Optimal control of a parabolic distributed parameter system via orthogonal polynomials

Sadek, Ibrahim; Bokhari, M. A.

doi:10.1002/(sici)1099-1514(199805/06)19:3<205::aid-oca613>3.3.co;2-n

Cited by 9 publications

(9 citation statements)

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“…Some popular global basis functions include Fourier series, orthogonal polynomials [11] and eigenfunctions of system [9], [12]. Because the not lowest model dimension of spectral based model, principal interaction patterns (PIP) have been developed by K.Hasselmann [13].…”

Section: Introductionmentioning

confidence: 99%

Low-dimensional approximation strategy for a class of nonlinear distributed parameter systems

Jiang

Deng

2011

2011 Second International Conference on Mechanic Automation and Control Engineering

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a new low-dimensional approximation strategy is proposed for a class of nonlinear distributed parameter systems (DPS) with nonlinear uncertainties. Firstly, spectral method is used to obtain spectral based model with nominal nonlinear terms of DPS. After neglecting the nonlinear terms of the spectral based model, balanced truncation model reduction is carried out to obtain a balanced transform matrix and reduced linear terms. Lastly, a low-dimensional hybrid intelligent neural network model is used to identify spectral based model, while neural network is trained to approximate uncertain nonlinear terms. The simulation for spatiotemperature evolution of catalytic rod are presented to show the effectiveness of this low dimensional approximation strategy.

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Section: Introductionmentioning

confidence: 99%

Low-dimensional approximation strategy for a class of nonlinear distributed parameter systems

Jiang

Deng

2011

2011 Second International Conference on Mechanic Automation and Control Engineering

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“…The most popular is the Riccati method for quadratic cost functions however this method results in a set of usually complicated differential equations which must be solved recursively [1]. In the last few decades orthogonal functions have been extensively used in obtaining an approximate solution of problems described by differential equations [2][3][4] . The approach, also known as the spectral method [5] , is based on converting the differential equations into an integral equation through integration.…”

Section: Introductionmentioning

confidence: 99%

Closed Form Solution to an Optimal Control Problem by Orthogonal Polynomial Expansion

Tavallaei¹,

Tousi²

2008

American J. of Engineering and Applied Sciences

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Abstract:In this study the use of orthogonal polynomials for obtaining a close form solution to optimal control problems with a weighed quadratic cost function, is proposed. The method consists of using the Orthogonal Polynomials for the expansion of the state variables and the control signal. This expansion results in a set of linear equations, from which the closed form solution is obtained. A numerical example is provided to demonstrate the applicability and effectiveness of the proposed method.

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“…In some of these approaches, the methods based on spectral decomposition techniques have been appear in [11][12][13][14][15][16]. In [17][18][19][20], the infinite-dimensional DPS were controlled by representing DPS with their dominant finitedimensional modes such as eigenfunctions or singular functions.…”

Section: Introductionmentioning

confidence: 99%

Feedback control for parabolic distributed parameter systems with time-delay

Xing

Zhao

Wang

2008

2008 7th World Congress on Intelligent Control and Automation

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The feedback control problem for the parabolic distributed parameter systems without or with time-delay are investigated. The system model contains convection terms. Firstly, the feedback control law is designed for a class of the parabolic distributed parameter systems without time delay. Then this result is extendHG to the case with time delay and the feedback control law is designed for a class of the parabolic distributed parameter systems with time delay. At last, the simulation examples are presented to illustrate effectiveness of the proposed methods. Index Terms-distributed parameter systems. Feedback control. Stability. time-delay.

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Optimal control of a parabolic distributed parameter system via orthogonal polynomials

Cited by 9 publications

References 0 publications

Low-dimensional approximation strategy for a class of nonlinear distributed parameter systems

Low-dimensional approximation strategy for a class of nonlinear distributed parameter systems

Closed Form Solution to an Optimal Control Problem by Orthogonal Polynomial Expansion

Feedback control for parabolic distributed parameter systems with time-delay

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