Robust adaptive control of discrete-time systems using persistent excitation

Abstract

An important result in the robust adaptive control of continuous-time systems, using the persistent excitation of the reference input, was recently given by Narendra and Annaswamy (1986, IEEE Trans. Aut. Control, AC-31, 306-315). According to this result, the global boundedness of all the signals in the adaptive system can be assured if the degree of persistent excitation of the reference input is larger than an appropriate bound on the external disturbance. The main theorem in Narendra and Annaswamy (1986) is proved for a class of plants characterized by the property that the reference model used in the adaptive controller could be chosen to be strictly positive real, a condition which involves constraints on the relative degree of the plant. This paper presents a generalization of the above result to plants of arbitrary relative degree. Together with the work reported in the earlier paper, it demonstrates that the boundedness of all the signals in an adaptive system in the presence of bounded disturbances and arbitrary initial conditions can be assured by increasing the degree of persistent excitation of the reference input. © 1988.