Geodesic
Classical characteristics of the Bellman equation in constructions of grid optimal synthesis
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and topology. II, Tome 271 (2010), pp. 259-277

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We consider optimal control problems with fixed final time and terminal–integral cost functional, and address the question of constructing a grid optimal synthesis (a universal feedback) on the basis of classical characteristics of the Bellman equation. To construct an optimal synthesis, we propose a numerical algorithm that relies on the necessary optimality conditions (the Pontryagin maximum principle) and sufficient conditions in the Hamiltonian form. We obtain estimates for the efficiency of the numerical method. The method is illustrated by an example of the numerical solution of a nonlinear optimal control problem. 
@article{TM_2010_271_a17,
     author = {N. N. Subbotina and T. B. Tokmantsev},
     title = {Classical characteristics of the {Bellman} equation in constructions of grid optimal synthesis},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {259--277},
     publisher = {mathdoc},
     volume = {271},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2010_271_a17/}
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N. N. Subbotina; T. B. Tokmantsev. Classical characteristics of the Bellman equation in constructions of grid optimal synthesis. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and topology. II, Tome 271 (2010), pp. 259-277. http://geodesic.mathdoc.fr/item/TM_2010_271_a17/