A new nonlinear optimal-control method-The tracking and relative direction imbedded system

A new method of determining the optimal control for non-linear systems is described. It employs a novel course correction mechanism to optimize the state with respect to the initial condition and then uses dynamic programming ot optimize the control with respect to the final condition. A non-linear closed-form relationship of the cost function was developed so that the multi-grid approach of dynamic programming is avoided. Unlike other solution methods for optimal control problems, it does not need an estimate of the nominal solution to start the algorithm. One backward pass generates the optimal state trajectory, which is then tracked during the execution of the manoeuver. Compared to the multipasses necessary for other methods, this new method provides a significant improvement in computation time.