Elimination of the real positivity condition in the design of parallel MRAS

All the algorithms developed hitherto in order to obtain a global asymptotically stable "parallel" MRAS (model reference adaptive system) require that a certain transfer function should be made strictly positive real. This condition is restrictive in the case of parallel MRAS used as identifiers or as adaptive state observers, because part of the unknown parameters of the plant to be identified appear in the transfer function, which should be made strictly positive real. A new algorithm is proposed in which the parameters of the compensator acting on the generalized error are no more constant but are adapted recursively. The new adaptation algorithm assures the global asymptotic stability of the adaptive system, without requiring the satisfaction of a positive-real condition. Simulation results illustrate that the proposed algorithm provides excellent results when used for identification in the presence of measurement noise. The design proposed can be extended also for adaptive state observers and adaptive model-following control systems.