A high level canonical piecewise linear representation : theory and applications /
The purpose of this thesis is to develop a high level explicit canonical expression for piecewise linera (PWL) functions and to study its properties and applications. At the beginning, the most significant results about the (explicit and implicit) canonical representations exposed in the literature...
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| Formato: | Libro |
| Idioma: | Spanish |
| Publicado: |
1999.
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| Sumario: | The purpose of this thesis is to develop a high level explicit canonical expression for piecewise linera (PWL) functions and to study its properties and applications. At the beginning, the most significant results about the (explicit and implicit) canonical representations exposed in the literature up to now are described. In this way, an introduction as well as an adequate theoretical background is provided for the reader. Next, the main contribution of the thesis is presented. It consists in the introduction of a canonical expression capable of representing PWL functions on a domain belonging to ... partitioned with a simplicial boundary configuration. This representation constitutes the first canonical expression designed specifically to be used in domains of arbitrary dimension. A numerical constructive methodology is developed that are necessary to determine a given function in a systematic and efficient manner. After that, two applications, which illustrate the potentialities of the approach in the numerical solution of nonlinear problems, are presented. The first application is related to the approximation of continuous functions. One of the main features of the proposed representation is that it can uniformly approximate a nonlinear function by this property, several optimal approximation methodologies are devised to obtain the parameters in a numerically efficient way. The second application is related to the stability analysis of nonlinear dynamical systems. It consist in a parametrization of all the PWL Lyapunov function candidates defined over a simplicial partition of the domain and its utilization for the numerical stability analysis of autonomous nonlinear dynamical systems, including uncertain systems. CALIFICACION DEPARTAMENTO DE GRADUADOS Calificación de la defensa oral: Sobresaliente - 10(diez) Fecha: 22/10/99 |
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| Descripción Física: | 177 p. : il. ; 30,5 cm.. |
| Bibliografía: | Incluye referencias bibliográficas. |