An algebraic Riccati equation approach to H∞ optimization
Systems & Control Letters
Solvability of general differential algebraic equations
SIAM Journal on Scientific Computing
Stochastic Linear Quadratic Regulators with Indefinite Control Weight Costs
SIAM Journal on Control and Optimization
Singular Control Systems
Neural Network Models: Theory and Projects
Neural Network Models: Theory and Projects
Artificial neural networks for solving ordinary and partial differential equations
IEEE Transactions on Neural Networks
Identification and control of dynamical systems using neural networks
IEEE Transactions on Neural Networks
Training feedforward networks with the Marquardt algorithm
IEEE Transactions on Neural Networks
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In this paper, 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.