Adaptive estimation and rejection of unknown disturbances through measurement feedback for a class of nonminimum phase nonlinear MIMO systems

This paper developed an adaptive estimation method to estimate unknown disturbances in a class of nonminimum phase nonlinear MIMO systems. The unknown disturbances are generated by an unknown linear exosystem. The frequencies, phases and amplitudes of the disturbances are unknown, the only available information of the disturbances is the number of distinctive frequencies. The system considered in this paper is a class of MIMO nonlinear systems in the output feedback form, the system can be nonminimum phase. The proposed estimation algorithm provides exponentially convergent estimates of system states, unknown disturbances in the system and frequencies of the disturbances characterized by the eigenvalues of the exosystem. Moreover, the disturbance rejection control law is constructed by combining the stabilization controller designed without considering the disturbances and the estimates of the disturbances. The control law compensates the unknown disturbances completely while maintains the stability of the whole closed-loop system.