NDLI: Computational method for the optimal control problem for the Korteweg-de Vries equation

Content Provider	IEEE Xplore Digital Library
Author	Xingong Cheng Xiju Zong Yongfeng Zhang
Copyright Year	2012
Description	Author affiliation: School of Control Science and Engineering, University of Jinan, Jinan, Shandong, China, 250022 (Xingong Cheng; Xiju Zong; Yongfeng Zhang)
Abstract	Pointwise control of the periodic Korteweg-de Vries(K-dV) equation on domain [0, 2π] is considered with the objective of minimizing the distance between the final state function and target profile along with the energy of the control. An efficient computational method is proposed for solving such problems, which is based on special orthonormal functions that satisfy the associated boundary conditions. Employing these orthonormal functions as a basis of a modal expansion method, the solution space is limited to the smallest lower subspace that is sufficient to describe the original problem. Consequently, the K-dV equation is reduced to a set of a minimal number of ordinary nonlinear differential equations. Thus, by the modal expansion method, the optimal control of a distributed parameter system described by the K-dV equation is converted to the optimal control of lumped parameter dynamical systems in finite dimension. The time-variant control is approximated by a finite term of the Fourier series whose unknown coefficients and frequencies giving an optimal solution are sought, thereby converting the optimal control problem into a mathematical programming problem. The solution space obtained is based on control parametrization by using the Runge-Kutta method. The efficiency of the proposed method is examined using a numerical example for various target functions.
Starting Page	1223
Ending Page	1227
File Size	208316
Page Count	5
File Format	PDF
ISBN	9781467325813
ISSN	21612927
e-ISBN	9789881563811
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2012-07-25
Publisher Place	China
Access Restriction	Subscribed
Rights Holder	Chinese Assoc of Automati
Subject Keyword	Korteweg-de Vries(K-dV) equation Control parametrization Optimal control Aerospace electronics Boundary conditions Controllability Eigenvalues and eigenfunctions Model expansion technique Mathematical model Equations
Content Type	Text
Resource Type	Article

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