On the Hamilton-Jacobi-Bellman equations in Banach spaces
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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 Hamiltonian-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.
Key WordsDistributed control problems viscosity solutions controlled delay equations
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- 3.Barbu, V., andDaPrato, G.,Hamilton-Jacobi Equations in Hilbert Spaces, Pitman, London, England, 1983.Google Scholar
- 6.Pazy, A.,Semigroup of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, New York, New York, 1983.Google Scholar
- 7.Hale, J. K.,Theory of Functional Differential Equations, Springer-Verlag, New York, New York, 1977.Google Scholar
- 9.Ahmed, N. U., andTeo, K. L.,Optimal Control of Distributed Parameter Systems, North-Holland, New York, New York, 1981.Google Scholar