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Solution of matrix Riccati differential equation for nonlinear singular system using genetic programming

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Abstract

In this paper, we propose a novel approach to find the solution of the matrix Riccati differential equation (MRDE) for nonlinear singular systems using genetic programming (GP). The goal is to provide optimal control with reduced calculation effort by comparing the solutions of the MRDE obtained from the well known traditional Runge Kutta (RK) method to those obtained from the GP method. We show that the GP approach to the problem is qualitatively better in terms of accuracy. Numerical examples are provided to illustrate the proposed method.

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Acknowledgements

The authors are very much thankful for the referees for the valuable comments and suggestions for improving the manuscript in this format. The work of the authors was supported by the DST Project Grant No. SR/S4/MS:485/07 New Delhi, India.

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Authors and Affiliations

  1. Department of Mathematics, Gandhigram Rural University, Gandhigram, 624 302, Tamilnadu, India

    P. Balasubramaniam

  2. Department of Computer Science and Applications, PSNA College of Engineering and Technology, Dindigul, 624 622, Tamilnadu, India

    A. Vincent Antony Kumar

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  1. P. Balasubramaniam
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Correspondence to A. Vincent Antony Kumar.

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Balasubramaniam, P., Vincent Antony Kumar, A. Solution of matrix Riccati differential equation for nonlinear singular system using genetic programming. Genet Program Evolvable Mach 10, 71–89 (2009). https://doi.org/10.1007/s10710-008-9072-z

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  • DOI: https://doi.org/10.1007/s10710-008-9072-z

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