A Fourier-based control vector parameterization for the optimization of nonlinear dynamic processes with a finite terminal time

Abstract

In this paper, a novel strategy for finding the optimal operation profiles for nonlinear dynamic processes is developed. Based on the direct sequential stochastic framework for dynamic optimization, this work proposes a technique based on Fourier series for the control vector parameterization, as an alternative to the traditional methods. This approach has the advantage of choosing a high degree of smoothness to avoid sharp changes for the input variables, which is preferred in most chemical and biological processes. On the other hand, when several arcs are present in the qualitative optimal profile, the number of param- eters can be increased for a better approximation. The proposed strategy was applied to four well-studied nonlinear processes, covering batch and fed-batch reactors, and multi-input systems. The algorithm was tested through simulations. Good performances were obtained in comparison to some previous results available in the literature.