The aim of this paper is to point out some new results on regional boundary gradient controllability for parabolic systems. First, we give a definition and some properties of this concept, then we concentrate on the determination of the control achieving regional boundary gradient target with minimum energy and we develop an approach that leads to numerical algorithm for the computation of the ...

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 ...

In this paper we provide a second order analysis for strong solutions in the optimal control of parabolic equations. We consider the case of box constraints on the control and final integral constraints on the state. In contrast to sufficient conditions assuring quadratic growth in the weak sense, i.e. when the cost increases at least quadratically for admissible controls uniformly near to the ...

We study an abstract nonlinear evolution equation governed by time-dependent operator of subdi erential type in a real Hilbert space. In this paper we discuss the convergence of solutions to our evolution equations. Also, we investigate the optimal control problems of nonlinear evolution equations. Moreover, we apply our abstract results to a quasilinear parabolic PDE with a mixed boundary cond...

Abstract We discuss two optimal control problems of parabolic equations, with mixed state and control constraints, for which the standard qualification condition does not hold. Our first example is a bottleneck problem, and the second one is an optimal investment problem where a utility type function is to be minimized. By an adapted penalization technique, we derive optimality conditions from ...

We study optimal control problems in which controls with certain sparsity patterns are preferred. For time-dependent problems the approach can be used to find locations for control devices that allow controlling the system in an optimal way over the entire time interval. The approach uses a nondifferentiable cost functional to implement the sparsity requirements; additionally, bound constraints...

We present a smooth, i.e. differentiable regularization of the projection formula that occurs in constrained parabolic optimal control problems. We summarize the optimality conditions in function spaces for unconstrained and control-constrained problems subject to a class of parabolic partial differential equations. The optimality conditions are then given by coupled systems of parabolic PDEs. ...

In this paper the authors consider a parameter estimation problem for a nonlinear systems, which consists of one parabolic equation for the concentration and two elliptic equations for the potentials. The measurements are given as boundary values for one of the potentials. For its numerical solution the Gauss Newton method is applied. To speed up the solution process, a reduced-order approach b...

In this paper we study the variational discretization and mixed finite element methods for optimal control problem governed by semilinear parabolic equations. The space discretization of the state variable is done using usual mixed finite elements. The state and the co-state are approximated by the lowest order RaviartThomas mixed finite element spaces and the control is not discreted. Then we ...

A distributed Pareto optimal control problem for an infinite order parabolic system is considered. The performance index has a vector form with two components in 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 was applied. © 2014 The Authors. Production and hosting b...