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This book presents the latest findings on stochastic dynamic programming models and on solving optimal control problems in networks. It includes the authors’ new findings on determining the optimal solution of discrete optimal control problems in networks and on solving game variants of Markov decision problems in the context of computational networks. First, the book studies the finite state space of Markov processes and reviews the existing methods and algorithms for determining the main characteristics in Markov chains, before proposing new approaches based on dynamic programming and combinatorial methods. Chapter two is dedicated to infinite horizon stochastic discrete optimal control models and Markov decision problems with average and expected total discounted optimization criteria, while Chapter three develops a special game-theoretical approach to Markov decision processes and stochastic discrete optimal control problems. In closing, the book’s final chapter is devoted to finite horizon stochastic control problems and Markov decision processes. The algorithms developed represent a valuable contribution to the important field of computational network theory.

Economics/Management Science. --- Operation Research/Decision Theory. --- Optimization. --- Operations Research, Management Science. --- Discrete Optimization. --- Algorithm Analysis and Problem Complexity. --- Economics. --- Computer software. --- Mathematical optimization. --- Operations research. --- Economie politique --- Logiciels --- Optimisation mathématique --- Recherche opérationnelle --- Management --- Business & Economics --- Management Theory --- Markov processes. --- Dynamic programming. --- Stochastic control theory. --- Analysis, Markov --- Chains, Markov --- Markoff processes --- Markov analysis --- Markov chains --- Markov models --- Models, Markov --- Processes, Markov --- Business. --- Decision making. --- Algorithms. --- Management science. --- Business and Management. --- Control theory --- Stochastic processes --- Mathematical optimization --- Programming (Mathematics) --- Systems engineering --- Operations Research/Decision Theory. --- Software, Computer --- Computer systems --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Operational analysis --- Operational research --- Industrial engineering --- Management science --- Research --- System theory --- Algorism --- Algebra --- Arithmetic --- Quantitative business analysis --- Problem solving --- Statistical decision --- Deciding --- Decision (Psychology) --- Decision analysis --- Decision processes --- Making decisions --- Management decisions --- Choice (Psychology) --- Foundations --- Decision making

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The study of discrete structures and networks becomes more and more important in decision theory. A relevant topic in modern control theory reflecting this fact is concerned with multiobjective control problems and dynamical games. The monograph presents recent developments and applications in the field of multiobjective control of time-discrete systems with a finite set of states. The dynamics of such systems is described by a directed graph in which each vertex corresponds to a dynamic state and the edges correspond to transitions of the system moving from one state to another. This characterization allows us to formulate the considered control models on special dynamic networks. Suitable algorithms are derived exploiting multilayered structures. Game theoretical properties are characterized. A multilayered game on a network can be used to model a certain trading procedure of emission certificates within Kyoto process. Optimal economic behavior and equilibria can be determined.

Numerical methods of optimisation --- Operational research. Game theory --- Production management --- Artificial intelligence. Robotics. Simulation. Graphics --- mechatronica --- speltheorie --- operationeel onderzoek --- kwaliteitscontrole --- kansrekening --- robots --- optimalisatie

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The study of discrete structures and networks becomes more and more important in decision theory. A relevant topic in modern control theory reflecting this fact is concerned with multiobjective control problems and dynamical games. The monograph presents recent developments and applications in the field of multiobjective control of time-discrete systems with a finite set of states. The dynamics of such systems is described by a directed graph in which each vertex corresponds to a dynamic state and the edges correspond to transitions of the system moving from one state to another. This characterization allows us to formulate the considered control models on special dynamic networks. Suitable algorithms are derived exploiting multilayered structures. Game theoretical properties are characterized. A multilayered game on a network can be used to model a certain trading procedure of emission certificates within Kyoto process. Optimal economic behavior and equilibria can be determined.

