Orthogonal Functions in Systems and Control

Datta, K. B.; Mohan, B.M.

doi:10.1142/2476

Cited by 125 publications

(68 citation statements)

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“…In such situations, neither the continuous basis functions nor piecewise constant basis functions taken alone would form an efficient basis in the representation of such solutions. Datta and Mohan [27] have correctly pointed out that, in general, the computed response of the delay systems via continuous or piecewise constant basis functions is not in good agreement with the exact response of the system. To meet these situations, we choose a suitable hybrid system of basis functions inherently possessing the required features of the solutions corresponding to delay systems.…”

Section: Main Feature Of the Methodsmentioning

confidence: 99%

Optimal Control of Delay Systems by Using a Hybrid Functions Approximation

Haddadi

Ordokhani

Razzaghi

2011

J Optim Theory Appl

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In this paper, a new numerical method for solving the optimal control of linear time-varying delay systems with quadratic performance index is presented. The method is based upon hybrid functions approximation. The properties of hybrid functions, consisting of block-pulse functions and Bernoulli polynomials, are presented. The operational matrices of integration, product, delay and the integration of the cross product of two hybrid functions of block-pulse and Bernoulli polynomials vectors are given. These matrices are then utilized to reduce the solution of the optimal control of delay systems to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique.

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Section: Main Feature Of the Methodsmentioning

confidence: 99%

Optimal Control of Delay Systems by Using a Hybrid Functions Approximation

Haddadi

Ordokhani

Razzaghi

2011

J Optim Theory Appl

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“…1. The results obtained via Lagrange polynomials [4], Triangular function [11] and adaptive Legendre-Gauss-Radau collocation method [17] are to that shown in Table 1. We mention in [17], N is the number of subintervals of the adaptive collocation method.…”

Section: Illustrative Examplesmentioning

confidence: 53%

“…In general, the computation of the delay systems via orthogonal functions is not in good agreement with the exact response of the system [19]. Special attention has been given to such applications as Walsh functions [3], hybrid functions [4] and Triangular functions [11]. Special attention has been given to applications of wavelets [6], Adomian decomposition method (ADM) [2], homotopy perturbation method (HPM) [15], recurrent neural networks (RNN) [33] and others.…”

Section: Introductionmentioning

confidence: 99%

Solution of linear time-varying multi-delay systems via variational iteration method

Mirhosseini-Alizamini¹,

Effati²,

Heydari³

2016

J. Math. Computer Sci.

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This work presents an approximate solution method for the linear time-varying multi-delay systems and time delay logistic equation using variational iteration method. The method is based on the use of Lagrange multiplier for identification of optimal value of a parameter in a functional. This procedure is a powerful tool for solving large amount of problems. Also, it provides a sequence which converges to the solution of the problem without discretization of the variables. In this study, an idea is proposed that accelerates the convergence of the sequence which results from the variational iteration formula for solving systems of delay differential equations. Illustrative examples are included to demonstrate the validity and applicability of the technique.

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“…is usually selected as standard orthonormal functions such as Fourier series, Legendre polynomials, Jacobi polynomials, and Chebyshev polynomials [26]. In this study, the KL decomposition [27][28][29][30] is chosen to identify the empirical spatial basis functions from the set of output data y(x j , t)x j ∈ , j = 1, .…”

Section: Spatio-temporal Volterra Seriesmentioning

confidence: 99%

Wavelet basis expansion-based spatio-temporal Volterra kernels identification for nonlinear distributed parameter systems

et al. 2014

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In practical industries, there are many systems belong to nonlinear distributed parameter systems (DPS); unfortunately, modeling of nonlinear DPS is a challenging task because of the infinite-dimensional and nonlinear properties. To model the nonlinear DPS, a spatio-temporal Volterra model is presented with a series of spatio-temporal kernels. It can be considered as a spatial extension of the traditional Volterra model. One question involved in modeling a spatiotemporal functional relationship between the input and output of nonlinear distributed parameter systems using spatio-temporal Volterra series is to identify the spatiotemporal Volterra kernel functions. In addition, in order to derive a low-order model, the Karhunen-Loève (KL) decomposition is used for the time/space separation. The basic routine of the approach is that, first, from the system outputs, KL decomposition is used for the time/space separation, where the spatio-temporal output is decomposed into a few dominant spatial basis functions with temporal coefficients. Second, according to temporal coefficients of outputs under multilevel excitations, the Volterra series outputs of different orders are estimated with the wavelet balance method. Third, the Volterra kernel functions of different orders are separately estimated through their

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Orthogonal Functions in Systems and Control

Cited by 125 publications

References 0 publications

Optimal Control of Delay Systems by Using a Hybrid Functions Approximation

Optimal Control of Delay Systems by Using a Hybrid Functions Approximation

Solution of linear time-varying multi-delay systems via variational iteration method

Wavelet basis expansion-based spatio-temporal Volterra kernels identification for nonlinear distributed parameter systems

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