Time–Domain Decomposition Preconditioners for the Solution of Discretized Parabolic Optimal Control Problems

We consider a controlled state equation of parabolic type on the halfline (0,+∞) with boundary conditions of Dirichlet type in which the unknown is equal to the sum of the control and of a white noise in time. We study finite horizon and infinite horizon optimal control problem related by menas of backward stochastic differential equations.

This paper develops a theory of singular arc, and the corresponding second order necessary and sufficient conditions, for the optimal control of a semilinear parabolic equation with scalar control applied on the r.h.s. We obtain in particular an extension of Kelley’s condition, and the characterization of a quadratic growth property for a weak norm.

We present a concise proof for existence and uniqueness of solutions of linear parabolic PDEs. It is based on an analysis of the corresponding differential operator and its adjoint in appropriate spaces and simple enough to be presented in the context of an introductory lecture on optimal control of PDEs. Our approach also clarifies some aspects in the structure of first order optimality condit...

The paper presents part of the created systematic methodology of solving optimal control problems formulated for systems with subsystems (possibly analog) that are changing scale, dimension or symmetry. In the paper we are interested in controlled processes that can be described by hyperbolic equations. The system described by such equation can locally change its qualitative properties. In the ...

We are here concerned with an optimal control problem for a state equation of parabolic type on a bounded real interval, which for convenience we take equal to [0, π]. We stress the fact that we consider Neumann boundary conditions in which the derivative of the unknown is equal to the sum of the control and of a white noise in time, namely:  ∂y ∂s (s, ξ) = ∂2y ∂ξ2 (s, ξ) + f(s, y(s, ξ)...

in this paper, the optimal boundary control problem for distributed parabolic systems, involving second orderoperator with an infinite number of variables, in which constant lags appear in the integral form both in the state equations and in the boundary condition is considered. some specific properties of the optimal control arediscussed.

We give an overview of the shooting technique for solving deterministic optimal control problems. This approach allows to reduce locally these problems to a finite dimensional equation. We first recall the basic idea, in the case of unconstrained or control constrained problems, and show the link with second-order optimality conditions and the analysis or discretization errors. Then we focus on...