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Approximation in control of nonlinear dynamic systems
Author(s) -
Tsang A. C. C.,
Luus Rein
Publication year - 1973
Publication title -
aiche journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.958
H-Index - 167
eISSN - 1547-5905
pISSN - 0001-1541
DOI - 10.1002/aic.690190218
Subject(s) - mathematics , scalar (mathematics) , optimal control , quadratic equation , riccati equation , matrix (chemical analysis) , linear quadratic gaussian control , control theory (sociology) , mathematical optimization , mathematical analysis , computer science , differential equation , control (management) , materials science , geometry , artificial intelligence , composite material
The type of system approximation in which the system state space x is mapped into a scalar domain V by a quadratic transformation\documentclass{article}\pagestyle{empty}\begin{document}$$ \begin{array}{*{20}c} {\rm V} & = & {\frac{1}{2}{\rm x}'{\rm Qx}} \\ \end{array} $$\end{document}where Q is appropriately determined, is used to develop a suboptimal control procedure for unconstrained lumped parameter dynamic systems via the application of Pontryagin's Maximum Principle. The optimization problem in the scalar domain becomes an initial value problem when the scalar adjoint variable is held constant through out the course of control. The resulting computational scheme includes an effective and simple way to construct the transformation matrix Q and a straightforward minimum seeking approach to locate the best constant overall average scalar adjoint parameter. For the class of problems with quadratic performance index, system equation approximation further reduces the determination of Q to the solution of a matrix Riccati equation. The application of the proposed suboptimal control procedure to four chemical engineering systems shows that the procedure is simple direct, and efficient and works particularly well for problems where the final time is large.