Wyniki wyszukiwania - BazTech

Ograniczanie wyników

4 Control and Cybernetics

Znaleziono wyników: 4

Liczba wyników na stronie

Wyniki wyszukiwania

Wyszukiwano:
w słowach kluczowych: pointwise state constraints

Sortuj według:

Ogranicz wyniki do:

Exact penalization of pointwise constraints for optimal control problems

Casas E.

Control and Cybernetics

2009

Vol. 38, no 4A

1131-1150

In this paper we consider a control problem governed by a semilinear elliptic equation with pointwise control and state constraints. We analyze the existence of an exact penalization of the state constraints. In particular, we prove that the first and second order optimality conditions imply the existence of such a penalization. Finally, we prove some extra regularity of the strict local minima of the control problem, assuming the existence of an exact penalization for them.

Optimality conditions for state-constrained PDE control problems with time-dependent controls

Los Reyes J. C. de, Merino P., Rehberg F., Troltzsch F.

Control and Cybernetics

2008

Vol. 37, no 1

5-38

The paper deals with optimal control problems for semilinear elliptic and parabolic PDEs subject to pointwise state constraints. The main issue is that the controls are taken from a restricted control space. In the parabolic case, they are Rm -vector-valued functions of time, while they are vectors of Rm in elliptic problems. Under natural assumptions, first- and second-order sufficient optimality conditions are derived. The main result is the extension of second-order sufficient conditions to semilinear parabolic equations in domains of arbitrary dimension. In the elliptic case, the problems can be handled by known results of semi-infinite optimization. Here, different examples are discussed that exhibit different forms of active sets and where second-order sufficient conditions are satisfied at the optimal solution.

On convergence of regularization methods for nonlinear parabolic optimal control problems with control and state constraints

Neitzel I., Troltzsch F.

Control and Cybernetics

2008

Vol. 37, no 4

1013-1043

Moreau-Yosida and Lavrentiev type regularization methods are considered for nonlinear optimal control problems governed by semilinear parabolic equations with bilateral pointwise control and state constraints. The convergence of optimal controls of the regularized problems is studied for regularization parameters tending to infinity or zero, respectively. In particular, the strong convergence of global and local solutions is addressed. Moreover, strong regularity of the Lavrentiev-regularized optimality system is shown under certain assumptions, which, in particular, allows to show that locally optimal solutions of the Lavrentiev regularized problems are locally unique. This analysis is based on a second-order sufficient optimality condition and a separation assumption on almost active sets.

Stability analysis of relaxed Dirichlet boundary control problems

Arada N., Raymond J.

Control and Cybernetics

1999

Vol. 28, no 1

35-51

We study the relaxation by Young measures of a Dirichlet control problem with pointwise state constraints. We give a necessary and sufficient condition for the properness of the relaxation. This condition is expressed in terms of stability properties, for the original control problem, with respect to geometrical perturbations of state constraints.