Adaptive natural entrainment via Andronov-Hopf oscillator

Abstract

When controlling mechanical systems to sustain oscillatory movements, a resonance, or a natural oscillation, may be exploited to achieve high energy efficiency. Such mechanisms are observed in animal movements, and the idea can be adopted for control of robotic locomotion systems. In this article, we consider the problem of designing a nonlinear adaptive feedback controller for uncertain linear mechanical systems so that a natural mode of oscillations is achieved for the closed-loop system. The controller structure is based on the Andronov-Hopf oscillator with additional estimation mechanisms for the natural frequency and damping parameters. We prove that, under certain conditions, the estimated parameters converge to their true values and entrainment to a natural oscillation is achieved as part of an orbitally stable limit cycle.