Optimal control for stochastic linear quadratic singular system using neural networks

In this paper, optimal control for stochastic linear 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 well known traditional Runge–Kutta (RK) method and nontraditional neural network method. To obtain the optimal control, the solution of MRDE is computed by feed forward neural network (FFNN). 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.