ADJOINT VARIABLE SOLUTIONS VIA AN AUXILIARY OPTIMIZATION PROBLEM

The problem addressed is to obtain an initial guess for the adjoint va riables along a trajectory suitable for use in an indirect optimal con trol method. The proposed method assumes that good estimates of the co ntrol and state histories are available. The adjoint estimates are obt ained through an auxiliary unconstrained optimization problem of low d imension. The goal of this optimization problem is to find the adjoint values at nodes along the trajectory that cause the control values fr om the application of the minimum principle to approach the estimated control values as closely as possible in a manner consistent with the adjoint differential equations and transversality conditions. Experien ce has shown that the method produces adjoint variable estimates suffi ciently accurate to cause convergence of a multiple-shooting indirect method.