Inference of piecewise linear systems with an improved method employing jump detection

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2007

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Selçuk, Ahmet Melih

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Inference of regulatory relations in dynamical systems is a promising active research area. Recently, most of the investigations in this field have been stimulated by the researches in functional genomics. In this thesis, the inferential modeling problem for switching hybrid systems is studied. The hybrid systems refers to dynamical systems in which discrete and continuous variables regulate each other, in other words the jumps and flows are interrelated. In this study, piecewise linear approximations are used for modeling purposes and it is shown that piecewise linear models are capable of displaying the evolutionary characteristics of switching hybrid systems approxi- mately. For the mentioned systems, detection of switching instances and inference of locally linear parameters from empirical data provides a solid understanding about the system dynamics. Thus, the inference methodology is based on these issues. The primary difference of the inference algorithm is the idea of transforming the switch- ing detection problem into a jump detection problem by derivative estimation from discrete data. The jump detection problem has been studied extensively in signal processing literature. So, related techniques in the literature has been analyzed care- fully and suitable ones adopted in this thesis. The primary advantage of proposed method would be its robustness in switching detection and derivative estimation. The theoretical background of this robustness claim and the importance of robustness for real world applications are explained in detail.

Subject Keywords

Scientific computing (General).

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http://etd.lib.metu.edu.tr/upload/12608789/index.pdf
https://hdl.handle.net/11511/17122

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Graduate School of Applied Mathematics, Thesis

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Citation Formats

A. M. Selçuk, “Inference of piecewise linear systems with an improved method employing jump detection,” M.S. - Master of Science, Middle East Technical University, 2007.