Adaptive high-gain λ-[lambda]-tracking with variable sampling rate
It is well known that proportional output feedback control can stabilize any relative-degree one, minimum-phase system if the sign of the feedback is correct and the proportional gain is high enough. Moreover, there exists simple adaptation laws for tuning the proportional gain (the so-called high-gain adaptive controllers) which are not based on system identification or plant parameter estimation algorithms or injection of probing signals. If tracking of signals is desired, then these simple controllers are also applicable without invoking an internal model if the tracking error is not necessarily supposed to converge to zero but towards a ball around zero of arbitrarily small but prespecified radius lambda>0. In this note we consider a sampled version of the high-gain adaptive lamda-tracking controller. The motivation for sampling arises from the possibility that the output of a system may not be available continuously, but only at discrete time instants. The problem is that the stiffness of the system increases as the proportional gain is increased. Our result shows that adaptive sampling tracking is possible if the product hk of the decreasing sampling rate h and the increasing proportional gain k decreases at a rate proportional to 1/log k.