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GEGENBAUER COLLOCATION INTEGRATION METHODS: ADVANCES IN COMPUTATIONAL OPTIMAL CONTROL THEORY

Part of: Existence theories Numerical approximation and computational geometry Numerical methods in calculus of variations and optimal control Partial differential equations, initial value and time-dependent initial-boundary value problems

Published online by Cambridge University Press:  05 February 2014

KAREEM ELGINDY
KAREEM ELGINDY*
Affiliation:
School of Mathematical Sciences, Monash University, Clayton, Victoria 3800, Australia email kareem.elgindy@monash.edu, kareem.elgindy@gmail.com
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Abstract

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Keywords

Chebyshev polynomialscollocation pointsdirect optimisation methodsGegenbauer collocation integration methodGegenbauer polynomialsGegenbauer quadratureLegendre polynomials

MSC classification

Secondary: 49J15: Optimal control problems involving ordinary differential equations 49M37: Methods of nonlinear programming type 65D30: Numerical integration 65D32: Quadrature and cubature formulas 65M70: Spectral, collocation and related methods
Type
Abstracts of Australasian PhD Theses
Information
Bulletin of the Australian Mathematical Society , Volume 89 , Issue 1 , February 2014 , pp. 168 - 170
Copyright
Copyright © 2014 Australian Mathematical Publishing Association Inc. 

References

Elgindy, K. T. and Smith-Miles, K. A., ‘Solving boundary value problems, integral, and integro-differential equations using Gegenbauer integration matrices’, J. Comput. Appl. Math. 237 (2013), 307–325.CrossRefGoogle Scholar
Elgindy, K. T. and Smith-Miles, K. A., ‘Optimal Gegenbauer quadrature over arbitrary integration nodes’, J. Comput. Appl. Math. 242 (2013), 82–106.Google Scholar
Elgindy, K. T. and Smith-Miles, K. A., ‘Fast, accurate, and small-scale direct trajectory optimization using a Gegenbauer transcription method’, J. Comput. Appl. Math. 251 (2013), 93–116.CrossRefGoogle Scholar
Elgindy, K. T. and Smith-Miles, K. A., ‘On the optimization of Gegenbauer operational matrix of integration’, Adv. Comput. Math. 39 (2013), 511–524.CrossRefGoogle Scholar
Elgindy, K. T.Smith-Miles, K. A. and Miller, B., ‘Solving optimal control problems using a Gegenbauer transcription method’, 2nd Australian Control Conference (AUCC), University of New South Wales. Sydney, 15–16 November 2012 (I.R. Peterson and Sarkin) (Engineers Australia and IEEE Xplore, 2012), 417–424.Google Scholar