Robust control of uncertain nonlinear mechanical systems using a high gain observer

We consider a general class of nonlinear uncertain mechanical systems. All uncertain terms belong to a known, nonempty compact set. A previously derived r-α robust tracker that guarantees global exponential convergence of the tracking error via state feedback is extended to achieve semi-global tracking using output feedback. The proposed controller has the same structure as the state feedback controller, however, all missing states are estimated using a high gain observer. The high gain observer proposed generalizes an existing observer in the literature for SISO systems and MIMO systems. The interconnection between the observer dynamics and the nonlinear mechanical dynamics are cast into a singularly perturbed system. This technique proves that the full order system closely approximates the behavior of the reduced order system, in this case a full state feedback. Simulation results for the attitude stabilization of a helicopter model are also included for illustration