Constrained Optimal Control Problems in Banach Spaces

Stochastic Optimal Control Problems and Parabolic Equations in Banach Spaces

We consider stochastic optimal control problems in Banach spaces, related to nonlinear controlled equations with dissipative non linearity. These problems are treated via the backward stochastic differential equations approach, that allows also to solve in mild sense Hamilton Jacobi Bellman equations in Banach spaces. We apply the results to controlled stochastic heat and wave equations with co...

Optimal Feedback Control of Fractional Semilinear Integro-differential Equations in The Banach Spaces

Recently, there has been significant development in the existence of mild solutions for fractional semilinear integro-differential equations but optimal control is not provided. The aim of this paper is studying optimal feedback control for fractional semilinear integro-differential equations in an arbitrary Banach space associated with operators ...

On an Augmented Lagrangian SQP Method for a Class of Optimal Control Problems in Banach Spaces

Ergodic BSDEs and Optimal Ergodic Control in Banach Spaces

In this paper we introduce a new kind of Backward Stochastic Differential Equations, called ergodic BSDEs, which arise naturally in the study of optimal ergodic control. We study the existence, uniqueness and regularity of solution to ergodic BSDEs. Then we apply these results to the optimal ergodic control of a Banach valued stochastic state equation. We also establish the link between the erg...

A virtual control concept for state constrained optimal control problems

where Ω ⊂ RN , N = 2, 3 is a bounded domain with C0,1-boundary, ν > 0 is a fixed number, yd and yc are given functions from L2(Ω). Furthermore, ua and ub are given real numbers with ua < ub. The difficulty of low regularity of solutions of problems with pointwise state constraints is pointed out in (1). Therefore, different regularization concepts are developed, see e.g. (2), (3), (4) and (5). ...