no. 1
Existence of optimal nonanticipating controls in piecewise deterministic control problems
ESAIM: Control, Optimisation and Calculus of Variations, Tome 19 (2013) no. 1, pp. 43-62.

Optimal nonanticipating controls are shown to exist in nonautonomous piecewise deterministic control problems with hard terminal restrictions. The assumptions needed are completely analogous to those needed to obtain optimal controls in deterministic control problems. The proof is based on well-known results on existence of deterministic optimal controls.

DOI : 10.1051/cocv/2011197
Classification : 93E20
Mots clés : piecewise deterministic problems, optimal controls, existence 
@article{COCV_2013__19_1_43_0,
     author = {Seierstad, Atle},
     title = {Existence of optimal nonanticipating controls in piecewise deterministic control problems},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {43--62},
     publisher = {EDP-Sciences},
     volume = {19},
     number = {1},
     year = {2013},
     doi = {10.1051/cocv/2011197},
     mrnumber = {3023059},
     zbl = {1258.93128},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/cocv/2011197/}
}
TY  - JOUR
AU  - Seierstad, Atle
TI  - Existence of optimal nonanticipating controls in piecewise deterministic control problems
JO  - ESAIM: Control, Optimisation and Calculus of Variations
PY  - 2013
SP  - 43
EP  - 62
VL  - 19
IS  - 1
PB  - EDP-Sciences
UR  - http://www.numdam.org/articles/10.1051/cocv/2011197/
DO  - 10.1051/cocv/2011197
LA  - en
ID  - COCV_2013__19_1_43_0
ER  - 
%0 Journal Article
%A Seierstad, Atle
%T Existence of optimal nonanticipating controls in piecewise deterministic control problems
%J ESAIM: Control, Optimisation and Calculus of Variations
%D 2013
%P 43-62
%V 19
%N 1
%I EDP-Sciences
%U http://www.numdam.org/articles/10.1051/cocv/2011197/
%R 10.1051/cocv/2011197
%G en
%F COCV_2013__19_1_43_0
Seierstad, Atle. Existence of optimal nonanticipating controls in piecewise deterministic control problems. ESAIM: Control, Optimisation and Calculus of Variations, Tome 19 (2013) no. 1, pp. 43-62. doi : 10.1051/cocv/2011197. http://www.numdam.org/articles/10.1051/cocv/2011197/

[1] D. Bertsekas and S.E. Shreve, Stochastic optimal control : the discrete-time case. Academic Press, New York (1978). | MR | Zbl

[2] L. Cesari, Optimization - Theory and Applications. Springer-Verlag, New York (1983). | MR | Zbl

[3] M.H.A. Davis, Markov Models and Optimization. Chapman & Hall, London, England (1993). | MR | Zbl

[4] M.H.A. Davis and M. Farid, Piecewise deterministic processes and viscosity solutions, in Stochastic analysis, control, optimization and applications, edited by W.M. Mc.Eneaney et al., A volume in honour of W.H. Fleming, on occation of his 70th birthday, Birkhäuser, Boston (1999) 249-286. | MR | Zbl

[5] M.A.H. Dempster, Optimal control of piecewise-deterministic Markov Processes, in Applied Stochastic Analysis, edited by M.A.H. Davis and R.J. Elliot. Gordon and Breach, New York (1991) 303-325. | MR | Zbl

[6] M.A.H. Dempster and J.J. Ye, A maximum principle for control of piecewise deterministic Markov Processes, in Approximation, optimization and computing : Theory and applications, edited by A.G. Law et al., NorthHolland, Amsterdam (1990) 235-240. | MR | Zbl

[7] M.A.H. Dempster and J.J. Ye, Necessary and sufficient optimality conditions for control of piecewise deterministic Markov processes. Stoch. Stoch. Rep. 40 (1992) 125-145. | MR | Zbl

[8] L. Forwick, M. Schäl and M. Schmitz, Piecewise deterministic Markov control processes with feedback controls and unbounded costs, Acta Appl. Math. 82 (2004) 239-267. | MR | Zbl

[9] O. Hernandez-Lerma et al., Markov processes with expected total cost criterion : optimality, stability, and transient models. Acta Appl. Math. 59 (1999) 229-269. | MR | Zbl

[10] A. Seierstad, Stochastic control in discrete and continuous time. Springer, New York, NY (2009). | MR | Zbl

[11] A. Seierstad, A stochastic maximum principle with hard end constraints. J. Optim. Theory Appl. 144 (2010) 335-365. | MR | Zbl

[12] D. Vermes, Optimal control of piecewise-deterministic Markov processes. Stochastics 14 (1985) 165-208. | MR | Zbl

[13] J.J. Ye, Generalized Bellman-Hamilton-Jacobi equations for piecewise deterministic Markov Processes, , in Systems modelling and optimization, Proceedings of the 16th IFIP-TC conference, Compiegne, France, July 5-9 1993, Lect. Notes Control Inf. Sci. 197, edited by J. Henry et al., London, Springer-Verlag (1994) 51-550. | MR | Zbl

[14] J.J. Ye, Dynamic programming and the maximum principle of piecewise deterministic Markov processses, in Mathematics of stochastic manufacturing systems, AMS-SIAM summer seminar in applied mathematics, June 17-22 1996, Williamsburg, VA, USA, Lect. Appl. Math. 33, edited by G.G. Yin et al., Amer. Math. Soc., Providence, RI (1997) 365-383. | MR | Zbl

Cité par Sources :