On the Hamilton-Jacobi-Bellmann equations in Banach spaces. (English) Zbl 0622.49010

Soner, H. Mete

J. Optimization Theory Appl. 57, No. 3, 429-437 (1988).

This paper is concerned with a certain class of distributed parameter control problems. The value function of these problems is shown to be the unique viscosity solution of the corresponding Hamilton-Jacobi-Bellman equation. The main assumption is the existence of an increasing sequence of compact invariant subsets of the state space. In particular, this assumption is satisfied by a class of controlled delay equations.

MSC:

49L20	Dynamic programming in optimal control and differential games
49L99	Hamilton-Jacobi theories
35D05	Existence of generalized solutions of PDE (MSC2000)
93C20	Control/observation systems governed by partial differential equations
35R10	Partial functional-differential equations

Keywords:

distributed parameter control; value function; viscosity solution; Hamilton-Jacobi-Bellman equation; controlled delay equations

References:

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