Optimal control of nonlinear systems using Multi-Layer Perceptron Neural Network and adaptive extended Kalman Filter

In this paper we present a nonlinear optimal control method based on approximating the solution of Hamilton-Jacobi-Bellman (HJB) equation. Value function is approximated as the output of Multilayer Perceptron Neural Network (MLPNN). Parameters of MLPNN are weights and biases of each layer that form structure of the proposed neural network. These parameters are unknown thus we apply an Adaptive Extended Kalman Filter to approximate unknown parameters. In so doing, the problem of solution of HJB equation is converted to estimation of MLPNN parameters. Also, convergence of the estimation error of MLPNN parameters is proven. Two examples have been brought to show the merits of the proposed approach and to compare the obtained results by applying the multilayer Perceptron and the Radial Basic Function Neural Network (RBFNN).