Equilibrium (Economics). --- Game theory. --- Mathematical optimization. --- Discrete-time systems --- Control theory --- Dynamic programming --- Optimization --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Operations Research --- Discrete-time systems. --- Control theory. --- Dynamic programming. --- Program transformation (Computer programming) --- Computer program optimization --- Computer program transformation --- Optimization of computer programs --- Transformation of computer programs --- DES (System analysis) --- Discrete event systems --- Sampled-data systems --- Mathematics. --- Operations research. --- Decision making. --- Calculus of variations. --- Control engineering. --- Robotics. --- Mechatronics. --- Quality control. --- Reliability. --- Industrial safety. --- Calculus of Variations and Optimal Control; Optimization. --- Operation Research/Decision Theory. --- Quality Control, Reliability, Safety and Risk. --- Control, Robotics, Mechatronics. --- Computer programming --- Mathematical optimization --- Programming (Mathematics) --- Systems engineering --- Dynamics --- Machine theory --- Digital control systems --- System analysis --- Linear time invariant systems --- System safety. --- Operations Research/Decision Theory. --- Safety, System --- Safety of systems --- Systems safety --- Accidents --- Industrial safety --- Operational analysis --- Operational research --- Industrial engineering --- Management science --- Research --- System theory --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- Prevention --- Mechanical engineering --- Microelectronics --- Microelectromechanical systems --- Automation --- Control engineering --- Control equipment --- Engineering instruments --- Programmable controllers --- Industrial accidents --- Industries --- Job safety --- Occupational hazards, Prevention of --- Occupational health and safety --- Occupational safety and health --- Prevention of industrial accidents --- Prevention of occupational hazards --- Safety, Industrial --- Safety engineering --- Safety measures --- Safety of workers --- System safety --- Dependability --- Trustworthiness --- Conduct of life --- Factory management --- Reliability (Engineering) --- Sampling (Statistics) --- Standardization --- Quality assurance --- Quality of products --- Deciding --- Decision (Psychology) --- Decision analysis --- Decision processes --- Making decisions --- Management --- Management decisions --- Choice (Psychology) --- Problem solving --- Isoperimetrical problems --- Variations, Calculus of --- Decision making

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This book presents recent findings and results concerning the solutions of especially finite state-space Markov decision problems and determining Nash equilibria for related stochastic games with average and total expected discounted reward payoffs. In addition, it focuses on a new class of stochastic games: stochastic positional games that extend and generalize the classic deterministic positional games. It presents new algorithmic results on the suitable implementation of quasi-monotonic programming techniques. Moreover, the book presents applications of positional games within a class of multi-objective discrete control problems and hierarchical control problems on networks. Given its scope, the book will benefit all researchers and graduate students who are interested in Markov theory, control theory, optimization and games.

Stochastic control theory. --- Operations research. --- Mathematics. --- Management science. --- Mathematical optimization. --- Algorithms. --- Operations Research and Decision Theory. --- Applications of Mathematics. --- Operations Research, Management Science. --- Optimization.

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At the end of the nineteenth century Lyapunov and Poincaré developed the so called qualitative theory of differential equations and introduced geometric-topological considerations which have led to the concept of dynamical systems. In its present abstract form this concept goes back to G.D. Birkhoff. This is also the starting point of Chapter 1 of this book in which uncontrolled and controlled time-continuous and time-discrete systems are investigated. Controlled dynamical systems could be considered as dynamical systems in the strong sense, if the controls were incorporated into the state space. We, however, adapt the conventional treatment of controlled systems as in control theory. We are mainly interested in the question of controllability of dynamical systems into equilibrium states. In the non-autonomous time-discrete case we also consider the problem of stabilization. We conclude with chaotic behavior of autonomous time discrete systems and actual real-world applications.

Ergodic theory. Information theory --- Operational research. Game theory --- Mathematical statistics --- Mathematics --- Classical mechanics. Field theory --- Electrical engineering --- Applied physical engineering --- Engineering sciences. Technology --- Planning (firm) --- Artificial intelligence. Robotics. Simulation. Graphics --- mechatronica --- superclaus proces --- industriële robots --- automatisering --- besluitvorming --- mathematische modellen --- speltheorie --- econometrie --- wiskunde --- operationeel onderzoek --- robots --- dynamica --- automatische regeltechniek --- informatietheorie