On a discrete approximation of the Hamilton-Jacobi equation of dynamic programming. (English) Zbl 0582.49019

Author’s abstract: An approximation of the Hamilton-Jacobi-Bellman equation connected with the infinite horizon optimal control problem with discount is proposed. The approximate solutions are shown to converge uniformly to the viscosity solution, in the sense of Crandall-Lions, of the original problem. Moreover, the approximate solutions are interpreted as value functions of some discrete-time control problem. This allows to construct by dynamic programming a minimizing sequence of piecewise constant controls.
Reviewer: M.Armsen


49L99 Hamilton-Jacobi theories
49L20 Dynamic programming in optimal control and differential games
49M99 Numerical methods in optimal control
90C39 Dynamic programming
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