Bursting Phenomena in the Adaptive Control of Time Varying Systems

In this paper is is shown that the standard normalized gradient algorithm with the parameter projection can be used for adaptive control of time-varying systems. By evaluating possible bursts in the adaptive loop, global stability and performance of the adaptive system are derived without using persistent excitation (PE) condition. Precise upper bound on the admissible speed of the parameter variations is established. When the reference signal is persistently exciting, it is shown that the parameter estimation error is of order of the rate of parameter variations.