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Analysis and Design of Nonlinear Dynamical Systems Using Mathematica
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| Organization: | Universidad de Los Andes, Facultad de Ingeniería |
| Department: | Dept. Sistemas de Control |
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| Nonlinear Analysis, Theory, Methods & Applications |
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The desire and/or the need of automating long, tedious, complex and error-prone sequences of mathematical symbolic computations has been a dream as old as mathematics itself. The realization of this dream is still quite far from complete, but the spring up of symbolic computation systems during the last thirty years seems to be a step forward in the right direction. Symbolic computation is not a panacea. However, it is not hard to imagine that its development, synergetically integrated with both graphical and traditional numerical computation techniques, will have an enormous impact on the evolution of mathematics and all other physical and mathematical sciences, in the near future. In this paper we will illustrate how symbolic computation tools can be successfully used to approach the solution of some elementary problems in the analysis of nonlinear dynamical systems, and the design of nonlinear controllers and observers for nonlinear controlled dynamical systems. The paper is organized as follows: section 2 covers some general aspects of symbolic computation and its application to nonlinear dynamics. Section 3 surveys the development of some symbolic computation tools for the analysis and design of nonlinear dynamical systems. In section 4 and 5 we present a survey of some of our own work on symbolic computation for the analysis of second order nonlinear dynamical systems and the design of nonlinear controlled dynamical systems. We illustrate these developments through appropriate case study examples.
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