Moment Vector Equation for Nonlinear Systems and Its Application to Optimal Control

Hideki SATOH  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E92-A   No.10   pp.2522-2530
Publication Date: 2009/10/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E92.A.2522
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Nonlinear Theory and its Applications)
Category: Nonlinear Problems
nonlinear,  MVE,  linearization,  linear quadratic,  optimal control,  

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A method was developed for deriving the control input for a multi-dimensional discrete-time nonlinear system so that a performance index is approximately minimized. First, a moment vector equation (MVE) is derived; it is a multi-dimensional linear equation that approximates a nonlinear system in the whole domain of the system state and control input. Next, the performance index is approximated by using a quadratic form with respect to the moment vector. On the basis of the MVE and the quadratic form, an approximate optimal controller is derived by solving the linear quadratic optimal control problem. A bilinear optimal control problem and a mountain-car problem were solved using this method, and the solutions were nearly optimal.