Control of the chaotic Duffing equation with uncertainty in all parameters

In this work, we deal with the open problem of controlling the periodically forced Duffing equation with uncertainty in all parameters. To date, several control schemes have been proposed to adapt for the linearly appearing unknown parameters but no solution exists for the case when the frequency of the periodic forcing is also unknown. We prove for the state feedback control case, global, asymptotic convergence for constant and time-varying references. We extend these results to the position feedback case and prove global ultimate boundedness.