Performance Enhancement for Adaptive Safe Control Systems Tracking Periodic Signals

This paper presents an adaptive safe repetitive control approach to improve the tracking performance for periodic reference signals in a class of controlled plants with state constraints and unknown parameters. First, a parameter estimation error extraction mechanism under persistent excitation conditions is employed. Next, an internal model of periodic reference signals, that is, a repetitive controller, is embedded into the reference model to enhance the capability of tracking control. Meanwhile, a new parameter update law based on estimation error is derived to approximate the parametric uncertainty, which enables the error signals in the adaptive control to converge exponentially to zero. Subsequently, an adaptive control barrier function is formulated using quadratic programming to handle state constraints. Safety criteria and error convergence conditions for the controller parameters are provided. Finally, numerical simulations demonstrate the effectiveness, and a comparison of the tracking performance of this method, conventional adaptive control, and other control methods highlights its superiority.