in this invention the results of this simulation are graphically depicted in fig2 4 fig2 is a plot of the optimal control inputs on the vertical axis versus the discrete time steps plotted on the horizontal axis fig3 is a similar plot but with the optimal trajectory of the first state variable plotted on the vertical axis while fig4 is a plot similar to fig3 but depicting the optimal trajectory for the second state variable as can be observed from these plots the results obtained with this invention closely match those obtained by solving the discrete riccati equation the latter solutions being plotted for comparison purposes in fig2 4 there are several advantages to using the approach of this invention for the solution of an optimal control problem first the optimization function of an optimal control problem can be directly mapped onto a neural network second the entire solution i e control inputs and optimal trajectories can be obtained simultaneously within a few time constants of the network these advantages have been illustrated through the description above of a preferred embodiment of the invention modifications and additional embodiments however will undoubtedly be apparent to those skilled in the art although for example the invention has been described in conjunction with a linear quadratic discrete time optimal control problem the same approach can also be used to solve linear quadratic gaussian optimal control problems in the latter application gaussian white noise can be introduced as.