Regularity properties of solutions to Hamilton-Jacobi equations in infinite dimensions and nonlinear optimal control

Abstract

This paper is concerned with the semi-concavity properties of the value function V(t, x) of an Optimal Control Problem (in Bolza form) for a Distributed Parameter System governed by the semilinear State Equation Formula presented Here, both the State Space X and the Control Space U are Banach spaces, A is the infinitesimal generator of an analytic semigroup on X and F is a nonlinear perturbation, possibly defined on a dense subspace of X. By using regularity results for solutions to (SE), we obtain one-sided bounds on V of the form Formula presented for all λ ε [0, 1]. The above estimate is also applied to analyze the structure of the generalized gradient ∂xV(t, X) and to derive the Feedback Formula. © 1989, Khayyam Publishing. All rights reserved.