Thesis Details

High order numerical method in modelling and control systems

Ph.D. Thesis Student: Veigend Petr Academic Year: 2023/2024 Supervisor: Šátek Václav, Ing., Ph.D.
Czech title
Numerická metoda vyššího řádu v modelování a řízení

Control systems are widely used as they enable precise management and regulation of complex processes across various industries. Ordinary differential equations are widely used in control theory because they provide a mathematical framework to describe the dynamic behaviour of control systems. They allow stability analysis, have good performance characteristics and can effectively regulate and optimise systems responses in real-time. The high-order numerical methods are not often used in the real-time context because of the large number of operations.   The thesis deals with the numerical solution of ordinary differential equations using a higher-order variable-step variable-order numerical method based on the Taylor series. The method is defined for linear and non-linear problems, and several optimisations to increase its performance are introduced. The positive properties of the method are thoroughly analysed and demonstrated on a set of real-world technical problems.  The results show that the Taylor-series-based method can be used in the area of control and regulation and outperforms the state-of-the-art methods in terms of speed and accuracy of the calculation.      


ordinary differential equations, higher-order numerical methods, Taylor series, technical initial value problems, control, regulation, modelling, controllers, regulators

Degree Programme
Computer Science and Engineering, Field of Study Computer Science and Engineering
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