Anna Krakowiak

Time-Optimal Boundary Control of an Infinite Order Parabolic System with Time Lags

Time-Optimal Boundary Control of an Infinite Order Parabolic System with Time Lags In this paper the time-optimal boundary control problem is presented for a distributed infinite order parabolic system in which time lags appear in the integral form both in the state equation and in the boundary condition. Some specific properties of the optimal control are discussed.

Time optimal control of retarded parabolic systems

In this paper, the time-optimal control problem for parabolic systems in which time lags appear in the integral form both in the state equation and in the Neumann boundary condition is presented. The particular properties of the optimal control are discussed.

Sensitivity analysis of infinite order hyperbolic optimal control problems

In the paper the first order sensitivity analysis is performed for a class of optimal control problems for infinite order hyperbolic equations. A singular perturbation of geometrical domain of integration is introduced in the form of a circular hole. The Steklov-Poincare´ operator on a circle is defined in order to reduce the problem to regular perturbations in the truncated domain. The optimality system is differentiated with respect to the small parameter and the directional derivative of the optimal control is obtained as a solution to an auxiliary optimal control problem.

Sensitivity Analysis of Optimal Control Parabolic Systems with Retardations

The first order sensitivity analysis is performed for a class of optimal control problems for time lag parabolic equations in which retarded arguments appear in the integral form with h ∈ (0, b) in the state equations and with k ∈ (0, c) in the Neumann boundary conditions. The optimality system is analyzed with the respect to a small parameter. The directional derivative of the optimal control is obtained as a solution to an auxiliary optimization problem. The control constraints for the auxilary optimization problem are received.

Sensitivity of optimal controls for time delay parabolic systems

The first order sensitivity analysis is performed for a class of optimal control problems for time delay parabolic equations in which retarded arguments appear in the integral form with h ϵ (0,6). The optimality system is analyzed with the respect to a small parameter. The directional derivative of the optimal control is obtained as a solution to an auxiliary optimization problem. The control constraints for the auxilary optimization problem are received.

Sensitivity analysis of time delay parabolic-hyperbolic optimal control problems

In the paper the first order sensitivity analysis is performed for a class of optimal control problems for time delay parabolic-hyperbolic equations. A singular perturbation of geometrical domain of integration is introduced in the form of a circular hole. The Steklov-Poincaré operator on a circle is defined in order to reduce the problem to regular perturbations in the truncated domain. The optimality system is differentiated with respect to the small parameter and the directional derivative of the optimal control is obtained as a solution to an auxiliary optimal control problem.

Sensitivity analysis of parabolic-hyperbolic optimal control problems

In the paper the first order sensitivity analysis is performed for a class of optimal control problems for parabolic-hyperbolic equations. A singular perturbation of geometrical domain of integration is introduced in the form of a circular hole. The Steklov-Poincaré operator on a circle is defined in order to reduce the problem to regular perturbations in the truncated domain. The optimality system is differentiated with respect to the small parameter and the directional derivative of the optimal control is obtained as a solution to an auxiliary optimal control problem.

Sensitivity Analysis of Time Delay Hyperbolic Optimal Control Problems

Abstract In the paper the first order sensitivity analysis is performed for a class of optimal control problems for time delay hyperbolic equations. A singular perturbation of geometrical domain of integration is introduced in the form of a circular hole. The Steklov-Poincare operator on a circle is defined in order to reduce the problem to regular perturbations in the truncated domain. The optimality system is differentiated with respect to the small parameter and the directional derivative of the optimal control is obtained as a solution to an auxiliary optimal control problem.

Sensivity analysis of infinite order parabolic optimal control problems

Abstract In the paper the first order sensitivity analysis is performed for a class of optimal control problems for infinite order parabolic equations. A singular perturbation of geometrical domain of integration is introduced in the form of a circular hole. The Steklov-Poincare operator on a circle is defined in order to reduce the problem to regular perturbations in the truncated domain. The optimality system is differentiated with respect to the small parameter and the directional derivative of the optimal control is obtained as a solution to an auxiliary optimal control problem.