NONLINEAR INVERSION-BASED OUTPUT TRACKING

An inversion procedure is introduced for nonlinear systems which const ructs a bounded input trajectory in the preimage of a desired output t rajectory, In the case of minimum phase systems, the trajectory produc ed agrees with that generated by Hirschorn's inverse dynamic system; h owever, the preimage trajectory is noncausal (rather than unstable) in the nonminimum phase case, In addition, the analysis leads to a simpl e geometric connection between the unstable manifold of the system zer o dynamics and noncausality in the nonminimum phase case, With the add ition of stabilizing feedback to the preimage trajectory, asymptotical ly exact output tracking is achieved, Tracking is demonstrated with a numerical example and compared to the well-known Byrnes-Isidori regula tor, Rather than solving a partial differential equation to construct a regulator, the inverse is calculated using a Picard-like interaction , When preactuation is not possible, noncausal inverse trajectories ca n be truncated resulting in the tracking-error transients found in oth er control schemes.