Ellipsoidal techniques for reachability analysis

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 1790, Issue , 2000, Pages 202-214

  Kurzhanski, Alexander B ^a   Varaiya, Pravin ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

HYBRID SYSTEMS; LINEAR CONTROL SYSTEMS; ORDINARY DIFFERENTIAL EQUATIONS;

APPROXIMATION SCHEME; COMPUTATIONAL BURDEN; ELLIPSOIDAL APPROXIMATIONS; ELLIPSOIDAL TECHNIQUE; PARAMETRIC REPRESENTATIONS; REACHABILITY ANALYSIS; REACHABILITY PROBLEM; TIME-VARYING COEFFICIENT;

TUBES (COMPONENTS);

EID: 84974693322     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-46430-1_19     Document Type: Conference Paper

References (16)

1. Botchkarev O., Tripakis S., Verification of Hybrid Systems with Linear Differential Inclusions using Ellipsoidal Approximations. Proceedings of this Conference, Pittsburg, 2000.
2. Boyd S., El Ghaoui L., Feron E., Balakrishnan V., Linear Matrix Inequalities in System and Control Theory, SIAM, Studies in Applied Mathematics, 1994.
3. Chernousko F.L., State Estimation for Dynamic Systems, CRC Press, 1994.
4. Henzinger T.A., Kopke P.W., Puri A. and Varaiya P., What’s Decidable about Hybrid Automata ? Proc. 27-th STOC, pp.373-382, 1995.
5. Kurzhanski A.B., Filippova T.F., On the Theory of Trajectory Tubes: a Mathematical Formalism for Uncertain Dynamics, Viability and Control, in: Advances in Nonlinear Dynamics and Control, ser. PSCT 17, pp.122-188, Birkhäuser, Boston, 1993.
6. Kurzhanski A. B., Vályi I. Ellipsoidal Calculus for Estimation and Control, Birkh¨auser, Boston, ser. SCFA, 1997.
7. Kurzhanski A. B., Varaiya P., Ellipsoidal techniques for reachability analysis. To appear.
8. Kurzhanski A. B., Varaiya P., Ellipsoidal techniques for reachability analysis. Internal approximations. To appear.
9. Lee E.B., Marcus L., Foundations of Optimal Control Theory, Wiley, NY, 1967.
10. Leitmann G., Optimality and reachability via feedback controls. In:Dynamic Systems and Mycrophysics, Blaquiere A., Leitmann G. eds.,1982.
11. Lempio F., Veliov V., Discrete Approximations of Differential Inclusions, Bayreuther Mathematische Schriften, Heft 54, pp. 149-232, 1998.
12. Pappas G.L., Sastry S., Straightening out differential inclusions. System and Control Letters, 35(2), pp.79-85, Sept.1998.
13. Puri A., Borkar V. and Varaiya P., ϵ-Approximations of Differential Inclusions, in: R.Alur, T.A.Henzinger, and E.D.Sonntag eds., Hybrid Systems,pp. 109-123, LNCS 1201, Springer, 1996.
14. Puri A., Varaiya P., Decidability of hybrid systems with rectangular inclusions. In D.Dill ed., Proc. CAV-94, LNCS 1066, Springer, 1996.
15. Rockafellar, R. T., Convex Analysis, 2-nd ed., Princeton University Press, 1999.
16. Varaiya P. Reach Set Computation Using Optimal Control, in Proc.of KIT Work-shop on Verification of Hybrid Systems, Verimag, Grenoble, 1998.