A Neural Network Approach for Solving Optimal Control Problems with Inequality Constraints and Some Applications

In this paper, a class of nonlinear optimal control problems with inequality constraints is considered. Based on Karush–Kuhn–Tucker optimality conditions of nonlinear optimization problems and by constructing an error function, we define an unconstrained minimization problem. In the minimization problem, we use trial solutions for the state, Lagrange multipliers, and control functions where these trial solutions are constructed by using two-layered perceptron. We then minimize the error function using a dynamic optimization method where weights and biases associated with all neurons are unknown. The stability and convergence analysis of the dynamic optimization scheme is also studied. Substituting the optimal values of the weights and biases in the trial solutions, we obtain the optimal solution of the original problem. Several examples are given to show the efficiency of the method. We also provide two applicable examples in robotic engineering.