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Abstract

Extremal problems for multiple time delay hyperbolic systems are presented. The optimal boundary control problems for hyperbolic systems in which multiple time delays appear both in the state equations and in theNeumann boundary conditions are solved. The time horizon is fixed. Making use of Dubovicki-Milutin scheme, necessary and sufficient conditions of optimality for the Neumann problem with the quadratic performance functionals and constrained control are derived.
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Authors and Affiliations

Adam Kowalewski
1

  1. AGH University of Science and Technology, Institute of Automatic Control and Robotics, 30-059 Cracow, al. Mickiewicza 30, Poland
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Abstract

Shifting living conditions, environmental change, and population migrations are all necessitating changes in how we manage the space in which we live. Does our living have a future?
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Authors and Affiliations

Przemysław Śleszyński
1
Adam Kowalewski
2

  1. Institute of Geography and Spatial Organization, Polish Academy of Sciences in Warsaw
  2. Foundation in Support of Local Democracy, in Warsaw
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Abstract

Abstract 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.
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Authors and Affiliations

Adam Kowalewski
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Abstract

Abstract 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.
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Authors and Affiliations

Adam Kowalewski
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Abstract

Zmieniające się warunki życia, przekształcenia środowiska i migracje ludności wymuszają zmiany w gospodarce przestrzennej. Czy nasza przestrzeń ma przyszłość?
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Authors and Affiliations

Przemysław Śleszyński
1
Adam Kowalewski
2

  1. Instytut Geografii i Przestrzennego Zagospodarowania PAN w Warszawie
  2. Fundacja Rozwoju Demokracji Lokalnej im. Jerzego Regulskiego w Warszawie
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Abstract

Praca zawiera analizy i oceny skutków wybranych regulacji polskiego prawa dotyczących gospodarki przestrzennej, zwłaszcza planowania przestrzennego. Różni się od poprzednich raportów położeniem większego nacisku na bariery blokujące naprawę wadliwego systemu publicznego zarządzania przestrzenią. Praca nie jest próbą oceny prawa pod względem jego poprawności jurydycznej i legislacyjnej.

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Authors and Affiliations

Adam Kowalewski
Maciej J. Nowak

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