Transformation of a Mismatched Nonlinear Dynamic System into Strict Feedback Form

Dynamic surface control is a robust nonlinear control technique. It is generally applied to mismatched dynamic systems in strict feedback form. We have developed a new method of defining states and state-dependent disturbances to transform a mismatched dynamic system into strict feedback form. We apply this method to a multi-input multi-output (MIMO) extended-state kinematic model of a bicycle. We show how a dynamic surface controller can be used for position tracking of the bicycle. The performance of the dynamic surface controller is compared with that of a controller designed using feedback linearization. Transformation of the dynamic system into strict feedback form allows us to successfully apply dynamic surface control. Both the dynamic surface controller and the feedback linearization controller perform well in the absence of disturbances. The dynamic surface controller is more robust when disturbances are introduced; however, a large control effort is required to reject the disturbances. Our method of defining new states and state-dependent disturbances to transform mismatched nonlinear dynamic systems into strict feedback form could be used on other systems requiring robust nonlinear control.