Terminal State Error Analysis Using Adjoint-Generated Sensitivities

Dynamic system error analysis techniques frequently require a measure of trajectory terminal error due to initial condition dispersions and random system variations. The adjoint method described herein is an expeditious technique for determining sensitivities of terminal error to initial condition errors in nonlinear time-varying systems. In addition, mean square error deviation from a nominal trajectory is obtained using adjoint-generated sensitivity functions. Also terminal error marginal probability density due to Gaussian time-invariant random system parameter variations is generated provided a statistical description of trajectory initial dispersions and variational parameters can be supplied. A simple second-order system is used in the first example to illustrate the computation of sensitivity functions. A thirty-third-order, six-degree-of-freedom homing missile model is then used as the fixed plant for an error analysis which illustrates the application of the technique to a realistic situation.