Oscillatory tracking control of a class of nonlinear systems

Vibration control is an effective alternative to conventional feedback and feedforward control. Motivated by its important application in physical systems and few results on general oscillatory tracking control, we consider tracking control of a class of nonlinear systems using oscillation in the paper. We propose a new oscillatory control design using general averaging analysis for the tracking problem. Based on the oscillation functions associated with accessible vibrating components of the system, oscillatory control is designed to track a desired trajectory. Comparing to existing oscillatory tracking control, our approach is robust to initial conditions. We show the effectiveness of the proposed method by two simulation examples, which include a second-order nonholonomic integrator and the inverted pendulum system. For the inverted pendulum system, we show that our designed oscillatory control does not need state feedback to track a desired trajectory, which is desirable for systems where state measurement is not feasible.