Adaptive Control of A First Order Plant with a Time-varying Parameter

Recent results in the adaptive control of linear systems with time-varying parameters mostly deal with situations in which such parameters vary slowly with time. In this paper, the adaptive control of a first-order plant with a single parameter is treated when the parameter varies arbitrarily in a compact set. It is shown that all the signals in the adaptive system are bounded for any bounded reference input. This result requires neither any modification of the standard adaptive law, nor the persistent excitation of the reference input. The extension of the result to more general cases is briefly discussed.