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1
Content available Pointwise observation of the state given by complex time lag parabolic system
Kowalewski A.
Archives of Control Sciences
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2017
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Vol. 27, no. 1
77--89
EN
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
2
Content available Pointwise observation of the state given by parabolic system with boundary condition involving multiple time delays
Kowalewski A.
Archives of Control Sciences
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2016
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Vol. 26, no. 2
189--197
EN
Various optimization problems for linear parabolic systems with multiple constant time delays are considered. In this paper, we consider an optimal distributed control problem for a linear parabolic system in which multiple constant time delays appear in the Neumann boundary condition. Sufficient conditions for the existence of a unique solution of the parabolic equation with the Neumann boundary condition involving multiple time delays 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 cost function with pointwise observation of the state and constrained control are derived.
3
Content available Feedback stabilization of one-dimensional parabolic systems related to formations
Sano H.
Bulletin of the Polish Academy of Sciences. Technical Sciences
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2015
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Vol. 63, nr 1
295--303
EN
This paper is concerned with the problem of stabilizing one-dimensional parabolic systems related to formations by using finitedimensional controllers of a modal type. The parabolic system is described by a Sturm-Liouville operator, and the boundary condition is different from any of Dirichlet type, Neumann type, and Robin type, since it contains the time derivative of boundary values. In this paper, it is shown that the system is formulated as an evolution equation with unbounded output operator in a Hilbert space, and further that it is stabilized by using an RMF (residual mode filter)-based controller which is of finite-dimension. A numerical simulation result is also given to demonstrate the validity of the finite-dimensional controller.
4
Content available Boundary control of retarded parabolic systems
Krakowiak A.
Control and Cybernetics
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2011
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Vol. 40, no 1
9-23
EN
Optimal boundary control problems for distributed parabolic systems in which retarded arguments appear in the integral form in the state equations are presented. Necessary and sufficient conditions of optimality are derived for the non-homogeneous Dirichlet problem. A simple example of application is also provided.
5
Content available remote Source localization and sensor placement in environmental monitoring
Khapalov A.
International Journal of Applied Mathematics and Computer Science
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2010
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Vol. 20, no 3
445-458
EN
In this paper we discuss two closely related problems arising in environmental monitoring. The first is the source localization problem linked to the question How can one find an unknown 'contamination source'? The second is an associated sensor placement problem: Where should we place sensors that are capable of providing the necessary 'adequate data' for that? Our approach is based on some concepts and ideas developed in mathematical control theory of partial differential equations.
6
Content available remote 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
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2008
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Vol. 18, no 2
189-198
EN
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.
7
Content available remote A system for implicit impulsive nonlinear parabolic functional-differential inequalities
Byszewski L.
Fasciculi Mathematici
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2007
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Nr 37
5-18
EN
A theorem about a system of weak implicit impulsive nonlinear parabolic functional-differential inequalities in an arbitrary parabolic set is proved. As a consequence of the theorem, maximum principles for the system of implicit impulsive nonlinear parabolic functional-differential inequalities and the uniqueness of a classical solution of a mixed implicit impulsive problem for a system of nonlinear parabolic functional-differential equations are obtained.
8
Content available remote 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
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2006
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Vol. 16, no 3
287-295
EN
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.
9
Content available remote Time-optimal control of a parabolic system with multiple time-varying lags
Kowalewski A., Krakowiak A.
Applied Mathematics and Computer Science
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1998
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Vol. 8, no 3
471-489
EN
In this paper, the time-optimal control problem for a distributed parabolic system in which different multiple time-varying lags appear both in the state equation and in the boundary condition is presented. Some particular properties of the optimal control are discussed.
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