Adaptive Estimation and Rejection of Unknown Sinusoidal Disturbances in A Class of Non-minimum-phase Nonlinear Systems

This paper deals with adaptive estimation of unknown disturbances in a class of nonminimum phase nonlinear systems, and the stabilization and disturbance rejection based on the estimated disturbances. The unknown disturbances are combination of sinusoidal disturbances with unknown frequencies, unknown phases and amplitudes. The only information of the unknown disturbances is the number of distinctive frequencies inside. The class of nonlinear systems considered in this paper consists of nonlinear systems in the output feedback form and the systems may be nonminimum phase, ie, with unstable zero dynamics. An adaptive estimation algorithm is developed to give exponentially convergent estimates of the unknown disturbance and the system states. The asymptotic convergent estimates of unknown frequencies are also obtained. The proposed estimation algorithm works for both minimum phase and nonminimum phase nonlinear systems in output feedback form. Disturbance rejection with stabilisation is achieved by combining the control designed for the stabilisation of the disturbance-free system and the exponentially convergent estimate of the disturbance. Under the conditions specified for the control design of the system with no disturbance, the overall stability and complete rejection of the unknown disturbance are guaranteed by the proposed control algorithm.