On Self-Learning Mechanism for the Output Regulation of Second-Order Affine Nonlinear Systems

• Published in: IEEE transactions on automatic control Vol. 67; no. 11; pp. 5964 - 5979
• Main Authors: Wu, Haiwen, Xu, Dabo, Jayawardhana, Bayu
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.11.2022; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Adaptation models; Adaptive control; certainty equivalence principle; Controllers; Feedforward systems; internal model principle; Kernel; Kernels; Learning; Nonlinear systems; output regulation; Parameter uncertainty; Position measurement; Reference signals; Regulation; servo systems; Task analysis; Trajectory; Trajectory control
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2021.3130881

This article studies global robust output regulation of second-order nonlinear systems with input disturbances that encompass the fully-actuated Euler-Lagrange systems. We assume the availability of relative output (w.r.t. a family of reference signals) and output derivative measurements. Based on a specific separation principle and self-learning mechanism, we develop an internal model-based controller that does not require a priori knowledge of reference and disturbance signals and it only assumes that the kernels of these signals are a family of exosystems with unknown parameters (e.g., amplitudes, frequencies, or time periods). The proposed control framework has a self-learning mechanism that extricates itself from requiring absolute position measurement nor precise knowledge of the feedforward kernel signals. By requiring the high-level task/trajectory planner to use the same class of kernels in constraining the trajectories, the proposed low-level controller is able to learn the desired trajectories, to suppress the disturbance signals, and to adapt itself to the uncertain plant parameters. The framework enables a plug-and-play control mechanism in both levels of control.