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Optimal control for stochastic nonlinear singular system using neural networks. (English) Zbl 1165.93343
Summary: Optimal control for stochastic nonlinear singular system with quadratic performance is obtained using neural networks. The goal is to provide optimal control with reduced calculus effort by comparing the solutions of the matrix Riccati differential equation (MRDE) obtained from the well-known traditional Runge-Kutta (RK) method and nontraditional neural network method. To obtain the optimal control, the solution of MRDE is computed by feedforward neural network (FFNN). The 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. 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:
 93E20 Optimal stochastic control (systems) 60H35 Computational methods for stochastic equations 62M45 Neural nets and related approaches (inference from stochastic processes) 49N10 Linear-quadratic optimal control problems 65L06 Multistep, Runge-Kutta, and extrapolation methods
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