Abstract
In this article, an optimization task with nonlinear differential-algebraic equations (DAEs) is considered. As a main result, a new solution procedure is designed. The computational procedure represents the sequential optimization approach. The proposed algorithm is based on a multiple shooting parametrization method. Two main aspects of a generalized parametrization approach are analyzed in detail: a control function and DAE model parametrization. A comparison between the original and modified DAEs is made. The new algorithm is applied to solve an optimization task in heat and mass transfer engineering.
Highlights
The dynamic development of engineering systems of parametric models can be observed
The introduced methodology is an extension of the sequential approach for optimization, where the outer differential-algebraic equations (DAEs) solver can be used and the obtained state and control trajectories can be modified by the numerical optimization procedure step-by-step
Much attention has been paid to the method of limiting the system dynamics in order to enable its numerical simulation
Summary
The dynamic development of engineering systems of parametric models can be observed. The parametric models, built from variables with a known interpretation connected with the equations of the laws of physics, are able to more and more accurately reflect the studied dependencies. The development of this type of model is limited only by the scope of natural science and computing capabilities. The parallel development of the mathematical models and numerical simulation algorithms can be observed in many fields of engineering, in particular in chemical engineering [1] and mechanical engineering [2]. Advanced computational techniques for the process design and optimization can have a positive impact on their quality and profitability
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