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Zbl 1107.65057
Balasubramaniam, P.; Abdul Samath, J.; Kumaresan, N.; Kumar, A.Vincent Antony
Solution of matrix Riccati differential equation for the linear quadratic singular system using neural networks. (English)
[J] Appl. Math. Comput. 182, No. 2, 1832-1839 (2006). ISSN 0096-3003

Summary: The solution of the matrix Riccati differential equation (MRDE) for the linear quadratic singular system is obtained using neural networks. The goal is to provide optimal control with reduced calculus effort by comparing the solutions of the MRDE obtained from well-known traditional methods like Runge-Kutta, Runge-Kutta Butcher and non-traditional method neural network. The neural training is performed using Levenberg-Marquardt algorithm. Accuracy of the solution of the neural network approach to the 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. An illustrative numerical example for the proposed method is given.

MSC 2000:: *65L05 Initial value problems for ODE (numerical methods)
65L06 Multistep, Runge-Kutta, and extrapolation methods
34A30 Linear ODE and systems
68T05 Learning and adaptive systems

Keywords: optimal control; Runge-Kutta method; Runge-Kutta Butcher method; matrix Riccati differential equation; Levenberg-Marquardt algorithm; numerical example

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