Adaptive Set-Theoretic Emulator Reference Architecture (ASTERA): Control of Uncertain Dynamical Systems with Performance Guarantees and Smooth Transients

摘要

In control of uncertain dynamical systems with model reference adaptive control methods, simultaneously achieving user-defined performance guarantees and smooth transients is a challenging problem. Motivated from this point, an adaptive set-theoretic emulator reference architecture (ASTERA) is proposed in this paper. Specifically, the ASTERA has two major components - a state emulator and a set-theoretic adaptive controller. Based on a given reference model capturing a desired closed-loop system performance, the state emulator alters the trajectories of this model with the system error (the difference between the uncertain dynamical system state and the state emulator state) for the purpose of achieving smooth transients - transients that do not necessarily exhibit high-frequency oscillations (a property that does not necessarily exist in standard set-theoretic model reference adaptive control methods). In addition, the set-theoretic adaptive controller assures the weighted Euclidean norm of this system error to be less than a-priori, user-defined scalar worst-case bound, which ensures the state emulator trajectories stay close to the given reference model trajectories as desired (a property that does not exist in standard state emulator-based standard adaptive control methods), for the purpose of achieving performance guarantees. An illustrative numerical example is also presented to complement the proposed theoretical contribution - the ASTERA.