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Deterministic global optimization of nonlinear dynamic systems

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Abstract

A new approach is described for the deterministic global optimization of dynamic systems, including optimal control problems. The method is based on interval analysis and Taylor models and employs a type of sequential approach. A key feature of the method is the use of a new validated solver for parametric ODEs, which is used to produce guaranteed bounds on the solutions of dynamic systems with interval-valued parameters. This is combined with a new technique for domain reduction based on the use of Taylor models in an efficient constraint propagation scheme. The result is that an ϵ-global optimum can be found with both mathematical and computational certainty. Computational studies on benchmark problems are presented showing that this new approach provides significant improvements in computational efficiency, well over an order of magnitude in most cases, relative to other recently described methods. © 2007 American Institute of Chemical Engineers AIChE J, 2007

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