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Metody aproximace plně pravděpodobnostního návrhu rozhodování za neúplné znalosti
Pištěk, Miroslav ; Kárný, Miroslav (advisor) ; Andrýsek, Josef (referee)
In this thesis, we introduce an efficient algorithm for an optimal decision strategy approximation. It approximates the optimal equations of dynamic programming without omitting the principal uncertainty stemming from an uncomplete knowledge of a controlled system. Thus, the algorithm retains the ability to constantly verify the actual knowledge, which is the essence of dual control. An integral part of solution proposed is a reduction of memory demands using HDMR approximation. We have developed a general method for numerical solution of linear integral equations based on this approximation, and applied it to solve a linearized variant of optimal equations. To achieve such a variant, it was necessary to apply a different control design called fully probabilistic design which allows easier finding of a linearized approximation. The result of this method is a pair of linear algebraic systems for the upper and lower bound on the central function describing the optimal strategy. One illustrative example has been completely resolved.
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Metody aproximace plně pravděpodobnostního návrhu rozhodování za neúplné znalosti
Pištěk, Miroslav ; Andrýsek, Josef (referee) ; Kárný, Miroslav (advisor)
In this thesis, we introduce an efficient algorithm for an optimal decision strategy approximation. It approximates the optimal equations of dynamic programming without omitting the principal uncertainty stemming from an uncomplete knowledge of a controlled system. Thus, the algorithm retains the ability to constantly verify the actual knowledge, which is the essence of dual control. An integral part of solution proposed is a reduction of memory demands using HDMR approximation. We have developed a general method for numerical solution of linear integral equations based on this approximation, and applied it to solve a linearized variant of optimal equations. To achieve such a variant, it was necessary to apply a different control design called fully probabilistic design which allows easier finding of a linearized approximation. The result of this method is a pair of linear algebraic systems for the upper and lower bound on the central function describing the optimal strategy. One illustrative example has been completely resolved.
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Základy Mixtools 3000
Andrýsek, Josef ; Pištěk, M. ; Šmídl, Václav ; Šterbák, O. ; Tkáč, M. ; Týnovský, M. ; Váňová, Irena
This paper is a first step in a larger project that aims is to create a toolbox for support of dynamic distributed decision making under uncertainty. This toolbox is designed as a new generation of the software platform that serves for testing of various decision-making-related algorithms. The new framework will replace older system mixtools, from which it inherits the main low-level algorithmic base.
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První experimenty s distribuovaným Bayesovským rozhodováním
Šmídl, Václav ; Andrýsek, Josef
Decision-making under uncertainty is a natural part of everyday life of every human being. In societal science, various aspects of decision-making were studied, mostly in the area of psychology. In technical science, the process was formalized using probability theory yielding so called Bayesian theory of decision making. However, one of the key assumptions of this theory is that the decision-maker is the only entity that intentionally influences the system. This assumption is certainly violated in more complicated systems, such as human society or distributed control. Recently, a series of papers attempts to offer an extension of the Bayesian theory for many decision-makers, i.e. decentralized stochastic control. Since there are no proofs of optimality of the proposed Bayesian distributed decision making available in the literature, we study this approach via experimental simulation studies.
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