Control of autoresonance in mechanical and physical models

Autoresonant energy transfer has been considered as one of the most effective methods of excitation and control of high-energy oscillations for a broad range of physical and engineering systems. Nonlinear time-invariant feedback control provides effective self-tuning and self-adaptation mechanisms targeted at preserving resonance oscillations under variations of the system parameters but its implementation may become extremely complicated. A large class of systems can avoid nonlinear feedback, still producing the required state due to time-variant feed-forward frequency control. This type of control in oscillator arrays employs an intrinsic property of a nonlinear oscillator to vary both its amplitude and the frequency when the driving frequency changes. This paper presents a survey of recently published and new results studying possibilities and limitations of time-variant frequency control in nonlinear oscillator arrays. This article is part of the themed issue ‘Horizons of cybernetical physics’.