Output Feedback Adaptive Tracking Control of Uncertain Parameter Systems via Dynamic Regressor Extension and Mixing

This work develops an output feedback adaptive tracking control method based on dynamic regressor extension and mixing (DREM) for discrete-time uncertain parameter systems. A piecewise DREM estimator is designed for the uncertain parameters under conditions strictly weaker than the persistently excited condition, exhibiting the ability to capture the actual system dynamics in finite time. Accurate parameter estimation guarantees the performance of the controller utilizing the DREM estimator. Then, an adaptive optimal controller for any given reference trajectory is designed within the framework of receding horizon control. The system state and control input are theoretically guaranteed to remain bounded during tracking. The adaptive controller is restructured in a nonminimal state space to achieve output feedback without a state estimator. The proposed output feedback adaptive controller is fully consistent with its state-feedback counterpart. Simulation results for tracking different reference signals demonstrate the efficacy of the proposed strategy.