Adaptive Output Regulation of Output Feedback Systems with Unknown Nonlinear Exosystems and Unknown High-Frequency Gain Sign

This paper addresses the problem of adaptive output regulation for a class of output feedback systems subject to unknown disturbances generated from nonlinear exosystems and no knowledge of high-frequency gain sign. The nonlinear internal model based on circle criterion is proposed to generate the feedforward input term for rejection of the disturbances, and some specific conditions are introduced for exosystems such that the proposed internal model can be applied. In the proposed adaptive control scheme, a type of Nussbaum gain is presented to deal with the unknown high-frequency gain sign and the adaptive backstepping technique is then used to establish the final control input if systems possess high relative degree. The proposed control algorithm ensures the convergence of the parameters in the adaptive internal model to the actual values and the measurement output to zero, and the boundedness of all state variables.