Neural networks for optimal control of nonlinear systems with bound constraints

A new kind of neural network model for solving optimal control problems with lower and upper bound constraints on both state and control vectors is proposed in this paper. Such bound constraints are dealt with by taking the advantage of the saturation characteristics of the corresponding neurons implemented by analog circuits, and the system dynamic equations are taken as the equality constraints and coped with by the Lagrange multiplier method. It can be shown that under certain conditions the proposed neural network converges to an equilibrium point which corresponds to an exact optimal solution to the original optimal control problem. The computational results for numerical examples are given to demonstrate the validity and performance of the proposed neural network model