On the time-discretization of control systems

SIAM Journal on Control and Optimization

Volumn 35, Issue 5, 1997, Pages 1470-1486

  Veliov, Vladimir ^a,b  

^a UNIVERSITY OF VIENNA   (Austria)

^b INSTITUTE OF MATHEMATICS AND INFORMATICS   (Bulgaria)

Author keywords

Control systems; Differential inclusion; Discrete approximation; Optimal control; Reachable set; Runge Kutta scheme

Indexed keywords

APPROXIMATION THEORY; DIFFERENTIAL EQUATIONS; DISCRETE TIME CONTROL SYSTEMS; MATHEMATICAL MODELS; NONLINEAR CONTROL SYSTEMS; OPTIMAL CONTROL SYSTEMS; PARAMETER ESTIMATION; SET THEORY;

RUNGE KUTTA TYPE DISCRETIZATION METHODS;

CONTROL SYSTEM ANALYSIS;

EID: 0031233819     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0363012995288987     Document Type: Article

References (23)

1. Z. ARTSTEIN, First order approximations for differential inclusions, Set-Valued Anal., 2 (1994), pp. 2-17.
2. J.-P. AUBIN AND H. FRANKOWSKA, Set-Valued Analysis, Birkhäuser, Boston, 1990.
3. R. BAIER, Mengenwertige Integration und die Diskrete Approximation Erreichbarer Mengen, Ph.D. thesis, Universität Bayreuth, Germany 1995; Bayreuther Mathematische Schriften, Heft 50.
4. R. BAIER AND F. LEMPIO, Computing Aumann's integrals, in Modeling Techniques for Uncertain Systems, A. Kurzhanski and V. Veliov, eds., Progress in Systems and Control Theory 18, Birkhäuser, Boston, 1994, pp. 71-90.
5. B. DOITCHINOV AND V. VELIOV, Parametrisations of integrals of set-valued mappings and applications, J. Math. Anal. Appl., 179 (1993), pp. 483-499.
6. A. DONTCHEV, Discrete approximations in optimal control, in Nonsmooth Analysis and Geometric Methods in Optimal Control, R. R. B. Mordukhovich and H. Sussmann, eds., Proc. IMA, Springer-Verlag, New York, 1994.
7. A. DONTCHEV, An a priori estimate for discrete approximations in nonlinear optimal control, SIAM J. Control Optim., 34 (1996), pp. 1315-1328.
8. A. DONTCHEV AND E. FARKHI, Error estimates for discretized differential inclusions, Computing, 41 (1989), pp. 349-358.
9. A. DONTCHEV AND W. HAGER, Euler approximation to the feasible set, Numer. Funct. Anal. Optim., 15 (1994), pp. 245-262.
10. A. DONTCHEV AND F. LEMPIO, Difference methods for differential inclusions: A survey, SIAM Review, 34 (1992), pp. 263-294.
11. G. HÄCKL, Numerical approximation of reachable sets and control sets, Random Comput. Dynamics, 1 (1992-1993), pp. 371-394.
12. W. HAGER, Rate of convergence for discrete approximations to unconstrained control problems, SIAM J. Numer. Anal., 13 (1976), pp. 449-472.
13. M. KRASTANOV AND N. KIROV, Dynamic interactive system for analysis of linear differential inclusions, in Modeling Techniques for Uncertain Systems, A. Kurzhanski and V. Veliov, eds., Progress in Systems and Control Theory 18, Birkhäuser, Boston, 1994, pp. 123-130.
14. A. B. KURZHANSKI AND I. VALYI, Ellipsoidal techniques for dynamic systems: Control synthesis for uncertain systems, Dynamics and Control, 2 (1992), pp. 87-111.
15. F. LEMPIO, Difference Methods for Differential Inclusions, Lecture Notes in Econom. and Math. Systems 378, Springer-Verlag, New York, 1992, pp. 236-273.
16. F. LEMPIO, Modified Euler methods for differential inclusions, in Set-Valued Analysis and Differential Inclusions, A. Kurzhanski and V. Veliov, eds., Progress in Systems and Control Theory 16, Birkhäuser, Boston, 1993, pp. 131-148.
17. B. MORDUKHOVICH, Discrete approximations and refined Euler-Lagrange conditions for non-convex differential inclusions, SIAM J. Control Optim., 3 (1995), pp. 882-915.
18. G. REDIEN, Collocation at Gauss points as a discretization in optimal control, SIAM J. Control Optim., 2 (1979), pp. 298-306.
19. D. SILIN, On discontinuous strategies in optimal control problems, J. Math. Systems Estim. Control, 4 (1994), pp. 205-217.
20. V. VELIOV, Second order discrete approximations to strongly convex differential inclusions, Systems Control Lett., 13 (1989), pp. 263-269.
21. V. VELIOV, Parametric and functional uncertainties in dynamical systems: Local and global relationship, in Computer Arithmetic and Enclosure Methods, L. Atanassova and J. Herzberger, eds., North-Holland, Amsterdam, 1992.
22. V. VELIOV, Second order discrete approximations to linear differential inclusions, SIAM J. Numer. Anal., 29 (1992), pp. 439-451.
23. P. WOLENSKI, The exponential formula for the reachable set of Lipschitz differential inclusion, SIAM J. Control Optim., 28 (1990), pp. 1148-1161.