In this paper models for two-target optimal controls of a linear diffusion equation are considered. That is, we seek to control the solution of the given PDE in order to guide it to a specified target within a given error at some fixed finite time. At the same time it is desired to keep the variation of the solution from a second target as small as possible. Thus the problem is essentially a mu...

In this paper we develop a priori error analysis for Galerkin finite element discretizations of optimal control problems governed by linear parabolic equations. The space discretization of the state variable is done using usual conforming finite elements, whereas the time discretization is based on discontinuous Galerkin methods. For different types of control discretizations we provide error e...

In this paper, we discuss the a posteriori error estimates of the mixed finite element method for quadratic optimal control problems governed by linear parabolic equations. The state and the co-state are discretized by the high order Raviart-Thomas mixed finite element spaces and the control is approximated by piecewise constant functions. We derive a posteriori error estimates for both the sta...

This paper deals with linear-quadratic optimal control problems constrained by a parametric or stochastic elliptic or parabolic PDE. We address the (difficult) case that the number of parameters may be countable infinite, i.e., σj with j ∈ N, and that the PDE operator may depend non-affinely on the parameters. We consider tracking-type functionals and distributed as well as boundary controls. B...

A boundary Pareto optimal control problem for the parabolic operator with infinite order is considered. The performance index has an integral form. Constraints on controls and on states are imposed. To obtain optimality conditions for the Neumann problem, the generalization of the Dubovitskii-Milyutin Theorem given by Walczak in Refs.[33,34], was applied. AMS Subject Classification : 35K20, 49J...

This paper introduces and analyzes a new parallel-in-time gradient type method for the solution of convex linear-quadratic discrete-time optimal control (DTOC) problems. Each iteration of the classical gradient method requires the solution of the forward-in-time state equation followed by the solution of the backward-in-time adjoint equation to compute the gradient. To introduce parallelism, th...

We discuss the indirect multiple shooting approach for the solution of PDE-based parabolic optimal control problems with control constraints. The method is formulated within an abstract function space setting and uses a space-time Galerkin finite element discretization. The emphasis is on the embedding of indirect multiple shooting into the optimal control framework as well as the detailed desc...

A gradient method for solving an optimal control problem described by a parabolic equation is considered. The gradient projection method is applied to solve the problem. The convergence of the projection algorithm is investigated.

Parametric optimal control problems for semilinear parabolic equations are considered. Using recent Lipschitz stability results for solutions of such problems, it is shown that, under standard coercivity conditions, the solutions are Bouligand differentiable (in L, p < ∞) functions of the parameter. The differentials are characterized as the solutions of accessory linear-quadratic problems. A u...

The studies of the control problems for an evolution system with a bounded derivative ( = the derivative with respect to time) of the control were stimulated by solving practical problems. Our problem is to find an optimal control of a thermal process where the control acts by means of boundary conditions. In more details, an iron body to be heated up is placed into a furnace which temperature ...