Numerical Time-Scale Separation for Rotorcraft Nonlinear Optimal Control Analyses

Kim, Chang-Joo; Sung, Sangkyung; Park, Soo Hyung; Jung, Sung Nam; Park, Tae San

doi:10.2514/1.59557

Cited by 19 publications

(20 citation statements)

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“…This kind of distribution can be inconvenient in some problems with rapid variations in function values around the midpoint of the computational domain, as shown in [11]. In addition, conventional quadrature weights and matrices for the integration and differentiation might be inadequate for good convergence in the iterative solution processes as the number of nodes is increased [11,15]. Spline interpolation combined with the present approaches to the CQFs can be a good alternative allowing an adaptive selection of nodes considering the solution properties.…”

Section: Extension To Spline Interpolationmentioning

confidence: 99%

“…The traditional quadrature nodes are highly clustered around two end points to preserve extreme accuracy, and there is no flexibility in adjusting their spacing. This kind of distribution can be inconvenient in some problems with rapid variations in function values around the midpoint of the computational domain, as shown in [11]. In addition, conventional quadrature weights and matrices for the integration and differentiation might be inadequate for good convergence in the iterative solution processes as the number of nodes is increased [11,15].…”

Section: Extension To Spline Interpolationmentioning

confidence: 99%

“…With the given set of . [11] showed the effect of the leading order, K, with the selection of the third-order transformation being recommended, since it provides the best integration accuracy for the series of polynomial test functions. The formulas for integration and differentiation can be defined easily in the transformed domain using (64) as However, it is not a simple task to find such interpolating functions with the required accuracy in real applications.…”

Section: Extension To Spline Interpolationmentioning

confidence: 99%

“…The G-SPIN formula allows multiple differentiation to get the p th derivatives of the function at each node, as shown in (10) and (11). If the components of the matrix…”

Section: Unified Quadrature Formulas Using Spline Interpolationmentioning

confidence: 99%

“…For this purpose, two different sets of nodes are considered. One is generated using the coordinate transformation devised by the authors [11] for more uniformly distributed nodes than those obtained using the traditional spectral method. The other is a set of uniform nodes known as the worst possible choice for polynomial interpolation, with which the derived formulas are extremely inaccurate as mentioned in [4] and [12].…”

Section: Introductionmentioning

confidence: 99%

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A New Unified Scheme Computing the Quadrature Weights, Integration and Differentiation Matrix for the Spectral Method

Kim¹,

Park²,

Sung³

2015

Journal of Electrical Engineering and Technology

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-A unified numerical method for computing the quadrature weights, integration matrix, and differentiation matrix is newly developed in this study. For this purpose, a spline-like interpolation using piecewise continuous polynomials is converted into a global spline interpolation formula, with which the quadrature formulas can be derived from integration and differentiation of the transformed function in an exact manner. To prove the usefulness of the suggested approach, both the Lagrange and tension spline interpolations are represented in exactly the same form as global spline interpolation. The applicability of the proposed method on arbitrary nodes is illustrated using two different sets of nodes. A series of validations using three test functions is conducted to show the flexibility in selecting computational nodes with the present method.

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Section: Extension To Spline Interpolationmentioning

confidence: 99%

Section: Extension To Spline Interpolationmentioning

confidence: 99%

Section: Extension To Spline Interpolationmentioning

confidence: 99%

“…The G-SPIN formula allows multiple differentiation to get the p th derivatives of the function at each node, as shown in (10) and (11). If the components of the matrix…”

Section: Unified Quadrature Formulas Using Spline Interpolationmentioning

confidence: 99%