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Janusz Ballenstedt i jego Teoria Minimum w Architekturze

Lenartowicz J. K.

Teka Komisji Urbanistyki i Architektury Oddział PAN w Krakowie

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2018

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T. 46

41--59

PL

W artykule przedstawiona została postać Janusza Ballenstedta (1929-2005), krakowskiego architekta, którego przypadki losu przemieściły w środowisko francuskie. Był projektantem znaczących obiektów w Polsce, człowiekiem ogromnej wiedzy, sprawnie używającym pióra. Swoje przemyślenia dotyczące całościowego widzenia architektury przenosił na papier. Powstała książka pt.: Architektura – Teoria i Historia (PWN 2000). W artykule uwaga została skupiona na wcześniej niepublikowanej pracy J. Ballenstedta, jego szczególnym manifeście, zatytułowanym Teoria Minimum w Architekturze.

EN

The article presents the person of Janusz Ballenstedt (1929-2005), a Cracow architect, whom twists of fate relocated to French circles. He was the designer of significant buildings in Poland, a man of great knowledge, skilful in his use of the pen. He transferred his thoughts regarding the all-encompassing viewing of architecture to paper. A valuable book, titled “Architecture – Theory and History” (PWN 2000) was written. The article is focused on J. Ballenstedt’s earlier unpublished work, a manifesto of the architect, titled Theory of Minimum in Architecture.

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Usage of a zero-sum differential game in the optimal control of an object described by a nonlinear model

Mikulski L., Kropiowska D.

Technical Transactions

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2018

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Vol. 115, iss. 9

109--121

EN

This article presents the usage of a zero-sum differential game to control a nonlinear object, which, in the analysed problem, was a mathematical pendulum. The obtained control was optimal with regard to adopted quality indicator for the worst interference. The two-point boundary value problem was solved numerically by means of the Dircol software application. Numerical solutions, meeting all the necessary optimality conditions, were obtained for different values of the rough parameter and for different values of damping.

PL

W artykule wykorzystano grę różniczkową o sumie zerowej do sterowania obiektem nieliniowym, jakim w analizowanym problemie jest wahadło matematyczne. Uzyskano sterowanie optymalne ze względu na przyjęty wskaźnik jakości, przy najgorszym zakłóceniu. Dwupunktowy problem brzegowy został rozwiązany numerycznie przy wykorzystaniu programu Dircol. Rozwiązania numeryczne spełniające wszystkie warunki konieczne optymalności zostały otrzymane dla różnych wartości parametru szorstkości oraz przy różnych wartościach tłumienia.

3

Control Structure in Optimization Problems of Bar Systems

Mikulski L.

International Journal of Applied Mathematics and Computer Science

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2004

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Vol. 14, no 4

515-529

EN

Optimal design problems in mechanics can be mathematically formulated as optimal control tasks. The minimum principle is employed in solving such problems. This principle allows us to write down optimal design problems as Multipoint Boundary Value Problems (MPBVPs). The dimension of MPBVPs is an essential restriction that decides on numerical difficulties. Optimal control theory does not give much information about the control structure, i.e., about the sequence of the forms of the right-hand sides of state equations appearing successively in time. The correctness of the assumed control structure can be checked after obtaining the solution of the boundary problem. For the numerical solution, we use hybrid procedures which are a connection of the multiple shooting method with that of collocation.

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Discrete approximation of nonconvex hyperbolic optimal control problems with state constraints

Chryssoverghi I., Bacopoulos A., Coletsos J., Kokkinis B.

Control and Cybernetics

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1998

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Vol. 27, no 1

29-50

EN

We consider an opitmal control problem for systems defined by nonlinear hyperbolic partial differential equations with state constraints. Since no convexity assumptions are made on the data, we also consider the control problem in relaxed form. We discretize both the classical and the relaxed problenms by using a finite element method in space and a finite difference scheme in time, the controls being approximated by piecevise constant ones. We develop the existence theory and the necessary conditions for optimality, for the continous and the discrete problems. Finally, we study the behaviour in the limit of discrete optimality, admissibility and extremality properties.