Balanced truncation for dissipative and symmetric nonlinear systems

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The problem of model order reduction plays a mayor role in engineering as the complexity and the dimensions of the nonlinear mathematical models of dynamical systems keeps on increasing, making them more difficult to simulate, analyze and control. The main idea of model reduction is to find a lower order/complexity mathematical model that approximates the original system. Nonlinear balanced truncation is an attractive and systematic tool to obtain reduced order models, based on throwing away the dynamics corresponding to the low gains between past input and future output energy i.e. badly reachable and (or) badly observable dynamics. The approximation preservers the stability of the original system. In this thesis we propose a method that deals with the preservation of dissipativity properties of systems. A dissipative reduced model is obtained by throwing away the more or less dissipative dynamics of the full order model of the system.

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