Robust control for a class of modified Duffing equations

In this paper, a new class of modified Duffing equations with coupled periodic forcing and damping terms is developed, and the robust control problem for the system with structural uncertainty is studied systematically. This type of modified Duffing equations originates from swimming dynamics of a shape-changing underwater vehicle. The set-point control problem is studied for the system with constant disturbance and general structural uncertainty separately. Then, the trajectory tracking problem is investigated based on the discontinuous Lyapunov control and the sliding mode control. These presented approaches do not require any statistical information of the uncertainties; only their bounds are used in the design. Simulation results are given to demonstrate the effectiveness of the control algorithms.