Nonparametric Steady-State Learning for Nonlinear Output Feedback Regulation

Abstract: 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 proposed nonadaptive framework facilitates the conversion of the nonlinear robust output regulation problem into a robust nonadaptive stabilization formulation for the augmented system endowed with Input-to-State Stable dynamics. This approach removes the need for constructing a specific Lyapunov function with positive semi-definite derivatives and avoids the common assumption of linear parameterization of the nonlinear system. The nonadaptive approach is extended by incorporating the nonparametric learning framework to ensure the feasibility of the nonlinear mapping, which can be tackled using a data-driven method. Moreover, the introduced nonparametric learning framework allows the controlled system to learn the dynamics of the steady-state input behaviour from the signal generated from the internal model with the output error as the feedback. As a result, the nonadaptive/nonparametric approach can be advantageous to guarantee the 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 benchmark example: a controlled duffing system and two practical examples: a continuously stirred tank reactor and a continuous bioreactor.