Semi‐global output regulation of continuous‐time linear systems subject to input saturation via output feedback: A model‐free method

• Published in: International journal of adaptive control and signal processing Vol. 38; no. 12; pp. 3756 - 3770
• Main Authors: Fu, Zhuofan, Zhao, Zhiyun
• Format: Journal Article
• Language: English
• Published: Bognor Regis Wiley Subscription Services, Inc 01.12.2024
• Subjects: Adaptive algorithms; adaptive dynamic programming; Algorithms; Control theory; Dynamic programming; Error analysis; Feedback control; Feedforward control; input saturation; Linear systems; model‐free; Output feedback; output regulation; System dynamics; Tracking errors
• ISSN: 0890-6327; 1099-1115
• DOI: 10.1002/acs.3898

Summary This article considers the output regulation problem of continuous‐time linear systems subject to input saturation in the scenario that the system dynamics are unknown. Based on the low‐gain technique and the output feedback technique, we construct an output feedback control law to solve the output regulation problem with input saturation. Since the system dynamics are unknown, we estimate the feedback and feedforward terms in the control law with a two‐step data‐driven method. An output feedback adaptive dynamic programming algorithm is proposed to estimate the feedback term. An online updating algorithm based on output tracking error is proposed to estimate the feedforward term directly without solving the output regulation equations. Both algorithms don't rely on the measurement of the internal states of the exosystem and the original system. We show that the input saturation caused by the iterative feedforward gain matrix in the online updating algorithm doesn't affect the convergence of the algorithm. With these two data‐driven algorithms, the control law doesn't rely on the dynamics anymore. The low‐gain control law obtained by the model‐free method prevents input saturation from occurring and hence solves the output regulation problem. Finally, a numerical example is provided to validate the theoretical results.