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1

An information based approach to stochastic control problems

Bania Piotr

International Journal of Applied Mathematics and Computer Science

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2020

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Vol. 30, no. 1

23--34

EN

An information based method for solving stochastic control problems with partial observation is proposed. First, information-theoretic lower bounds of the cost function are analysed. It is shown, under rather weak assumptions, that reduction in the expected cost with closed-loop control compared with the best open-loop strategy is upper bounded by a non-decreasing function of mutual information between control variables and the state trajectory. On the basis of this result, an information based control (IBC) method is developed. The main idea of IBC consists in replacing the original control task by a sequence of control problems that are relatively easy to solve and such that information about the system state is actively generated. Two examples of the IBC operation are given. It is shown that the method is able to find an optimal solution without using dynamic programming at least in these examples. Hence the computational complexity of IBC is substantially smaller than that of dynamic programming, which is the main advantage of the proposed method.

2

Time-series analysis and modelling to predict aviation safety performance index

Lališ A.

Transport Problems

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2017

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T. 12, z. 3

51--58

EN

Safety performance index is a tool with the potential to grasp the intangible domain of aviation safety, based on quantification of meaningful aviation safety system properties. The tool itself was developed in the form of Aerospace Performance Factor and is already available for the aviation industry. However, the tool turned out to be rather unsuccessful as its potential was not fully recognised by the industry. This paper introduces performed analysis on the potential and it outlines new features, utilising time-series analysis, which can improve both the recognition of the index by the industry as well as the motivations to further research and develop methodologies to evaluate overall aviation safety performance using its quantified system properties. This paper discusses not only the features but also their embedding into the existing approach for the development of aviation safety, highlighting possible deficiencies to overcome and relating the scientific work already performed in the domain. Various types of appropriate time-series methodologies are addressed and key specifications of their use with respect to the discussed issue concerning safety performance index are stated.

3

Optimal dividend policy in discrete time

Marciniak E., Trybuła J.

Demonstratio Mathematica

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2014

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Vol. 47, nr 1

258--270

EN

A problem of optimal dividend policy for a firm with a bank loan is considered. A regularity of a value function is established. A numerical example of calculating value function is given.

4

Sterowanie stochastyczne jako podstawa planowania ruchu robotów manipulacyjnych

Kost G.

Pomiary Automatyka Kontrola

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2005

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R. 51, nr 5

31-34

PL

Artykuł przedstawia metodę komputerowo wspomaganego programowania off-line robotów przemysłowych wykorzystującej do analizy przestrzeni roboczej manipulacyjnych robotów przemysłowych procesy decyzyjne Markowa. Przedstawiono koncepcję oraz wymagania jakie powinien spełniać sprawny informatycznie i technologicznie komputerowy system programowania off-line robotów przemysłowych. Koncepcję systemu oparto na metodzie uczenia się ze wzmocnieniem. Zdefiniowano podstawowe parametry omawianego procesu planowania opartego na sterowaniu stochastycznym, takie jak: proces Markowa, funkcje prawdopodobieństw warunkowych przejścia i osiągnięcia typowanych przemieszczeń robota.

EN

The scope of the paper is the presentataion of computer-aided method of programming off-line industrial robots based on Markov`s decision processes applied to analyze the operation space of manipulative industrial robots. The concept of a computer system of programming off-line industrial robots is discussed as well as the requirements that it should fulfill to secure IT and technical efficiency. The concept of the system is based on a method of machine learning with reinforcement. The fundamental parameters of the stochastic process planning are defined, including: the Markov`s decision process, the space of the robot state, conditional probability functions of robot passage and destinations as specified by stochastic planning process.

5

Planowanie bezpiecznych ścieżek robotów oparte na funkcji ocen

Kost G. G.

