol. 3210, pp. 430–441. Springer, Heidelberg (2004)
Korovina, M., Vorobjov, N.: Upper and lower Bounds on Sizes of Finite Bisimulations of Pfaffian Hybrid Systems. In: Beckmann, A., et al. (eds.) CiE 2006. LNCS, vol. 3988, pp. 235–241. Springer, Heidelberg (2006)
Lafferriere, G., Pappas, G.J., Sastry, S.: O-minimal hybrid systems. Math. Control Signals Systems 13, 1–21 (2000)
Pericleous, S., Vorobjov, N.: New complexity bounds for cylindrical decompositions of sub-Pfaffian sets. In: Aronov, B., et al. (eds.) Discrete and Computational Geometry. Goodman-Pollack Festschrift, pp. 673–694. Springer, Heidelberg (2003)
van den Dries, L.: Tame Topology and O-minimal Structures. London Mathematical Society Lecture Notes Series, vol. 248. Cambridge University Press, Cambridge (1998)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Korovina, M., Vorobjov, N. (2007). Satisfiability of Viability Constraints for Pfaffian Dynamics. In: Virbitskaite, I., Voronkov, A. (eds) Perspectives of Systems Informatics. PSI 2006. Lecture Notes in Computer Science, vol 4378. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70881-0_23
Download citation
DOI: https://doi.org/10.1007/978-3-540-70881-0_23
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-70880-3
Online ISBN: 978-3-540-70881-0
eBook Packages: Computer ScienceComputer Science (R0)