Optimal control for nonlinear singular systems with quadratic performance using neural networks

Abstract

In this paper, optimal control for nonlinear singular system with quadratic performance is obtained using neural networks. This control is in the form of a state feedback function plus a time function. Furthermore, the main feature is that optimality is always preserved by this control; hence, this control is called a quasi-feedback optimal control. To obtain the optimal control, the solution of matrix Riccati differential equation (MRDE) is obtained by feedforward neural network (FFNN). Accuracy of the neural network solution to the optimal control problem is qualitatively better than Runge–Kutta (RK) solution. 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. A numerical example is presented to illustrate the implementation of artificial neural networks (ANN) to obtain optimal control.