Adaptive Cancellation of Unmatched Unknown Periodic Disturbances for Unknown LTI Systems by Output Feedback

This paper focuses on designing an adaptive controller for unknown minimum-phase LTI systems with known relative degree and system order. The controller objective is to reject the unknown, unmatched sinusoidal disturbances and make the output track a given trajectory with the output feedback. The controller design procedure is composed of three steps: disturbance parametrization, K-filter technique and adaptive backstepping. Firstly, the K-filter approach is employed to redefine the system states. Then, parametrization technique is used for the representation of the disturbance information in the output signal. In this way, the problem is converted to an adaptive control problem. After that, an adaptive output feedback controller is designed using a backstepping approach. It is proven that the equilibrium at the origin is globally stable and the output signal tracks the reference signal asymptotically. Finally, the performance of the controller is validated with a numerical simulation.