Adaptive sampling control of high-gain stabilizable systems

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 exist simple adaptation laws for tuning the proportional gain (so-called high-gain adaptive controllers) which do not need to know the system and do not attempt to identify system parameters. The authors consider sampled versions of the high gain adaptive controller. The motivation for sampling arises from the possibility that the output of a system may not be available continuously, but only at sampled times. The main point of interest is the need to develop techniques for adapting the sampling rate, since the stiffness of the system increases as the proportional gain is increased. Our main result shows that adaptive sampling stabilization is possible if the product hk of the decreasing sampling interval h and the increasing proportional gain k decreases at a rate proportional to 1/log k.