Dynamic optimization based on higher order differential model representations

Abstract:
A novel method for solving path and endpoint dynamic optimization problems is proposed. State-of-the-art direct optimization techniques, approximate the continuous optimization problem to a nonlinear algebraic programming (NLP) problem either by state and control vector or by control vector parameterization only. The novel optimization approach presented here is based on the reformulation of the nonlinear dynamical system into a higher order differential representation comprising a set of algebraic equations in the state variables as well as in the control and auxiliary variables and their derivatives. Hence, the dynamic optimization problem can often be converted into a formulation in which the state variables and their derivatives are entirely eliminated. This system representation combined with a suitable parameterization strategy leads to compact NLPs which promise significant reduction of computational effort compared to established approaches. The method is illustrated with the productivity optimization of a semi-batch reactor

Keywords:
Dynamic optimization, direct method, path constraints, higher order differential representation, flat systems, optimal control

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