An application of rationalized Haar functions to solution of linear differential equations

Ohkita, Masaaki; Kobayashi, Yasuhiro

doi:10.1109/tcs.1986.1086019

Cited by 50 publications

(27 citation statements)

References 3 publications

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“…If each waveform is divided into eight intervals, the magnitude of the waveform can be represented as [19] b U kÂk can be expressed as b U kÂk ¼ ½Uð1=2kÞ; Uð3=2kÞ; . .…”

Section: Function Approximationmentioning

confidence: 99%

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Rationalized Haar approach for nonlinear constrained optimal control problems

Marzban

Razzaghi

2010

Applied Mathematical Modelling

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a b s t r a c tThis paper presents a numerical method for solving nonlinear optimal control problems including state and control inequality constraints. The method is based upon rationalized Haar functions. The differential and integral expressions which arise in the system dynamics, the performance index and the boundary conditions are converted into some algebraic equations which can be solved for the unknown coefficients. Illustrative examples are included to demonstrate the validity and applicability of the technique.

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“…If each waveform is divided into eight intervals, the magnitude of the waveform can be represented as [19] b U kÂk can be expressed as b U kÂk ¼ ½Uð1=2kÞ; Uð3=2kÞ; . .…”

Section: Function Approximationmentioning

confidence: 99%

“…Refs. [19][20][21][22] applied the RH functions to solve differential and integral equations. Haar functions are notable for their rapid convergence for the expansion of functions, and this capability makes them very useful in regard to the wavelets theory.…”

Section: Introductionmentioning

confidence: 99%

Rationalized Haar approach for nonlinear constrained optimal control problems

Marzban

Razzaghi

2010

Applied Mathematical Modelling

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“…However, the problems considered so far for orthogonal functions-based solutions include response analysis, optimal control, parameter estimation, model reduction, controller design, and state estimation. They have been applied to linear time-invariant and time-varying systems, nonlinear and distributed parameter systems, which include scaled systems, stiff systems, delay systems, singular systems and multivariable systems [16].…”

Section: Introductionmentioning

confidence: 99%

Vibration Control of a Base-Isolated Building using Wavelets

Karimi

2011

IFAC Proceedings Volumes

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This paper proposes a numerical approach for finding an optimal control based on wavelet functions for vibration reduction of a base-isolated building subjected to actual earthquakes. The objective is two-fold: (1) to find a computational method using properties of Haar functions, and (2) to calculate controller gains approximately by solving only algebraic equations instead of solving the Riccati differential. Simulation results are included to demonstrate the validity and applicability of the technique.

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Section: Introductionmentioning

confidence: 99%

Wavelet-Based Optimal Control of a Wind Turbine System: A Computational Approach

Karimi

2011

JAMDSM

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This paper deals with a computational optimization approach to the problem of state-feedback control design for a wind turbine system. The first step of the study is to develop a reduced order model for the system by considering the most important physical phenomena of aerodynamics and structural dynamics. Moreover, the behavior of the system can be influenced by the coupled dynamics between the tower motions and the blade pitch and turbine speed which can cause instabilities in the control loops in the worst case. By using a suitable wavelet funcation, called Haar functions, a recursive computational procedure is established for finding the system dynamics approximately by solving only algebraic equations instead of solving the Riccati differential. Simulation results are given to illustrate the usefulness of the proposed control methodology.

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An application of rationalized Haar functions to solution of linear differential equations

Cited by 50 publications

References 3 publications

Rationalized Haar approach for nonlinear constrained optimal control problems

Rationalized Haar approach for nonlinear constrained optimal control problems

Vibration Control of a Base-Isolated Building using Wavelets

Wavelet-Based Optimal Control of a Wind Turbine System: A Computational Approach

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