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The Newton-Like Properties of the Updating Mechanism of a Model-Reality Differences Algorithm

Rohanin Ahmad, and Mohd Ismail Abd Aziz, (2003) The Newton-Like Properties of the Updating Mechanism of a Model-Reality Differences Algorithm. Matematika, 19 (1). pp. 1-13. ISSN 01278274

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Official URL: http://www.fs.utm.my/matematika/images/stories/matematika/200319106.pdf

Affiliations

Universiti Teknologi Malaysia, Department of Mathematics
Universiti Teknologi Malaysia, Department of Mathematics

Abstract

The Dynamic Integrated Systems Optimization and Parameter Estimation (DISOPE) algorithm is an algorithm for solving nonlinear optimal control problems and is of the gradient descent type. The updating step of DISOPE plays an important role in terminating the iterations of the algorithm and hence in determining its rate of convergence. In this paper, the mechanism was shown to have Newton-like properties and the order convergence established.

Item Type:Journal
Keywords:Composite maps, Newton’s method, Error function, Initial solutions, Order of convergence
Subjects:Q Science, Computer Science
ID Code:5724

[1] R. Ahmad, and B.A.A Mohd Ismail, “The Convergence Analysis of the Updating Mechanism of the Dynamic Integrated Systems Optimization Algorithm,”, Prosiding Simposium Kebangsaan Sains Matematik Ke-10,2002, pg 326-332.

[2] M.S. Bazaraa, H.D. Sherali and C.M. Shetty, “Nonlinear Programming: Theory and Algorithms”, John Wiley and Sons, Inc., New York, 1993.

[3] V.M. Becerra, “Development and Applications of Novel Optimal Control Algorithms”, PhD Thesis, Dept. Of Electrical, Electronics and Information Engineering, City University, London, 1994.

[4] A.E. Bryson and Y.C. Ho, “Applied Optimal Control”, Hemisphere Publishing Corporation, Washington D¿C., 1975.

[5] J.L Buchanan and P.R. Turner, “Numerical Methods and Analysis”, McGraw-Hill, Inc., New York, 1992.

[6] J.C. Craig, “, Introduction to Robotics”, Addison-Wesley, Reading, USA, 1989.

[7] W.Gautschi, “Numerical Analysis”, Birkhuser, Boston, 1997.

[8] D.E.Kirk, “, Optimal Control Theory”, Prentice-Hall Inc., Englewood Cliffs, 1970.

[9] E. Polak, “Optimization: Algorithms and Consistent Approximations”,Springer-Verlag New York Inc., New York, 1997.

[10] P.D. Roberts, “An Algorithm for Optimal Control of Nonlinear Systems with Model- Reality Differences”, Proceedings of 12th IFAC World Congress on Automatic Control, 8(1993), 407-412.

[11] P.D. Roberts, “Two-Dimensional Analysis of an Iterative Nonlinear Optimal Control Algorithm”, IEEE Transactions on Circuits and Systems-I: Fundamental Theory and Applications. 49: No. 6, (2002), 872-878.

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