Low-Frequency Learning for a Discrete Uncertain System

Adaptive control techniques are ubiquitous methods for controlling dynamic systems, particularly because of their ability to improve system performance in the presence of uncertainties. However, a downside to these adaptive controllers is that particular learning rates are often required to ensure system performance requirements, creating high-frequency oscillations in the control input signal. These oscillations can potentially cause the system to become unstable or to have unacceptable performance. Thus, in this letter, we introduce a low-frequency learning adaptive control architecture for a discrete dynamical system with system uncertainties. In this framework, the update law is modified to include a filtered version of the updated parameter, allowing for high-frequency content to be removed while preserving system performance requirements. Lyapunov stability analysis is provided to guarantee asymptotic tracking error convergence of the closed-loop system. The results of a numerical simulation illustrates the reduction of high-frequencies in the system response.