A sampling method and approximation results for impulsive systems

SIAM Journal on Control and Optimization

Volumn 46, Issue 3, 2007, Pages 983-998

  Wolenski, Peter R ^a   Žabić, Stanislav ^a  

^a LOUISIANA STATE UNIVERSITY   (United States)

Author keywords

Approximate solutions; Calculus of variations; Impulsive systems; Optimal control; Sampling

Indexed keywords

APPLIED MATHEMATICS; APPROXIMATION RESULTS; CLASSICAL SYSTEMS; DIFFERENTIAL INCLUSIONS; DISCRETE TIME (DT); IMPULSIVE DYNAMICAL SYSTEMS; IMPULSIVE SYSTEMS; LIPSCHITZ; SAMPLING METHODS;

APPROXIMATION THEORY; COMPUTER NETWORKS; DIFFERENTIAL EQUATIONS; GRAPH THEORY;

DYNAMICAL SYSTEMS;

EID: 44649127411     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/040620734     Document Type: Article

References (25)

1. J. P. AUBIN AND A. CELLINA, Differential Inclusions, Springer, Berlin, 1984.
2. A. BRESSAN, Impulsive control systems, in Nonsmooth Analysis and Geometric Methods in Deterministic Optimal Control, B. Mordukhovich and H. J. Sussmann, eds., Springer, New York, 1996, pp. 1-22.
3. A. BRESSAN AND F. RAMPAZZO, Impulsive systems with commutative vector fields, J. Optim. Theory Appl., 71 (1991), pp. 67-83.
4. A. BRESSAN AND F. RAMPAZZO, Impulsive control systems without commutativity assumptions, J. Optim. Theory Appl., 81 (1994), pp. 435-457.
5. F. H. CLARKE, Optimization and Nonsmooth Analysis, Canadian Mathematical Society, Wiley-Interscience, Toronto, 1983.
6. F. H. CLARKE, YU, S. LEDYAEV, R. J. STERN, AND P. R. WOLENSKI, Nonsmooth Analysis and Control Theory, Springer, New York, 1998.
7. G. DAL MASO AND F. RAMPAZZO, On systems of ordinary differential equations with measures as controls, Differential Integral Equations, 4 (1991), pp. 739-765.
8. G. B. FOLLAND, Real Analysis, Modern Techniques and Their Applications, John Wiley, New York, 1984.
9. R. GOEBEL AND A. R. TEEL, Solutions to hybrid inclusions via set and graphical convergence with stability theory applications, Automatica, 24 (2006), pp. 573-587.
10. O. HAJEK, Review of "Differential Systems Involving Impulses" (by S. G. Pandit and S. G. Deo), Bull. Amer. Math. Soc. (N.S.), 12 (1985), pp. 272-279.
11. E. HEWITT AND K. STROMBERG, Real and Abstract Analysis, Springer, New York, 1965.
12. A. S. MATVEEV AND A. V. SAVKIN, Qualitative Theory of Hybrid Dynamical Systems, Birkhäuser, Boston, 2000.
13. B. S. MORDUKHOVICH, Discrete approximations and refined Euler-Lagrange conditions for nonconvex differential inclusions, SIAM J. Control Optim., 33 (1995), pp. 882-915.
14. M. MOTTA AND F. RAMPAZZO, Dynamic programming for nonlinear systems driven by ordinary and impulsive controls, SIAM J. Control Optim., 34 (1996), pp. 199-225.
15. J. M. MURRAY, Existence theorems for optimal control and calculus of variations problems where the states can jump, SIAM J. Control Optim., 24 (1986), pp. 412-438.
16. F. RAMPAZZO AND C. SARTORI, The minimum time function with unbounded controls, J. Math. Systems Estim. Control, 8 (1998), pp. 1-34.
17. R. W. RISHEL, An extended Pontryagin principle for control systems whose control laws contain measures, J. Soc. Indust. Appl. Math. Ser. A Control, 3 (1965), pp. 191-205.
18. R. T. ROCKAFELLAR, Dual problems of Lagrange for arcs of bounded variation, in Calculus of Variations and Control Theory, D. L. Russell, ed., Academic Press, New York, 1976, pp. 155-192.
19. A. V. SAVKIN AND R. J. EVANS, Hybrid Dynamical Systems, Controller and Sensor Switching Problems, Birkhäuser, Boston, 2002.
20. G. N. SILVA AND R. B. VINTER, Measure driven differential inclusions, J. Math. Anal. Appl., 202 (1996), pp. 767-746.
21. G. N. SILVA AND R. B. VINTER, Necessary conditions for optimal impulsive control problems, SIAM J. Control Optim., 35 (1997), pp. 1829-1846.
22. G. V. SMIRNOV, Introduction to the Theory of Differential Inclusions, AMS, Providence, RI, 2002.
23. R. B. VINTER AND F. M. F. L. PEREIRA, A maximum principle for optimal processes with discontinuous trajectories, SIAM J. Control Optim., 26 (1988), pp. 205-229.
24. J. WARGA, Optimal Control of Differential and Functional Equations, Academic Press, New York, 1972.
25. P. R. WOLENSKI AND S. ŽABIĆ, A differential solution concept for impulsive systems, Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal., 13B (2006), pp. 199-210.