Optimization and estimation in nonlinear systems with application to inertial guidance

In the application of optimal control theory to practical problems, one difficulty which arises is that the resulting control laws are difficult or expensive to mechanize. This problem is formulated as a problem in the calculus of variations. This results in an explicit minimization of a terminal error performance index for a nonlinear system. This takes the form of a two point boundary value problem. These results are applied to an inertial guidance problem and a numerical solution obtained by a modification of the gradient method. Estimation or filtering in the context of a nonlinear problem, viz., estimation of the state of an inertially guided reentry vehicle is examined. It is demonstrated by numerical example that a linearized filter based on statistical optimization performs much better than the extended Kalman filter in this application.