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The Control of Chaos: Methods and Applications
Švihálková, Kateřina ; Dvořák, Jiří (referee) ; Matoušek, Radomil (advisor)
The diploma thesis is focused on the use of heuristic and metaheuristic methods to stabilization and controlling the selected systems distinguished by the deterministic chaos behavior. There are discussed parameterization of chosen optimization methods, which are the genetic algorithm, simulated annealing and pattern search. The thesis also introduced the suitable controlling methods and the definition of the objective function. In the theoretical part of the thesis there is a brief introduction to the deterministic chaos theory. The next chapters describes the most common and deployed methods in~the~control theory, especially OGY and Pyragas methods. The practical part of the thesis is divided into two chapters. The first one describes the~stabilization of the artifical chaotic systems with the time delayed Pyragas method - TDAS and its modification ETDAS. The second chapter shows the real chaotic system control. The Duffing oscillator system was chosen to serve this purpose.
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THE CONTROL OF CHAOS: METHODS AND APPLICATIONS
Kořenek, Miroslav ; Dvořák, Jiří (referee) ; Matoušek, Radomil (advisor)
This thesis deals with methods of stabilizing deterministic chaos. The first part provides a brief overview of the problem of deterministic chaos, including the framework used to describe and analyze chaotic systems. Furthermore, the most well-known chaotic systems are described in detail, with the logistic map and the Hénon map selected for experimental stabilization. The description of conventional methods for chaos stabilization, namely TDAS and ETDAS, follows. The principle of their optimization is also explained. Next chapter is dedicated to describing genetic programming and its potential use in chaos stabilization. In the practical part of the thesis, conventional methods and various implementations of genetic programming were applied to stabilize the selected systems. The utilization and experimentation with genetic programming to find stabilizing sequences are the most significant contributions of this work.
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The Control of Chaos: Methods and Applications
Švihálková, Kateřina ; Dvořák, Jiří (referee) ; Matoušek, Radomil (advisor)
The diploma thesis is focused on the use of heuristic and metaheuristic methods to stabilization and controlling the selected systems distinguished by the deterministic chaos behavior. There are discussed parameterization of chosen optimization methods, which are the genetic algorithm, simulated annealing and pattern search. The thesis also introduced the suitable controlling methods and the definition of the objective function. In the theoretical part of the thesis there is a brief introduction to the deterministic chaos theory. The next chapters describes the most common and deployed methods in~the~control theory, especially OGY and Pyragas methods. The practical part of the thesis is divided into two chapters. The first one describes the~stabilization of the artifical chaotic systems with the time delayed Pyragas method - TDAS and its modification ETDAS. The second chapter shows the real chaotic system control. The Duffing oscillator system was chosen to serve this purpose.
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