Dynamic programming for nonlinear systems driven by ordinary and impulsive controls

SIAM Journal on Control and Optimization

Volumn 34, Issue 1, 1996, Pages 199-225

  Motta, Monica ^a   Rampazzo, Franco ^a  

^a UNIVERSITY OF PADOVA   (Italy)

Author keywords

Dynamic programming; Impulsive control; Minimum problem

Indexed keywords

DIFFERENTIAL EQUATIONS; DYNAMIC PROGRAMMING; FUNCTIONS; MAXIMUM PRINCIPLE; NONLINEAR CONTROL SYSTEMS;

DYNAMIC PROGRAMMING EQUATION; IMPULSIVE CONTROL; MINIMUM PROBLEM; VALUE FUNCTION;

CONTROL THEORY;

EID: 0029733049     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/S036301299325493X     Document Type: Article

References (42)

1. J. P. AUBIN AND A. CELLINA, Differential Inclusion, Springer-Verlag, Berlin, 1984.
2. M. BARDI AND P. SORAVIA, A comparison result for Hamilton-Jacobi equations and applications to some differential games lacking controllability, Funkcial. Ekvac., 37 (1994), pp. 19-43.
3. G. BARLES, Deterministic impulse control problems, SIAM J. Control Optim., 23 (1985), pp. 419-432.
4. _, Uniqueness and regularity results for first-order Hamilton-Jacobi equations, Indiana Math. J., 39 (1990), pp. 443-466.
5. _, An approach of deterministic control problems with unbounded data, Ann. Inst. Henri Poincaré Anal Non Linéaire, 7 (1990), pp. 235-258.
6. E. N. BARRON AND R. JENSEN, Optimal control problems with no turning back, J. Differential Equations, 36 (1980), pp. 223-248.
7. _, The Pontrjagin maximum principle from dynamic programming and viscosity solutions to first order partial differential equations, Trans. Amer. Math. Soc., 298 (1986), pp. 635-641.
8. E. N. BARRON, R. JENSEN, AND J. L. MENALDI, Optimal control and differential games with measures, Nonlinear Anal., 21 (1993), pp. 241-268.
9. A. BRESSAN, On differential systems with impulsive controls, Rend. Sem. Mat. Univ. Padova, 78 (1987), pp. 227-236.
10. A. BRESSAN AND F. RAMPAZZO, On differential systems with vector-valued impulsive controls, Boll. Un. Mat. Ital. B(7), 2 (1988), pp. 641-656.
11. _, Impulsive control systems with commutative vector fields, J. Optim. Theory Appl., (1991), pp. 67-83.
12. _, Impulsive control systems without commutativity assumption, J. Optim. Theory Appl., to appear.
13. A. BRESSAN, Hyperimpulsive motions and controllizable coordinates for Lagrangean systems, Atti Accad. Naz. Lincei, Mem. Cl. Sc. Fis. Mat. Natur., 19 (1991), pp. 195-246.
14. _, On some control problem concerning the ski and the swing, Atti Accad. Naz. Lincei Mem. Cl. Sc. Fis. Mat. Natur., Series IX, 1 (1991), pp. 149-196.
15. A. BRESSAN AND M. MOTTA, Some optimization problems with a monotone impulsive character. Approximation by means of structural discontinuities, Mem. Mat. Acc. Lincei, Series IX, 2 (1994), pp. 31-52.
16. I. CAPUZZO-DOLCETTA AND P. L. LIONS, Hamilton-Jacobi equations and state constrained problems, Trans. Amer. Math. Soc., 318 (1990), pp. 643-668.
17. C. W. CLARK, F. H. CLARKE, AND G. R. MUNRO, The optimal exploitation of renewable resource stocks, Econometrica, 48 (1979), pp. 25-47.
18. M. G. CRANDALL, L. C. EVANS, AND P. L. LIONS, Some properties of viscosity solutions of Hamilton-Jacobi equations, Trans. Amer. Math. Soc. (1984), p. 282.
19. G. DAL MASO AND F. RAMPAZZO, On systems of ordinary differential equations with measures as controls, Differential Integral Equations, 4 (1991), pp. 739-765.
