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Efficient optimization approaches to nonlinear model predictive control
Author(s) -
Mahadevan R.,
J. Doyle III F.
Publication year - 2003
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.820
Subject(s) - nonlinear system , model predictive control , flatness (cosmology) , control theory (sociology) , nonlinear control , nonlinear programming , mathematical optimization , optimization problem , optimal control , computer science , mathematics , control (management) , artificial intelligence , physics , cosmology , quantum mechanics
Efficient optimization approaches for nonlinear model predictive control (NMPC) are described in this paper. The first approach is based on the differential flatness property of a system of ordinary differential equations. The nonlinear process model is represented in terms of the flat outputs and their derivatives, and the nonlinear dynamic optimization problem is transformed into a nonlinear programming problem, with exact representation of the system dynamics. The approach is illustrated through the control of substrate concentration of a fed‐batch bioreactor. The second approach is motivated by the idea of differential flatness, but is applicable to broader class of nonlinear systems. Here, the nonlinear process model is recast through the elimination of a subset of the system variables. This results in a nonlinear dynamic optimization with a reduced number of system variables that have to be solved for, as well as the dynamic equations. Applications of this approach to the optimization of a recombinant product in a fed‐batch bioreactor and the control of a chemical reactor are presented. Both the approaches discussed in this paper provide up to a five fold improvement in the solution time for the optimization problem as compared to the traditional formulation. Copyright © 2003 John Wiley & Sons, Ltd.