Optimization and Multiobjective Control of Time-Discrete Systems : Dynamic Networks and Multilayered Structures / by Stefan Pickl, Dmitrii Lozovanu.

Springer eBooks

Multi-Objective Control of Time-Discrete Systems and Dynamic Games on Networks -- Max-Min Control Problems and Solving Zero-Sum Games on Networks -- Extension and Generalization of Discrete Control Problems and Algorithmic Approaches for its Solving -- Discrete Control and Optimal Dynamic Flow Problems on Networks -- Applications and Related Topics.

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.

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