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Nonlinear Control of Complex Systems by Utilization of Evolutionary Approaches
Minář, Petr ; Ošmera, Pavel (referee) ; Oplatková,, Zuzana Komínková (referee) ; Matoušek, Radomil (advisor)
Control theory of complex systems by utilization of artificial intelligent algorithms is relatively new science field and it can be used in many areas of technical practise. Best known algorithms to solved similar tasks are genetic algorithm, differential evolution, HC12 Nelder-Mead method, fuzzy logic and grammatical evolution. Complex solution is presented at selected examples from mathematical nonlinear systems to examples of anthems design and stabilization of deterministic chaos. The goal of this thesis is present examples of implementation and utilization of artificial algorithms by multi-objective optimization. To achieve optimal results is used designed software solution by multi-platform application, which used Matlab and Java interfaces. The software solution integrate every algorithms of this thesis to complex solution and it extends possible application of those approaches to real systems and practical world.
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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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Rational linear dependencies of periodic points of the logistic map
Mik, Matěj ; Žemlička, Jan (advisor) ; Růžička, Pavel (referee)
Period-n points of a polynomial f are roots, and hence elements of the splitting field, of the polynomial fn (x) − x, where fn denotes the nth iterate of f. In the thesis, we will focus on describing rational linear dependencies of period-n points of the polynomial f(x) = 4x(1 − x), which defines the so-called logistic map. We will present a description of the dependencies for n = 1, . . . , 5 and a partial result for n = 6. We will be using computer- calculated factorizations of polynomials over rational numbers and some finite field extensions. The factorizations will give us coordinates of the periodic points relative to some basis of their linear span, which will allow us to use a simple way of describing their dependencies. In the end of the thesis, we will put together an algorithm for describing the dependencies for a general n.
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Nonlinear Control of Complex Systems by Utilization of Evolutionary Approaches
Minář, Petr ; Ošmera, Pavel (referee) ; Oplatková,, Zuzana Komínková (referee) ; Matoušek, Radomil (advisor)
Control theory of complex systems by utilization of artificial intelligent algorithms is relatively new science field and it can be used in many areas of technical practise. Best known algorithms to solved similar tasks are genetic algorithm, differential evolution, HC12 Nelder-Mead method, fuzzy logic and grammatical evolution. Complex solution is presented at selected examples from mathematical nonlinear systems to examples of anthems design and stabilization of deterministic chaos. The goal of this thesis is present examples of implementation and utilization of artificial algorithms by multi-objective optimization. To achieve optimal results is used designed software solution by multi-platform application, which used Matlab and Java interfaces. The software solution integrate every algorithms of this thesis to complex solution and it extends possible application of those approaches to real systems and practical world.
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Nonlinear Control of Complex Systems by utilization of Evolutionary Approaches
Minář, Petr ; Matoušek, Radomil (advisor)
Control theory of complex systems by utilization of artificial intelligent algorithms is relatively new science field and it can be used in many areas of technical practise. Best known algorithms to solved similar tasks are genetic algorithm, differential evolution, HC12 Nelder-Mead method, fuzzy logic and grammatical evolution. Complex solution is presented at selected examples from mathematical nonlinear systems to examples of anthems design and stabilization of deterministic chaos. The goal of this thesis is present examples of implementation and utilization of artificial algorithms by multi-objective optimization. To achieve optimal results is used designed software solution by multi-platform application, which used Matlab and Java interfaces. The software solution integrate every algorithms of this thesis to complex solution and it extends possible application of those approaches to real systems and practical world.
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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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