A generalization to set-theoretic model reference adaptive control architecture for enforcing user-defined time-varying performance bounds

It is a challenge to achieve user-defined performance guarantees while utilizing model reference adaptive control laws in the feedback loop. To this end, we recently introduced a set-theoretic model reference adaptive control framework. The key feature of this approach allows the distance between the state of an uncertain dynamical system and the state of a reference model (i.e., the system error) to be less than a user-defined constant performance bound. In this paper, the set-theoretic model reference adaptive control framework is generalized to enforce user-defined time-varying performance bounds on the system error, which gives user the flexibility to control the closed-loop system performance as desired on different time intervals (e.g., transient time interval and steady-state time interval). For this purpose, an architecture is proposed for adaptive command following, where two numerical examples are provided to illustrate the efficacy of the proposed contribution.