Zbigniew Emirsajlow

Infinite-dimensional Sylvester equations

Infinite-dimensional Sylvester equations: Basic theory and application to observer design This paper develops a mathematical framework for the infinite-dimensional Sylvester equation both in the differential and the algebraic form. It uses the implemented semigroup concept as the main mathematical tool. This concept may be found in the literature on evolution equations occurring in mathematics and physics and is rather unknown in systems and control theories. But it is just systems and control theory where Sylvester equations widely appear, and for this reason we intend to give a mathematically rigorous introduction to the subject which is tailored to researchers and postgraduate students working on systems and control. This goal motivates the assumptions under which the results are developed. As an important example of applications we study the problem of designing an asymptotic state observer for a linear infinite-dimensional control system with a bounded input operator and an unbounded output operator.

On certain optimization problems with applications to control problems with constraints

The paper studies certain unconstrained optimization problems dependent of scalar parameters and defined on infinite-dimensional Hilbert spaces. The performed asymptotic analysis with respect to the scalar parameters shows that the unconstrained parametrized optimization problems provide solutions to some optimal control problems for infinite dimensional control systems with constraints. Applicability of the general results is illustrated with two examples.

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.

Remarks on the existence and uniqueness of solutions to the infinite dimensional sylvester equations

In various control problems for infinite-dimensional systems (see, e.g., [1], [2], [3], [4], [7]) one can found usefulness of Sylvester type operator equations. The aim of the paper is to popularize the implemented semigroup framework (e.g. [8], [5], [6]) by showing how it helps to deal with the infinite-dimensional algebraic Sylvester equation both in differential (DSE) and in the algebraic (ASE) form. The main emphasis is put on some basic results concerning the existence and uniqueness of solutions. The collected results are presented from the point of view of potential applications in the systems and control theory.

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.

Welcome from the MMAR 2011 organizing committee

I would like to invite you to Międzyzdroje, Poland for the 16th International Conference on Methods and Models in Automation and Robotics. Almost 100 draft papers have been submitted, from which the International Program Committee, chaired by Professor Tadeusz Kaczorek, has selected 79 papers for presentation. As before also this years Conference is organized under the auspices of the IEEE Robotics & Automation Society, the IEEE Control Systems Society. And as usual it is co-sponsored by the Committee of Automation and Robotics of the Polish Academy of Sciences and Polish Society for Measurement, Automatic Control and Robotics.

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.