Numerical methods for solving deterministic and stochastic problems in dynamic decision systems
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StatusThe thesis was presented on the 22 June, 2011Approved by NCAA on the 5 October, 2011 Abstract – 0.26 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 timeSummary
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#.
Oficial Reviewers
- Dumitru Solomon
doctor habilitat, associate professor (docent), Moldova State University - Anatol Godonoagă
doctor, associate professor (docent), Academy of Economic Studies of Moldova
Council's Members
- Petru Soltan, president
doctor habilitat, professor, Moldova State University - Sergiu Cataranciuc, secretary
doctor habilitat, professor, Moldova State University - Gheorghe Mişcoi, member
doctor habilitat, professor, Institute of Mathematics and Computer Science - Emilian Guţuleac, member
doctor habilitat, professor, Technical University of Moldova - Boris Hâncu, member
doctor, associate professor (docent), Moldova State University
Theses
