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.

I. Introduction

A reference model, an update law, and a controller are the main ingredients of model reference adaptive control architectures. Briefly, a desired closed-loop system performance can be captured by the reference model, where its output or state is compared with the output or state of an uncertain dynamical system to form a system error. This system error drives the update law and then the controller adapts feedback gains to suppress the system error using the information received from the update law. It is a challenge to achieve user-defined performance guarantees while utilizing model reference adaptive control laws in the feedback loop, although these controllers have the capability to cope with adverse effects resulting from exogenous disturbances and system uncertainties. To this end, the authors of this paper recently introduced a set-theoretic model reference adaptive control framework [1] and [2].