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Optimal control of linear and nonlinear systems by two‐level optimization
Author(s) -
Robertson Grant E.,
Hawkins David J.,
Luus Rein
Publication year - 1971
Publication title -
the canadian journal of chemical engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.404
H-Index - 67
eISSN - 1939-019X
pISSN - 0008-4034
DOI - 10.1002/cjce.5450490522
Subject(s) - optimal control , nonlinear system , control theory (sociology) , decomposition , convergence (economics) , computation , mathematical optimization , quadratic equation , linear system , mathematics , optimization problem , computer science , control (management) , algorithm , ecology , mathematical analysis , physics , geometry , quantum mechanics , artificial intelligence , economics , biology , economic growth
The decomposition of a system into simpler subsystems, followed by the optimization of the individual subsystems, and then co‐ordinating the subsystem optimal solutions to yield the optimal control policy for the original system, is considered. Lasdon's co‐ordination algorithm, in which the subsystems are regarded as being completely independent, is improved by including the interdependence of the adjacent subsystems. For linear systems with a quadratic performance index, this procedure yields the optimal control policy in a single iteration from an arbitrary initial guess of the decomposition parameters. For nonlinear systems, the method includes linearizing the state equations, the calculation of the optimal control for the linearized system, and the adjustment of the corresponding decomposition parameters of the original problem until convergence is achieved. For the optimization of a nonlinear continuous stirred tank reactor such a procedure requires considerably more computation time than the standard techniques, and the optimum policies are less accurate.