• CONTROL THEORY AND APPLICATION •

### Open-loop and closed-loop $D^{\alpha}$ -type iterative learning control for fractional-order linear multi-agent systems with state-delays

Bingqiang LI1(), Tianyi LAN2,*(), Yiyun ZHAO1(), Shuaishuai LYU3()

1. 1 School of Automation, Northwestern Polytechnical University, Xi’an 710129, China
2 School of Electrical and Control Engineering, Shaanxi University of Science and Technology, Xi’an 710021, China
3 College of Electronics and Information, Hangzhou Dianzi University, Hangzhou 310018, China
• Received:2020-05-27 Online:2021-02-25 Published:2021-02-25
• Contact: Tianyi LAN E-mail:libingqiang@nwpu.edu.cn;iamlty1111@163.com;zhaoyiyun@mail.nwpu.edu.cn;lvshuai@hdu.edu.cn
• About author:|LI Bingqiang was born in 1982. He received his B.E. degree and M.E. degree both in electrical engineering and Ph.D. degree in control science and engineering from Northwestern Polytechnical University, Xi’an, China, in 2004, 2007 and 2010, respectively. He is currently an associate professor and the dean of the Department of Electrical Engineering, Northwestern Polytechnical University, a postdoctoral fellow with Xi’an Aviation Brake Technology Co., Ltd. His research interests include iterative learning control, fractional order control, servo control, multi-agent system and their applications. E-mail: libingqiang@nwpu.edu.cn||LAN Tianyi was born in 1981. He received his B.S. degree and M.S. degree both in applied mathematics and Ph.D. degree in control science and engineering from Northwestern Polytechnical University, Xi’an, China, in 2004, 2007 and 2017, respectively. He is currently a postdoctoral fellow with the School of Automation, Northwestern Polytechnical University. His research interests include iterative learning control, fractional order control, control theory, and multi-agent system. E-mail: iamlty1111@163.com||ZHAO Yiyun was born in 1995. He received his B.E. degree in electrical engineering from Northwestern Polytechnical University, Xi ’an, China, in 2017. He is currently working towards his Ph.D. degree in the School of Automation, Northwestern Polytechnical University, Xi’an, China. His research interests include servo drive control, nonlinear system control and electromechanical brake control. E-mail: zhaoyiyun@mail.nwpu.edu.cn||LYU Shuaishuai was born in 1986. He received his B.E. and Ph.D. degrees from the School of Automation, Northwestern Polytechnical University, in 2011 and 2016, respectively. Since 2016, he has been a lecturer with the College of Electronics and Information, Hangzhou Dianzi University. His research interests include iterative learning control, fractional order control, finite time control of linear and nonlinear systems, network control system, and consensus of distributed multi-agent system and its applications. E-mail: lvshuai@hdu.edu.cn
• Supported by:
This work was supported by the National Natural Science Foundation of China (51777170), the Natural Science Basic Research Plan in Shaanxi Province of China (2020JM-151), and the Fundamental Research Funds for the Central Universities (3102020ZX006)

Abstract:

This study focuses on implementing consensus tracking using both open-loop and closed-loop $D^{\alpha}$ -type iterative learning control (ILC) schemes, for fractional-order multi-agent systems (FOMASs) with state-delays. The desired trajectory is constructed by introducing a virtual leader, and the fixed communication topology is considered and only a subset of followers can access the desired trajectory. For each control scheme, one controller is designed for one agent individually. According to the tracking error between the agent and the virtual leader, and the tracking errors between the agent and neighboring agents during the last iteration (for open-loop scheme) or the current running (for closed-loop scheme), each controller continuously corrects the last control law by a combination of communication weights in the topology to obtain the ideal control law. Through the rigorous analysis, sufficient conditions for both control schemes are established to ensure that all agents can achieve the asymptotically consistent output along the iteration axis within a finite-time interval. Sufficient numerical simulation results demonstrate the effectiveness of the control schemes, and provide some meaningful comparison results.