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Construction of optimal feedback controls. (English) Zbl 0736.49020

The authors give an algorithm for constructing an optimal process (i.e., an optimal control and the corresponding optimal state) from a given solution to the Hamilton-Jacobi-Bellman equation associated with an optimal control problem, as a limit of processes with piecewise constant controls. The hypotheses involved are expressed directly in terms of the data. A related algorithm was proposed by L. D. Berkovitz [SIAM J. Control Optimization 27, No. 5, 991-1006 (1989; Zbl 0684.49008)], but the hypotheses are of a somewhat implicit nature.
Reviewer: O.Cârjá (Iaşi)

MSC:

49L20 Dynamic programming in optimal control and differential games
93B52 Feedback control
93B40 Computational methods in systems theory (MSC2010)
49L25 Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games
93B50 Synthesis problems
93C10 Nonlinear systems in control theory

Citations:

Zbl 0684.49008
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References:

[1] Aubin, J. P.; Cellina, A., Differential Inclusions (1984), Springer-Verlag: Springer-Verlag New York
[2] Berkovitz, L. D., Optimal feedback controls, SIAM J. Control Optim., 27, 991-1007 (1989) · Zbl 0684.49008
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