A solution to the MRAC design without knowledge of the sign of the high frequency gain

This paper presents a solution to the problem of designing continuous-time adaptive controllers when the sign of the high frequency gain of the plant is not available a priori. The proposed algorithm estimates the high frequency gain and uses its sign in the adaptation laws of the controller parameters. It is shown that a continuous counterpart of the prediction error used in discrete-time systems plays a fundamental role in the proposed adaptive scheme. A sketch of the stability proof is proposed for the case of a first order plant where the high frequency gain is the only unknown parameter. Simulations illustrate the behavior of the new algorithm.