This paper investigates the roll parameter estimation of periodic disturbances where the amplitude, frequency, offset, and phase are hardly recognized in real practice. The key problem is to make an estimation that could eliminate the unknown disturbance parameters. An adaptive mechanism applies these four parameters to the globally exponential convergence using linear second-order filters and parameter estimation errors. Then, a backstepping controller is employed to make an exponential convergence to zero of the state variables. Moreover, reservoir computing is used to forecast chaotic roll motions to support predictability using Lyapunov exponents and the Poincaré map. Numerical simulations are demonstrated to validate the dynamical behaviors and efficacy of the proposed control scheme with machine learning.