INDIRECT MODEL-REFERENCE ADAPTIVE-CONTROL WITH DYNAMIC ADJUSTMENT OF PARAMETERS

The paper discusses in detail a new method for indirect model referenc e adaptive control (MRAC) of linear time-invariant continuous-time pla nts with unknown parameters. The method involves not only dynamic adju stment of plant parameter estimates but also those of the controller p arameters. Hence the overall system can be described by a set of non-l inear differential equations as in the case of direct control. Many of the difficulties encountered in the conventional indirect approach, w here an algebraic equation is solved to determine the control paramete rs, are consequently bypassed in this method. The proof of stability o f the equilibrium state of the overall system is found to be different from that used in direct control. Using Lyapunov's theory, it is firs t shown that the parameter errors between the parameter estimates of t he identifier and the true parameters of the plant, as well as those b etween the actual parameters of the controller and their desired value s, are bounded. Following this, using growth rates of signals in the a daptive loop as well as order arguments, it is shown that the error eq uations are globally uniformly stable and that the tracking (control) error tends to zero asymptotically. This in turn establishes the fact that both direct and indirect model reference adaptive schemes require the same amount of prior information to achieve stable adaptive contr ol.