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		Jalal NAZARZADEH,Hamidreza RADMANESH.[en_title][J].Control Theory and Technology,2011,9(4):487~492.[Copy]

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JalalNAZARZADEH,HamidrezaRADMANESH
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(Department of Electrical Engineering, Shahed University)

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Received:March 13, 2010Revised:September 28, 2010

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Hybrid extended Fourier series for optimal control of nonlinear algebraic dynamical systems

Jalal NAZARZADEH,Hamidreza RADMANESH

(Department of Electrical Engineering, Shahed University)

Abstract:

The paper introduces a new method for finding optimal control of algebraic dynamic systems. The structure of algebraic dynamical systems is nonlinear with quadratic and bilinear terms. A new hybrid extended Fourier series is introduced, and state and control variables of the system are expanded by this series. Moreover, properties of new series are presented, and integration and product operational matrices are obtained. Using operational matrices, optimal control of the systems is converted to a set of simultaneous nonlinear algebraic relations. An illustrative example is included to compare our results with those in the literature.

Key words: Bilinear systems Hybrid extended Fourier series Nonlinear algebraic dynamic systems Quadratic systems Optimal control