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CNAA / Theses / 2011 / June /

Numerical methods for solving deterministic and stochastic problems in dynamic decision systems


Author: Lazari Alexandru
Degree:doctor of physics and mathematics
Speciality: 01.01.09 - Mathematical cybernetics and operation research
Year:2011
Scientific adviser: Dmitrii Lozovanu
doctor habilitat, professor, Moldova State University
Institution: Moldova State University
Scientific council: DH 30-01.01.09
Moldova State University

Status

The thesis was presented on the 22 June, 2011
Approved by NCAA on the 5 October, 2011

Abstract

Adobe PDF document0.26 Mb / in romanian

Keywords

discrete optimal control, dynamic programming, extended network, Markov process, the matrix of limiting state probabilities, differential components, homogeneous linear recurrence, evolution time, average cost, total alert time

Summary

Thesis structure: The thesis is written in romanian and consists of an introduction, four chapters, conclusion, bibliography of 109 titles and two annexes. The main text of the thesis comprises 120 pages. The basic results of the thesis are published in 20 scientific papers.

Field of study of the thesis: deterministic and stochastic dynamic decision systems. The aim of research: Elaboration of numerical methods and algorithms for solving deterministic and stochastic problems in dynamic decision systems.

Scientific novelty and originality: Dynamic programming method for discrete optimal control problems with varying time of states transitions has been argued; algorithms for finding optimal stationary strategies for dynamic systems with infinite time horizon are developed; the basic properties of homogeneous linear recurrent equations for dynamic discrete systems are formulated; the polynomial algorithms for determining the probability limit matrix and differential components in discrete Markov processes are proposed and grounded; methods for finding the main probabilistic characteristics of evolution time for discrete stochastic systems with the final sequence states, the first alert moments and the total alert time of stochastic systems with the final critical state are elaborated.

The theoretical significance: The results presented in the thesis can serve as scientific suport for further research in studying an solving the relevant deterministic and stochastic decision problems for complex dynamic systems.

Applicative value of the thesis: The obtained results can be applied to studying various physical, economical, biological and others processes, which mathematically are modeled by discrete deterministic and stochastic dynamic decision systems.

The implementation of the scientific results: The elaborated algorithms have been implemented as a software program using C#.