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Solution of generalized matrix Riccati differential equation for indefinite stochastic linear quadratic singular fuzzy system with cross-term using neural networks

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Abstract

In this paper, solution of generalized matrix Riccati differential equation (GMRDE) for indefinite stochastic linear quadratic singular fuzzy system with cross-term is obtained using neural networks. The goal is to provide optimal control with reduced calculus effort by comparing the solutions of GMRDE obtained from well-known traditional Runge Kutta (RK) method and nontraditional neural network method. To obtain the optimal control, the solution of GMRDE is computed by feed forward neural network (FFNN). Accuracy of the solution of the neural network approach to this problem is qualitatively better. The advantage of the proposed approach is that, once the network is trained, it allows instantaneous evaluation of solution at any desired number of points spending negligible computing time and memory. The computation time of the proposed method is shorter than the traditional RK method. An illustrative numerical example is presented for the proposed method.

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Acknowledgments

The author is very much thankful to the referees for their valuable comments and suggestions for improving this manuscript. The funding of this work by the UMRG grant (Account No: RG099/10AFR) is gratefully acknowledged.

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  1. Faculty of Science, Institute of Mathematical Sciences, University of Malaya, Kuala Lumpur, 50603, Malaysia

    N. Kumaresan

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  1. N. Kumaresan
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Correspondence to N. Kumaresan.

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Kumaresan, N. Solution of generalized matrix Riccati differential equation for indefinite stochastic linear quadratic singular fuzzy system with cross-term using neural networks. Neural Comput & Applic 21, 497–503 (2012). https://doi.org/10.1007/s00521-010-0431-3

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  • DOI: https://doi.org/10.1007/s00521-010-0431-3

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