Journal of Industrial and Management Optimization (JIMO)

Optimal control of a parabolic distributed parameter system using a fully exponentially convergent barycentric shifted Gegenbauer integral pseudospectral method
Page number are going to be assigned later 2017

doi:10.3934/jimo.2017056      Abstract        References        Full text (558.1K)      

Kareem T. Elgindy - Mathematics Department, Faculty of Science, Assiut University, Assiut, 71516, Egypt (email)

1 H. Alzer, Sharp upper and lower bounds for the gamma function, Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 139 (2009), 709-718.       
2 J. A. Burns, J. Borggaard, E. Cliff and L. Zietsman, An optimal control approach to sensor/actuator placement for optimal control of high performance buildings, In: International High Performance Buildings Conference, 2012.
3 S. P. Chakrabarty and F. B. Hanson, Distributed parameters deterministic model for treatment of brain tumors using Galerkin finite element method, Mathematical Biosciences, 219 (2009), 129-141.       
4 R.-Y. Chang and S.-Y. Yang, Solution of two-point-boundary-value} problems by generalized orthogonal polynomials and application to optimal control of lumped and distributed parameter systems, International Journal of Control, 43 (1986), 1785-1802.       
5 C.-P. Chen and F. Qi, The best lower and upper bounds of harmonic sequence, RGMIA research report collection, 2003.
6 B. Cushman-Roisin and J. Beckers, Introduction to Geophysical Fluid Dynamics: Physical and Numerical Aspects, 2nd Edition. Vol. 101 of International Geophysics Series. Academic Press, 2011.
7 K. Elgindy, Gegenbauer collocation integration methods: Advances in computational optimal control theory, Bull. Aust. Math. Soc., 89 (2014), 168-170.       
8 K. T. Elgindy, High-order adaptive Gegenbauer integral spectral element method for solving non-linear optimal control problems, Optimization, (2017), 811-836.
9 K. T. Elgindy, High-order numerical solution of second-order one-dimensional hyperbolic telegraph equation using a shifted Gegenbauer pseudospectral method, Numerical Methods for Partial Differential Equations, 32 (2016), 307-349.       
10 K. T. Elgindy, High-order, stable, and efficient pseudospectral method using barycentric Gegenbauer quadratures, Applied Numerical Mathematics, 113 (2017), 1-25.       
11 K. T. Elgindy and K. A. Smith-Miles, Fast, accurate, and small-scale direct trajectory optimization using a Gegenbauer transcription method, Journal of Computational and Applied Mathematics, 251 (2013), 93-116.       
12 K. T. Elgindy and K. A. Smith-Miles, Optimal Gegenbauer quadrature over arbitrary integration nodes, Journal of Computational and Applied Mathematics, 242 (2013), 82-106.       
13 D. R. Gardner, S. A. Trogdon and R. W. Douglass, A modified tau spectral method that eliminates spurious eigenvalues, Journal of Computational Physics, 80 (1989), 137-167.
14 I.-R. Horng and J.-H. Chou, Application of shifted Chebyshev series to the optimal control of linear distributed-parameter systems, International Journal of Control, 42 (1985), 233-241.       
15 G. Mahapatra, Solution of optimal control problem of linear diffusion equations via Walsh functions, IEEE Transactions on Automatic Control, 25 (1980), 319-321.       
16 R. Padhi and S. Balakrishnan, Proper orthogonal decomposition based optimal neurocontrol synthesis of a chemical reactor process using approximate dynamic programming, Neural Networks, 16 (2003), 719-728, Advances in Neural Networks Research: IJCNN '03.
17 M. A. Patterson and A. V. Rao, GPOPS-II: A MATLAB software for solving multiple-phase optimal control problems using hp-adaptive Gaussian quadrature collocation methods and sparse nonlinear programming, ACM Transactions on Mathematical Software (TOMS), 41 (2014), Art. 1, 37 pp.       
18 J. Rad, S. Kazem and K. Parand, Optimal control of a parabolic distributed parameter system via radial basis functions, Communications in Nonlinear Science and Numerical Simulation, 19 (2014), 2559-2567.       
19 W. F. Ramirez, Application of Optimal Control Theory to Enhanced Oil Recovery, Vol. 21. Elsevier, 1987.
20 A. P. Sage and C. C. White, Optimum Systems Control, Prentice Hall, 1977.
21 L. N. Trefethen, Spectral Methods in MATLAB, SIAM, Philadelphia, 2000.       
22 M.-L. Wang and R.-Y. Chang, Optimal control of linear distributed parameter systems by shifted Legendre polynomial functions, Journal of Dynamic Systems, Measurement, and Control, 105 (1983), 222-226.       
23 J.-M. Zhu and Y.-Z. Lu, Application of single-step method of block-pulse functions to the optimal control of linear distributed-parameter systems, International Journal of Systems Science, 19 (1988), 2459-2472.       

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