Nonparametric Steady-state Learning for Robust Output Regulation of Nonlinear Output Feedback Systems

This article addresses the nonadaptive and robust output regulation problem of the general nonlinear output feedback system with error output. The global robust output regulation problem for a class of general output feedback nonlinear systems with an uncertain exosystem and high relative degree can be tackled by constructing a linear generic internal model provided that a continuous nonlinear mapping exists. Leveraging the presented nonadaptive framework facilitates the conversion of the nonlinear robust output regulation problem into a robust nonadaptive stabilization endeavour for the augmented system endowed with Input-to-State Stable dynamics, removing the need for constructing a specific Lyapunov function with positive semidefinite derivatives. To ensure the feasibility of the nonlinear mapping, the approach is extended by incorporating the nonparametric learning framework. Moreover, the introduced nonparametric learning framework provides the ability to learn the dynamics of the steady-state/input behaviour from the signal generated from the internal model only using the output error feedback. As a result, the nonadaptive/nonparametric approach can be advantageous by guaranteeing convergence of the estimation and tracking error even when the underlying controlled system dynamics are complex or poorly understood. The effectiveness of the theoretical results is illustrated for a controlled duffing system and a continuously stirred tank reactor