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Articulated vehicle kinematics
Roman, Matej ; Glos, Jan (referee) ; Pohl, Lukáš (advisor)
The goal of this thesis, is to create a kinematic model of an articulated vehicle. The first part deals with finding equations of state of this system and its control driving in reverse. The second part is dedicated to implement the model in the Matlab Simulink environment and to simulate and demonstrate the functionality of control on simple examples, typical for driving in reverse. In the last part a real model is created to test the functionality of control.
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Stability of the Zero Solution of Stochastic Differential System
Klimešová, Marie
Stability of stochastic differential equations (SDEs) has become a very popular theme of recent research in mathematics and its applications. The method of Lyapunov functions for the analysis of qualitative behavior of SDEs provide some very powerful instruments in the study of stability properties for concrete stochastic dynamical systems, conditions of existence the stationary solutions of SDEs and related problems.
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Travelling Salesman Problem
Kolář, Adam ; Rozman, Jaroslav (referee) ; Zbořil, František (advisor)
The aim of this bachelor's thesis is to design a testing environment for the traveling salesman problem and compare the effectiveness of different approaches to the solution. The first part discussed the possibility of genetic algorithms, depending on the setting of a crossover, mutations and population size. In the second part, there is the same problem using two types of neural networks. The representative of the self-learning net was chosen Kohonen neural network. Hopfield neural network represents a method of minimizing the energy function with fixed coefficients. At both neural networks, there were described possible advantages and disadvantages. In the end, all the findings were interpreted in a global context.
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Stability of the Stochastic Differential Equations
Klimešová, M.
Stability of stochastic differential equations (SDEs) has become a very popular theme of recent research in mathematics and its applications. The method of Lyapunov functions for the analysis of qualitative behavior of SDEs provide some very powerful instruments in the study of stability properties for concrete stochastic dynamical systems, conditions of existence the stationary solutions of SDEs and related problems. The study of exponential stability of the moments makes natural the consideration of certain properties of the moment Lyapunov exponents. Another important characteristic for stability (or instability) of the stochastic systems is the stability index.
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Optimization of Linear Differential Systems by Lyapunov's Direct Method
Demchenko, H.
Two approaches to solving optimization problems of dynamic systems are well-known. The first approach needs to find a fixed control (program control) for which the system described by differential equations reaches a predetermined value and minimizes an integral quality criterion. Proposed by L.S. Pontryagin, this method was in essence a further development of general optimization methods for dynamical systems. The second method consists in finding a control function (in the form of a feedback) guaranteeing that, simultaneously, the zero solution is asymptotically stable and an integral quality criterion attains a minimum value. This method is based on what is called the second Lyapunov method and its founder is N.N. Krasovskii. In the paper, the latter method is applied to linear differential equations and systems with integral quality criteria.
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