Optimal control of finite horizon type for a multidimensional delayed switching system

Discrete and Continuous Dynamical Systems - Series B

Volumn 5, Issue 2, 2005, Pages 239-264

  Bagagiolo, Fabio ^a  

^a UNIVERSITY OF TRENTO   (Italy)

Author keywords

Delayed switchings; Discontinuous viscosity solutions; Exit time; Optimal control

Indexed keywords

EID: 18144400023     PISSN: 15313492     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcdsb.2005.5.239     Document Type: Article

References (19)

1. H. W. Alt, On the thermostat problem, Control Cybernet., 14 (1985), 171-193.
2. P. Bagagiolo, An infinite horizon optimal control problem for some switching systems, Discrete Contin. Dyn. Syst. Ser. B, l (2001), no. 4, 443-462.
3. P. Bagagiolo, Viscosity solutions for an optimal control problem with Preisach hysteresis nonlinearities, ESAIM Control Optim. Calc. Vȧr., 10 (2004), 271-294.
4. P. Bagagiolo, M. Bardi, Singular perturbation of a finite horizon problem with state-space constraints, SIAM J. Control Optim., 38 (1998), 2040-2060.
5. M. Bardi, I. Capuzzo Dolcetta, "Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations", Birkhäuser, Boston, 1997.
6. G. Barles, "Solutions de Viscosté des Équations de Hamilton-Jacobi", volume 17 of Mathematiques et Applications, Springer, Paris, 1994.
7. G. Barles, B. Perthame, Discontinuous solutions of deterministic optimal stopping time problems, KAIRO Modél. Math. Anal. Numér., 21 (1987), 557-579.
8. G. Barles, B. Perthame, Exit time problems in optimal control and vanishing viscosity method, SIAM J. Control Optim., 26 (1988), 1133-1148.
9. E. N. Barron, R. Jensen, Semicontinuous viscosity solutions of Hamilton-Jacobi equations with convex Hamiltonians, Comm. Partial Differential Equations, 15 (1990), 1713-1742.
10. A.-P. Blanc, Deterministic exit time control problem with discontinuous exit costs, SIAM J. Control Optim., 35 (1997), 399-434.
11. A.-P. Blanc, Comparison principle for the Cauchy problem for Hamilton-Jacobi equations with discontinuous data, Nonlinear Anal., 45 (2001), 1015-1037.
12. H. Ishii, A boundary value problem of the Dirichlet type for Hamilton-Jacobi equations, Ann. Scuola Norm. Pisa Cl. Sci., 18 (1989), 105-135.
13. M. A. Krasnoselskii, A. V. Pokrovskii, "Systems with Hysteresis", Springer, Berlin, 1989.
14. S. M. Lenhart, T. I. Seidman, J. Yong, Optimal control of a bioreactor with modal switching, Math. Models Methods Appl. Sci., 11 (2001), 933-949.
15. T. I. Seidman: Switching systems I, Control Cybernet., 19 (1990), 63-92.
16. H. M. Soner, Optimal control problems with state space constraint I, SIAM J. Control Optim., 24 (1986), 552-561.
17. P. Soravia, Discontinuous viscosity solutions to Dirichlet problems for Hamilton-Jacobi equations with convex Hamiltonians, Comm. Partial Differential Equations, 18 (1993), 1493-1514.
18. A. Visintin, "Differential Models of Hysteresis", Springer, Heidelberg, 1994.
19. J. Warga, "Optimal Control of Differential and Functional Equations", Academic Press, New York, 1972.