Optimal feedback controller approximation using neural networks and nonlinear programming techniques

A direct method for creating a neural network to approximate an optimal feedback controller is presented in this paper. The method is direct in the sense that the weight adaptation is tied directly to the solution of the optimal control problem. To achieve this goal, the optimal control problem is first converted into a parameter optimization problem with the weights and biases of the network being the adaptable parameters. Any state and/or control limitations are turned into the appropriate equality or inequality constraints. Then a nonlinear programming algorithm is used to solve the resulting constrained minimization problem. The method is demonstrated by solving three example optimal control problems of varying complexity. Recommendations for future improvements are given.