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Abstract: A method for the construction of the pseudolinearizing controller and extended linearizing observer for single-input, multi-output nonlinear systems is presented. The technique uses spline functions to approximate the elements of gradient vectors which arise during the derivation of the pseudolinearizing controller and extended linearizing observer. The construction of both is computer automated and can be accomplished regardless of the complexity of the original nonlinear model. Further, the structure of the controller and observer makes their implementation computationally efficient.
The stability of the controller for set-point and time-varying desired trajectories is rigorously investigated. Controller construction is illustrated for a robotic mechanism called the acrobot. The pseudolinearizing controller's regulation of the acrobot is contrasted with two linear controllers via numerical simulation. Trajectory tracking performance and computational efficiency of the controller are verified in three experiments carried out with actual acrobot hardware.
The state estimate error for the extended linearizing observer is shown to be locally exponentially stable. A separation principle which allows state estimates generated by the observer to be substituted into the controller is discussed. The observer construction and performance are illustrated via simulation for an extension of the acrobot called the rolling acrobot.