The reachable sets concept applied to a class of min-max optimization problems

• Autorzy: Terlikowski T.
• Języki publikacji: EN

Abstrakty

EN

A multi-criteria control problem over the infinite time horizon for periodical system is considered. our aim is solve problems of type using the known idea of reachable sets. The worst case approach applied concerns e.g. a system of water resources distribution. The min-max opimisation problem obtained occurs to fit naturally the scheme of reachable sets concept. applicability of this concept to that particular case is discussed and the algorithm is presented.

Słowa kluczowe

EN

reachable sets; min-max optimization; reference point method; periodical control problem

• Wydawca: Polish Academy of Sciences, Committee of Automatic Control and Robotics
• Czasopismo: Archives of Control Sciences
• Rocznik: 2003
• Tom: Vol. 13, no. 1
• Strony: 47--58
• Opis fizyczny: Bibliogr. 12 poz., wzory

Twórcy

autor

Terlikowski T.

• Institute of Geophysics, Polish Academy of Sciences, ul. Księcia Janusza 64, Warsaw 01-452, Poland,

Bibliografia

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• [4] J.D. Glover and F.C. Schweppe: Control of Linear Dynamic Systems with Set Constrained Disturbances. IEEE Trans. AC, 16 (1971).
• [5] A. Karbowski: Optimal Infinite-Horizon Multicriteria Feedback Control of Stationary Systems with Min-max Objectives and Bounded Disturbances. J. of Optimisation Theory and Applications, 101 (1). (1999).
• [6] A. Karbowski and R. Soncini-Sessa: Design and control of water systems in presence of inflow scenarios. Engineering Risk in Natural Resources Management. NATO ASI Series, Kluwer Academic Publishers, 1994.
• [7] P. Korhonen and J. Laakso: A visual interactive method for solving the multiple criteria problem. European J. of Operational Research, 24(2), (1986).
• [8] J. Napiórkowski, T. Terlikowski and V. Woebring: Multiobjectivc Approach to the Operational Control Synthesis - the Wupper Reservoir System Case Study. Presented at Operational Water Management Conference. Denmark, (1997).
• [9] T. Terlikowski. J. Napiórkowski and A. Karbowski: Operational Control of Water Reservoir System with Mini max Objectives. Presented at Operational Water Management Conference, Denmark, (1997).
• [10] T. Terlikowski: Reachable sets concept-a general abstract analysis. Control & Cybernetics, 32(4), (2003).
• [11] T. Terlikowski: A Logical Approach to Control. Some New Logical Concepts and their Application to the Notion of Safety for Control Variants. Fundamenta Informaticae, 52(4), (2002), pp. 377-394.
• [12] A.P. Wierzbicki: A Mathematical Basis for Satisfying Decision Making. Mathematical Modeling, 3 (1962).