Approximation of control problems involving ordinary and impulsive controls

Fabio Camilli; Maurizio Falcone

ESAIM: Control, Optimisation and Calculus of Variations (1999)

  • Volume: 4, page 159-176
  • ISSN: 1292-8119

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Camilli, Fabio, and Falcone, Maurizio. "Approximation of control problems involving ordinary and impulsive controls." ESAIM: Control, Optimisation and Calculus of Variations 4 (1999): 159-176. <http://eudml.org/doc/90539>.

@article{Camilli1999,
author = {Camilli, Fabio, Falcone, Maurizio},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {approximation scheme; dynamic programming; viscosity solution; impulsive controls},
language = {eng},
pages = {159-176},
publisher = {EDP Sciences},
title = {Approximation of control problems involving ordinary and impulsive controls},
url = {http://eudml.org/doc/90539},
volume = {4},
year = {1999},
}

TY - JOUR
AU - Camilli, Fabio
AU - Falcone, Maurizio
TI - Approximation of control problems involving ordinary and impulsive controls
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 1999
PB - EDP Sciences
VL - 4
SP - 159
EP - 176
LA - eng
KW - approximation scheme; dynamic programming; viscosity solution; impulsive controls
UR - http://eudml.org/doc/90539
ER -

References

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  1. [1] M. Bardi and I. Capuzzo Dolcetta, Viscosity solutions of Bellman equation and optimal deterministic control theory. Birkhäuser, Boston ( 1997). Zbl0890.49011MR1484411
  2. [2] M. Bardi and M. Falcone, An approximation scheme for the minimum time function. SIAM J. Control Optim. 28 ( 1990) 950-965. Zbl0723.49024MR1051632
  3. [3] G. Barles, Deterministic Impulse control problems. SIAM J. Control Optim. 23 ( 1985) 419-432. Zbl0571.49020MR784578
  4. [4] G. Barles and P. Souganidis, Convergence of approximation scheme for fully nonlinear second order equations. Asymptotic Anal. 4 ( 1991) 271-283. Zbl0729.65077MR1115933
  5. [5] E. Barron, R. Jensen and J.L. Menaldi, Optimal control and differential games with measures. Nonlinear Anal. TMA 21 ( 1993) 241-268. Zbl0799.90139MR1237586
  6. [6] A. Bensoussan and J.L. Lions, Impulse control and quasi-variational inequalities. Gauthier-Villars, Paris ( 1984). MR756234
  7. [7] Aldo Bressan, Hyperimpulsive motions and controllizable coordinates for Lagrangean systems. Atti Accad. Naz. Lincei, Mem Cl. Sc. Fis. Mat. Natur. 19 ( 1991). MR1163634
  8. [8] A. Bressan and F. Rampazzo, Impulsive control systems with commutative vector fields. J. Optim. Th. et Appl. 71 ( 1991) 67-83. Zbl0793.49014MR1131450
  9. [9] F. Camilli and M. Falcone, Approximation of optimal control problems with state constraints: estimates and applications, in Nonsmooth analysis and geometric methods in deterministic optimal control (Minneapolis, MN, 1993) Springer, New York ( 1996) 23-57. Zbl0860.65055MR1411705
  10. [10] I. Capuzzo Dolcetta and M. Falcone, Discrete dynamic programming and viscosity solutions of the Bellman equation. Ann. Inst. H.Poincaré Anal. Nonlin. 6 ( 1989) 161-184. Zbl0674.49028MR1019113
  11. [11] I. Capuzzo Dolcetta and H. Ishii, Approximate solutions of Bellman equation of deterministic control theory. Appl. Math. Optim. 11 ( 1984) 161-181. Zbl0553.49024MR743925
  12. [12] M.G. Crandall, L.C. Evans and P.L. Lions, Some properties of viscosity solutions of Hamilton-Jacobi equation. Trans. Amer. Math. Soc. 282 ( 1984) 487-502. Zbl0543.35011MR732102
  13. [13] C. W. Clark, F.H. Clarke and G.R. Munro, The optimal exploitation of renewable resource stocks. Econometrica 48 ( 1979) 25-47. Zbl0396.90026
  14. [14] J.R. Dorroh and G. Ferreyra, Optimal advertising in exponentially decaying markets. J. Optim. Th. et Appl. 79 ( 1993) 219-236. Zbl0797.90055MR1252135
  15. [15] J.R. Dorroh and G. Ferreyra, A multistate multicontrol problem with unbounded controls. SIAM J. Control Optim. 32 ( 1994) 1322-1331. Zbl0823.90073MR1288253
  16. [16] M. Falcone, A numerical approach to the infinite horizon problem. Appl. Math. et Optim. 15 ( 1987) 1-13 and 23 ( 1991) 213-214. Zbl0715.49023MR866164
  17. [17] M. Falcone, Numerical solution of Dynamic Programming equations, Appendix to M. Bardi and I. Capuzzo Dolcetta, Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations. Birkhäuser, Boston ( 1997). 
  18. [18] W. Fleming and H.M. Soner, Controlled Markov processes and viscosity solutions. Springer-Verlag ( 1992). Zbl0773.60070MR2179357
  19. [19] H. Kushner and P. Dupuis, Numerical methods for stochastic control problems in continuous time. Springer-Verlag ( 1992). Zbl0754.65068MR1217486
  20. [20] J.P. Marec, Optimal space trajectories. Elsevier ( 1979). Zbl0435.70029
  21. [21] B.M. Miller, Generalized solutions of nonlinear optimization problems with impulse control I, II. Automat. Remote Control 55 ( 1995). 
  22. [22] B.M. Miller, Dynamic programming for nonlinear systems driven by ordinary and impulsive controls. SIAM J. Control Optim. 34 ( 1996) 199-225. Zbl0843.49021MR1372911
  23. [23] M. Motta and F. Rampazzo, Space-time trajectories of nonlinear system driven by ordinary and impulsive controls. Differential and Integral Equations 8 ( 1995) 269-288. Zbl0925.93383MR1296124
  24. [24] F. Rampazzo, On the Riemannian Structure of a Lagrangian system and the problem of adding time-dependent constraints as controls. Eur. J. Mech. A/Solids 10 ( 1991) 405-431. Zbl0769.70020MR1129328
  25. [25] E. Rouy, Numerical approximation of viscosity solutions of first-order Hamilton-Jacobi equations with Neumann type boundary conditions. Math. Meth. Appl. Sci. 2 ( 1992) 357-374. Zbl0764.65052MR1181342
  26. [26] P. Souganidis, Approximation schemes for viscosity solutions of Hamilton-Jacobi equations. J. Diff. Eq. 57 1-43. Zbl0536.70020MR803085

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