20. J. R. DORROH AND G. FERREYRA, A multi-state, multi-control problem with unbounded controls, SIAM J. Control Optim., 32 (1994), pp. 1322-1331.
21. V. A. DYKHTA, Impulse trajectory extension of degenerated optimal control problems, in The Liapunov Functions Methods and Applications, P. Borne and V. Matrosov, eds., J. C. Baltzer AG, 1990, pp. 103-109.
22. W. H. FLEMING AND H. M. SONER, Controlled Markov Processes and Viscosity Solutions, Springer-Verlag, New York, 1993.
23. O. HÁJEK, Book review, Bull. Amer. Math. Soc., 12 (1985), pp. 272-279.
24. H. ISHII, A boundary value problem of the Dirichlet type for Hamilton-Jacobi equations, Ann. Scuola Norm. Sup. Pisa Cl. Sci., (4) 16 (1989), pp. 105-135.
25. D. F. LAWDEN, Optimal Trajectories for Space Navigation, Butterworth, London, 1963.
26. E. B. LEE AND L. MARKUS, Foundations of Optimal Control Theory, SIAM Series in Applied Mathematics, John Wiley, New York, London, Sydney, 1977.
27. P. L. LIONS, Generalized Solutions of Hamilton-Jacobi Equations, Pitman, London, 1982.
28. W. LIU AND H. J. SUSSMANN, Limit of hight oscillatory controls and the approximation of general paths by admissible trajectories, Proc. C.D.C. IEEE, 1991.
29. J. P. MAREC, Optimal Space Trajectories, Elsevier, Amsterdam Oxford, 1979.
30. B. M. MILLER, Optimization of dynamic systems with a generalized control, translated from Avtomat. i Telemekh., 6 (1989), pp. 23-34.
31. B. M. MILLER, Conditions for the optimality in problems of generalized control. I. Necessary conditions for optimality, translated from Avtomat. i Telemekh., 3 (1992), pp. 50-58.
32. M. MOTTA AND F. RAMPAZZO, Space-time trajectories of nonlinear systems driven by ordinary and impulsive controls, Differential Integral Equations, 8 (1995), pp. 269-288.
33. L. W. NEUSTADT, A general theory of minimum-fuel space trajectories, SIAM J. Control, 3 (1965), pp. 317-356.
34. F. RAMPAZZO, Optimal impulsive controls with a constraint on the total variation, in New Trends in Systems Theory, Progress in Systems and Control Theory, G. Conte, A. M. Perdon, and B. F. Wyman, eds., Springer-Verlag, Boston, MA, 1990, pp. 606-613.
35. _, On the Riemannian structure of a Lagrangian system and the problem of adding time-dependent constraints as controls, European J. Mech. A Solids, 10 (1991), pp. 405-431.
36. R. W. RISHEL, An extended Pontryagin principle for control systems whose control laws contain measures, SIAM J. Control, 3 (1965), pp. 191-205.
37. A. V. SARYCHEV, Nonlinear systems with impulsive and generalized function controls, Proc. Conf. on Nonlinear Synthesis, Sopron, Hungary, 1989.
38. W. W. SCHMAEDEKE, Optimal control theory for nonlinear differential equations containing measures, SIAM J. Control, 3 (1965), pp. 231-279.
39. S. P. SETHI, Dynamic optimal control problems in advertising: a survey, SIAM Rev., 19 (1977), pp. 685-725.
40. H. M. SONER, Optimal control with state-space constraints, SIAM J. Control Optim., 24 (1986), pp. 552-561, 1110-1122.
41. H. J. SUSSMANN, On the gap between deterministic and stochastic ordinary differential equations, Ann. Probab., 6 (1978), pp. 17-41.
42. R. B. VINTER AND M. F. L. PEREIRA, A maximum principle for optimal processes with discontinuous trajectories, SIAM J. Control Optim., 26 (1988), pp. 205-229.