ON THE ABSENCE OF POSITIVE REALNESS CONDITIONS IN SELF-TUNING REGULATORS BASED ON EXPLICIT CRITERION MINIMIZATION

Local convergence properties of an adaptive control algorithm that, under suitable assumptions, is known to be globally convergent to the optimal LQ regulator, are studied. In this connection, it is shown that, as in more standard adaptive controllers, a 'transfer function' H(q), depending on the innovation C(q)-polynomial, plays a central role. The peculiarity of the algorithm under consideration is that the special form of the corresponding H(q) implies its positive realness.