Optimal insider control of stochastic partial differential equations

Optimal Control of Partial Differential Equations

1 Motivating Examples 4 1.1 Stationary Optimal Heating Problems . . . . . . . . . . . . . . . . . . . 4 1.1.1 General Setting . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.1.2 Boundary Control . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.1.3 Distributed Control . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.2 Transient Optimal Heating Problems . . . . . . . . . . ....

Stochastic Partial Differential Equations

Optimal control of partial differential equations with affine control constraints

Numerical solution of PDE optimal control problems involving affine pointwise control constraints is investigated. Optimality conditions are derived and a semi-smooth Newton method is presented. Global and local superlinear convergence of the method are obtained for linear problems. Differently from box constraints, in the case of general affine constraints a proper weighting of the control cos...

Optimal Control of a Class of Parabolic Partial Differential Equations

In this paper we, apply the classical control theory to a parabolic partial differential equation in a bounded domain with diffusivity-interior-boundary actuation. We first we study the existence of the solution of the parabolic partial differential equation, then we study the solution bound estimate which are used to prove the existence of the solution of the optimal control problem in a Banac...

Backward Stochastic Partial Differential Equations with Jumps and Application to Optimal Control of Random Jump Fields

We prove an existence and uniqueness result for a general class of backward stochastic partial differential equations with jumps. This is a type of equations which appear as adjoint equations in the maximum principle approach to optimal control of systems described by stochastic partial differential equations driven by Lévy processes.