In this paper a reduced-order strategy is applied to solve a multiobjective optimal control problem governed by semilinear parabolic partial differential equations. These problems often arise in practical applications, where the quality of the system behavior has to be measured by more than one criterium. The weighted sum method is exploited for defining scalar-valued nonlinear optimal control ...

This paper derives linear quadratic regulator (LQR) results for boundary controlled parabolic partial differential equations (PDEs) via weak-variations. Research on optimal control of PDEs has a rich 40-year history. This body of knowledge relies heavily on operator and semigroup theory. Our research distinguishes itself by deriving existing LQR results from a more accessible set of mathematics...

We present an extension from two dimensions to three dimensions of a boundary control law, which stabilizes the parabolic profile of an infinite channel flow. The controller acts on the normal component of the velocity only. The stability is achieved without any a priori condition on the viscosity coefficient, that is on Reynolds number.

Hierarchical (H)-matrices approximate full or sparse matrices using a hierarchical data sparse format. The corresponding H-matrix arithmetic reduces the time complexity of the approximate H-matrix operators to almost optimal while maintains certain accuracy. In this paper, we represent a scheme to solve the saddle point system arising from the control of parabolic partial differential equations...

Optimal control problems in measure spaces governed by parabolic equations are considered, which are known to promote sparse solutions. Optimality conditions are derived and some of the structural properties of their solutions, in particular sparsity, are discussed. A framework for their approximation is proposed which is efficient for numerical computations and for which convergence is proved ...

The paper is concerned with fully nonlinear second order Hamilton{Jacobi{Bellman{ Isaacs equations of elliptic type in separable Hilbert spaces which have unbounded rst and second order terms. The viscosity solution approach is adapted to the equations under consideration and the existence and uniqueness of viscosity solutions is proved. A stochastic optimal control problem driven by a paraboli...

A class of parametric optimal control problems for semilinear parabolic equations is considered. Using recent regularity results for solutions of such equations, suucient conditions are derived under which the solutions to optimal control problems are locally Lipschitz continuous functions of the parameter in the L 1-norm. It is shown that these conditions are also necessary, provided that the ...

There has been an awful lot of people who helped me in the creation of this thesis, be it through their own work, like Prof. G. Dziuk, their advocacy, like Prof. J. Struck-meier, or their encouragement. For the latter my foremost thanks go to my companion Christine and to my mother Brigitte who have always been there for me. Finally, I want to thank Prof. H. Garcke who greatly helped to improve...

In this paper, a priori error estimates for space-time finite element discretizations of optimal control problems governed by semilinear parabolic PDEs and subject to pointwise control constraints are derived. We extend the approach from [23, 24], where linear-quadratic problems have been considered, discretizing the state equation by usual conforming finite elements in space and a discontinuou...

In this paper we consider a parabolic optimal control problem with a pointwise (Dirac type) control in space, but variable in time, in two space dimensions. To approximate the problem we use the standard continuous piecewise linear approximation in space and the piecewise constant discontinuous Galerkin method in time. Despite low regularity of the state equation, we show almost optimal h2 + k ...