Inżynieria Maszyn

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2005

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R. 10, z. 1/2

165-182

PL

Planowanie zadań robotów jest jednym z najważniejszych obszarów badawczych robotyki. Obejmuje zagadnienia związane z planowaniem zadań elementarnych procesów obsługi robotów manipulacyjnych i związane z problemem planowania bezkolizyjnych trajektorii. Planowanie bezkolizyjnych trajektorii robotów manipulacyjnych jest zagadnieniem wieloetapowym, w którym pierwszym etapem jest zadanie wyznaczenia bezkolizyjnych ścieżek w przestrzeni zadaniowej. Trudności, jakie się z nim wiążą powodują, że brak jest dostatecznie efektywnych metod jego rozwiązywania. Przyczyną takiego stanu rzeczy jest wymagana przy rozwiązywaniu zadania planowania trajektorii robotów analiza przestrzeni zadaniowej robota. Wymusza ona konieczność poszukiwania rozwiązań dopuszczalnych ścieżek bezkolizyjnych w modelu grafowym (oktalne drzewo decyzyjne) przestrzeni zadaniowej, za pomocą mało efektywnych czasowo algorytmów heurystycznych. W prezentowanej pracy przedstawiono problem planowania bezkolizyjnego ruchu robotów przemysłowych. Zaprezentowano metodę planowania bezpiecznych ścieżek robotów manipulacyjnych opartą na, typowej dla robotów stacjonarnych, metodzie oktalnej analizy przestrzeni robota. Zaprezentowano nową strategię analizy oktalnego drzewa decyzyjnego, która dzięki zastosowanemu procesowi sterowania stochastycznego, pozwala wyeliminować charakterystyczne dla tego typu zadań algorytmy przeszukiwania heurystycznego. Całość omawianych zagadnień zilustrowano przykładami symulacyjnymi, potwierdzającymi skuteczność obliczeniową uzyskanej metody.

EN

The planning of tasks to be performed by robots constitutes one of the most important research areas of robotics. It includes the issues of planning the tasks of elementary (basic) operational processes performed by manipulative robots as well as planning their collision free trajectories. The latter is a multi-stage task, the first step of which is the designation of collision-free paths in the external operational space. In view of difficulty involved in this task there is an insufficiency of methods that are effective enough to solve the task. The source of the difficulty is the analysis of the operational space of the robot, which leads to the need of searching for the solutions of allowable collision-free paths in a graph model (octant decision tree) of the operational space of the robot by means of time-consuming heuristic algorithms. The scope of the paper is the problem of planning collision-free motions of industrial robots. The discussed method of planning safe paths of manipulative robots is based on the method of octant space analysis commonly applied to stationary robots. A new strategy of analyzing the octant decision tree makes use of the process of stochastic control, enabling the elimination of heuristic search algorithms so typical of such types of tasks. The discussion is illustrated by examples of simulations which substantiate the computational efficiency of the method.

6

Two-level stochastic control for a linear system with nonclassical information

Duda Z., Brandys W.

International Journal of Applied Mathematics and Computer Science

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2004

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Vol. 14, no 2

161-166

EN

A problem of control law design for large scale stochastic systems is discussed. Nonclassical information pattern is considered. A two-level hierarchical control structure with a coordinator on the upper level and local controllers on the lower level is proposed. A suboptimal algorithm with a partial decomposition of calculations and decentralized local control is obtained. A simple example is presented to illustrate the proposed approach.

7

Optimal control for a nonstationary linear system with a quadratic cost functional

Czornik Adam

Matematyka Stosowana : matematyka dla społeczeństwa

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1997

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Nr 40

3--11

EN

This paper is about optimal control of infinite-horizon nonstationary stochastic linear processes with a quadratic cost criterion. The synthesis problem of optimal control is solved under the assumptions that the criterion is an average expected cost and that the process' matrices possess limits for the time approaching infinity. Furthermore, the limit matrices are such that the "limit" process is both observable and controllable. The paper documents existence of an optimal feedback control policy. The policy is such that the gain matrix is a (scaled) solution to a Riccati stationary matrix equation. The equation is stationary in that its coefficients are the limits of the process' non-stationary matrices.