A Set-Theoretic Model Reference Adaptive Control Architecture with Dead-Zone Effect

By introducing a system error dependent learning rate, the recently proposed set-theoretic model reference adaptive control architecture provides user-defined worst-case performance guarantees on the system error between an uncertain dynamical system of interest and a given reference model. In this architecture, the adaptation process is always active. However, it is of practical interest to stop the adaptation process when it is not needed (i.e., in the presence of small system errors). Motivated from this standpoint, we present a new set-theoretic model reference adaptive control architecture with dead-zone effect. The key feature of our framework utilizes a modified and continuous generalized restricted potential function in the adaptation update law, where it not only stops the adaptation process inside the dead-zone (i.e., when the system error is small) but also allows the norm of the system error to be less than a-priori, user-defined worst-case performance bound. The efficacy of the proposed architecture is also demonstrated through an illustrative numerical example.