Rapid convergence to optimum solutions using a Min-H strategy.

A general problem in the calculus of variations is formulated and the necessary conditions for an extremal solution given. Two iterative methods of solution based upon a strategy that minimizes the variational Hamiltonian flXMin-H Strategy) are proposed. The way in which the calculus-of-variations, steepest-ascent, and Min-H methods are related is established, and a means for including the effect of constraint violations in the Min-H process is developed. An extension of the formulation provides for control parameters as well as control variables, and allows the convergence rates of the parameters and variables to be separately specified. Feedback optimization is possible using the extended formulation. In an illustrative example, the pay load that a three-stage launch vehicle can place into a 72-hr transfer ellipse to the moon, after having passed through a parking orbit, is maximized, and convergence is shown to be both extremely rapid and sure.