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Solution of generalized matrix Riccati differential equation for indefinite stochastic linear quadratic singular system using neural networks. (English) Zbl 1157.65397
Summary: The solution of a generalized matrix Riccati differential equation (GMRDE) for an indefinite stochastic linear quadratic singular system is obtained using neural networks. The goal is to provide an optimal control with reduced calculus effort by comparing the solutions of GMRDE obtained from the well known traditional Runge Kutta (RK) method and a nontraditional neural network method.
To obtain the optimal control, the solution of the GMRDE is computed by a feed forward neural network (FFNN). The accuracy of the solution of the neural network approach to the problem is qualitatively better. The neural network solution is also compared with the solution of ode45, a standard solver available in MATLAB which implements the RK method for a variable step size.
The advantage of the proposed approach is that, once the network is trained, it allows an instantaneous evaluation of the 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.

MSC:
65K10 Numerical optimization and variational techniques
49N10 Linear-quadratic optimal control problems
49J55 Existence of optimal solutions to problems involving randomness
65C30 Numerical solutions to stochastic differential and integral equations
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
Software:
Matlab
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