Set-Theoretic Model Reference Adaptive Control with Bandwidth Regulation

This paper introduces a novel set-theoretic model reference adaptive control framework with bandwidth regulation, which has the capability to provide strict closed-loop performance guarantees without inducing high-frequency oscillations. While standard model reference adaptive control approaches aim to reduce the error between an uncertain dynamical system and a reference model, they cannot impose a user-defined bound on this error—a critical requirement for safety-critical applications. Set-Theoretic model reference adaptive control employs generalized Lyapunov barrier functions to ensure the error strictly remains within a user-defined bound. However, as the error approaches this bound, high-gain learning rates may induce high-frequency oscillations that potentially lead to system instability in practice. The key feature of the proposed framework is an adaptive bandwidth regulation mechanism, which adjusts the error dynamics to prevent such oscillations. The presented system-theoretical analysis confirms the stability of the proposed framework and an illustrative numerical example demonstrates its effectiveness in maintaining error bounds while ensuring smooth state and control histories.