International Journal of Mathematics Trends and Technology
Volume 26 | Number 1 | Year 2015 | Article Id. IJMTT-V26P503 | DOI : https://doi.org/10.14445/22315373/IJMTT-V26P503
In this article, the problem of optimal control of time-varying singular systems with quadratic performance index has been studied via Adomian Decomposition Method (ADM). The results obtained via RK-Butcher algorithm (RKB)[10] and ADM are compared with the exact solutions of the time-varying optimal control of linear singular systems. It is observed that the results obtained using ADM is closer to the true solution of the problem. Error graphs for the simulated results and exact solutions are presented in graphical form to highlight the efficiency of the ADM. This ADM can be easily implemented in a digital computer and the solution can be obtained for any length of time.
[1] G. Adomian, “Solving Frontier Problems of Physics: Decomposition method”, Kluwer, Boston, MA, 1994.
[2] K. Balachandran and K. Murugesan, “Optimal control of singular systems via single-term Walsh series”, International Journal Computer Mathematics, 43 (1992), 153-159.
[3] J. C. Butcher, “The Numerical Methods for Ordinary Differential Equations”, 2003, John Wiley & Sons, U.K.
[4] C. F. Chen and C. H. Hsiao, “Walsh series analysis in optimal control”, Int. J. Control, 21, (1975), 881-897.
[5] W. L. Chen and Y. P. Shih, “Analysis and optimum control of time varying linear systems via Walsh functions”, Int. J. Control, 27, (1978), 917-932.
[6] D. Cobb, “Descriptor variable systems and optimal state regulation”, IEEE Trans. Auto. Control, 28, (1983), 601-611. [7] H. Maurer, “Numerical solution of singular control problems using multiple shooting techniques”, J. Optim. Theory Appl., 18(2) (1976), 235257.
[8] H. J. Oberle, “Numerical computation of singular control functions intrajectory optimization problems”, J. Guidance Control Dynam., 13(1) (1990), 153159.
[9] L. Pandolfi, “On the regulator problem for linear degenerate control systems”, J. Optimization Theory and Appl., 33 (1981), 241-254.
[10] J. Y. Park, David J. Evans, K. Murugesan and S. Sekar, “Optimal control of time-varying singular systems using the RK-Butcher algorithm”, International Journal of Computer Mathematics, Vol. 82, No. 5, 2005, pp. 617-627.
[11] H. J. Pesch, “A practical guide to the solution of real-life optimal control problems”, Control Cybernet., 23(1-2) (1994), 760.
[12] M. Razzaghi and H. Marzban, “Optimal control of singular systems via piecewise linear polynomial functions”, Mathematical Methods in the Applied Sciences, 25 (2002), 399-408.
[13] S. Sekar and A. Kavitha, “Numerical Investigation of the Time Invariant Optimal Control of Singular Systems Using Adomian Decomposition Method”, Applied Mathematical Sciences, vol. 8, no. 121, pp. 6011-6018, 2014.
[14] S. Sekar and A. Kavitha, “Analysis of the linear timeinvariant Electronic Circuit using Adomian Decomposition Method”, Global Journal of Pure and Applied Mathematics, vol. 11, no. 1, pp. 10-13, 2015.
[15] S. Sekar and M. Nalini, “Numerical Analysis of Different Second Order Systems Using Adomian Decomposition Method”, Applied Mathematical Sciences, vol. 8, no. 77, pp. 3825-3832, 2014.
[16] S. Sekar and M. Nalini, “Numerical Investigation of Higher Order Nonlinear Problem in the Calculus of Variations Using Adomian Decomposition Method”, IOSR Journal of Mathematics, vol. 11, no. 1 Ver. II, (Jan-Feb. 2015), pp. 74- 77.
[17] S. Sekar and M. Nalini, “A Study on linear time-invariant Transistor Circuit using Adomian Decomposition Method”, Global Journal of Pure and Applied Mathematics, vol. 11, no. 1, pp. 1-3, 2015.
S. Sekar, A. Kavitha, "Numerical Study of the Optimal Control of time-varying Singular Systems via Adomian Decomposition Method," International Journal of Mathematics Trends and Technology (IJMTT), vol. 26, no. 1, pp. 9-12, 2015. Crossref, https://doi.org/10.14445/22315373/IJMTT-V26P503
PDF 
Abstract 
Keywords 
References 
Citation