Averaging method for discontinuous Mayer's problem of singularly perturbed control systems

Nonlinear Analysis, Theory, Methods and Applications

Volumn 54, Issue 5, 2003, Pages 819-837

  Quincampoix, M ^a   Watbled, F ^b,c  

^a UNIVERSITÉ DE BRETAGNE OCCIDENTALE   (France)

^b UNIVERSITÉ DE BRETAGNE SUD   (France)

^c UNIVERSITÉ DE RENNES 1   (France)

Author keywords

Differential inclusions; Hamilton Jacobi Bellman equations; Optimal control; Singular perturbations

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; OPTIMIZATION; PERTURBATION TECHNIQUES; PROBLEM SOLVING;

AVERAGING METHOD;

CONTROL SYSTEMS;

EID: 0038007970     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(03)00094-4     Document Type: Article

References (18)

1. Alvarez O., Bardi M. Viscosity solutions methods for singular perturbations in deterministic and stochastic control. SIAM J. Control Optim. 40(4):2001;1159-1188.
2. Artstein Z., Gaitsgory V. The value function of singularly perturbed control systems. Appl. Math. Optim. 41:2000;425-445.
3. Barron E.N., Jensen R. Semicontinuous viscosity solutions for Hamilton-Jacobi equations with convex Hamiltonian. Comm. Partial Differential Equations. 15:1990;1713-1742.
4. Binding P. Singularly perturbed optimal control problems. SIAM J. Control Optim. 14(4):1976;591-612.
5. Donchev T., Slavov I. Averaging method for one sided Lipschitz differential inclusions with generalized solutions. SIAM J. Control Optim. 37(5):1999;1600-1613.
6. Frankowska H. Lower semicontinuous solutions of Hamilton-Jacobi-Bellman equations. SIAM J. Control Optim. 31(1):1993;257-272.
7. Gaitsgory V. Suboptimization of singularly perturbed control systems. SIAM J. Control Optim. 30(5):1992;1228-1249.
8. Grammel G. Singularly perturbed differential inclusions, an averaging approach. Set-valued Anal. 4:1996;361-374.
9. Grammel G. Averaging of singularly perturbed systems. Nonlinear Anal. Theory. 28(11):1997;1851-1865.
10. Plaskacz S., Quincampoix M. Discontinuous Mayer control problem under state-constraints. Topol. Methods Nonlinear Anal. 15:2000;91-100.
11. Plaskacz S., Quincampoix M. Value-functions for differential games and control systems with discontinuous terminal cost. SIAM J. Control Optim. 39(5):2001;1485-1498.
12. A. Plotnikov V. Averaging method for differential inclusions and its application to optimal control problems. Differential Equations. 15:1979;1013-1018.
13. Quincampoix M. Singular perturbations for differential equations and inclusions. an approach through constrained systems Nonlinear Anal. 32(5):1998;697-710.
14. Quincampoix M., Zhang H. Singular perturbations in nonlinear optimal control systems. Differential Integral Equations. 8(4):1995;931-944.
15. Sanders J.A., Verhulst F. Averaging Methods in Nonlinear Dynamical Systems. 1985;Springer, Berlin.
16. Tichonov A.N. Systems of differential equations containing small parameter near derivatives. Mat. Sb. 31:1952;575-586.
17. Veliov V. A generalization of the Tikhonov theorem for singularly perturbed differential inclusions. J. Dyn. Control Systems. 3(3):1997;291-319.
18. Volosov V. Averaging in systems of ordinary differential equations. Russian Math. Survey. 17:1962;1-26.