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Pointwise observation of the state given by complex time lag parabolic system

Kowalewski A.

Archives of Control Sciences

2017

Vol. 27, no. 1

77--89

Various optimization problems for linear parabolic systems with multiple constant time lags are considered. In this paper, we consider an optimal distributed control problem for a linear complex parabolic system in which different multiple constant time lags appear both in the state equation and in the Neumann boundary condition. Sufficient conditions for the existence of a unique solution of the parabolic time lag equation with the Neumann boundary condition are proved. The time horizon T is fixed. Making use of the Lions scheme [13], necessary and sufficient conditions of optimality for the Neumann problem with the quadratic performance functional with pointwise observation of the state and constrained control are derived. The example of application is also provided

Optimal distributed control problems of retarded parabolic systems

Kowalewski A., Krakowiak A.

Archives of Control Sciences

2009

Vol. 19, no. 3

279-293

Optimal distributed control problems of retarded parabolic systems are presented. Necessary and sufficient conditions of optimality are derived for the Neumann problem. A simple example of application is also presented.

Time-optimal boundary control of an infinite order parabolic system with time lags

Kowalewski A., Krakowiak A.

International Journal of Applied Mathematics and Computer Science

2008

Vol. 18, no 2

189-198

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.

Mathematical models of the air separation through polymer membranes at magnetic field

Strzelewicz A., Grzywna Z. J.

Ars Separatoria Acta

2007

No. 5

34-44

This paper is addressed to the membrane air separation i.e. the gas mixture of quite similar gases in many respects, except one: oxygen is paramagnetic whereas nitrogen is diamagnetic. This fact forms the basis for their separation. The numerical studies and theoretical predictions concerning the air membrane separation in the presence of a magnetic field are discussed. Some experimental data concerning the „magnetic membranes” i.e. ethylcellulose membranes with neodymium powder, are also presented.

Time-optimal boundary control of a parabolic system with time lags given in integral form

Kowalewski A., Krakowiak A.

International Journal of Applied Mathematics and Computer Science

2006

Vol. 16, no 3

287-295

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