A robust model reference adaptive control without strictly positive real condition

Abstract

This paper considers the model reference adaptive control problem for the system (1) with unmodelled dynamics m n dominated by a small constant k multiplied by a quantity dependent on the input, output and noise. Using bounded external excitation and randomly varying truncation techniques, we give design method of a model reference adaptive controller which is similar to that in Meyn and Brown (1992). It is shown that the closed-loop system is globally stable, the estimation error for parameter contained in the modelled part is of order k, and the closed-loop system under the model reference adaptive control law is suboptimal in the sense of lim sup 1/n n (A m (z) y i+1 - B m (z)z* i - C m (z) w i+1 ) 2 h O( k 2 ) + n 2 b 1 2 while the SPR condition usually used in other papers is replaced by a stability condition.