Set-theoretic model reference adaptive control with time-varying performance bounds

One of the fundamental problems in model reference adaptive control design is the ability of the controlled system to achieve not only stability but also a user-defined performance in the presence of exogenous disturbances and system uncertainties. To this end, we recently proposed a set-theoretic model reference adaptive control framework, which guarantees the norm of the system error to be less than a user-defined constant performance bound. The contribution of this paper is to generalise the set-theoretic model reference adaptive control framework for enforcing user-defined time-varying performance bounds on the system error, which gives the control designer a flexibility to control the closed-loop system performance as desired on different time intervals (e.g. transient time interval and steady-state time interval). Two adaptive command following control architectures are proposed and their stability and performance properties are rigorously established using system-theoretic methods.