Fully distributed robust consensus control of multi-agent systems with heterogeneous unknown fractional-order dynamics

ABSTRACT

This paper investigates the robust consensus control problem of heterogeneous unknown nonlinear fractional-order multi-agent systems (FOMASs) without leader and with multiple leaders of bounded inputs. More specifically, FOMASs with nonidentical unknown coupling nonlinearities and external disturbances are considered in this paper, which takes the first-order MASs as its special case. Based on the σ-modification adaptive control technique, some class of discontinuous robust adaptive control protocols are proposed to solve the leaderless consensus problem and containment consensus problem, respectively. By means of the set-valued maps theory and by artfully choosing Lyapunov function, it is shown that the proposed consensus protocols are user friendly in that they are capable of compensating uncertain coupling nonlinearities, rejecting disturbances, rendering smaller control gains and thus requiring smaller amplitude on the control input while preserving global consensus convergence. All of the proposed robust adaptive consensus protocols are independent of any global and unknown information and thus are fully distributed. Some numerical simulations are provided to validate the correctness of the obtained results.

KEYWORDS:

• Robust adaptive control
• fractional-order multi-agent systems (FOMASs)
• consensus
• multiple leaders

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Ping Gong http://orcid.org/0000-0003-1935-6990

Weiyao Lan http://orcid.org/0000-0002-0614-2259

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant numbers 61374035 and 61873219].

Notes on contributors

Ping Gong

Ping Gong received his Ph.D. degree from Xiamen University, Xiamen, China, in 2018. He is currently working at School of Mathematical Sciences, South China Normal University, Guangzhou, China. His research interests include nonlinear control, fractional-order equations and systems, distributed optimisation and control of multi-agent systems.

Kun Wang

Kun Wang is currently pursuing the Ph.D. degree in basic mathematics from Xiamen University, Xiamen, China. Her current research interests include fractional differential equation, multiple complex function, and complex Fensler geometry.

Weiyao Lan

Weiyao Lan received his B.S. degree in precision instrument from Chongqing University, Chongqing, China, in 1995, M.S. degree in control theory and control engineering from Xiamen University, Xiamen, China, in 1998, and Ph.D. degree in automation and computer aided engineering from the Chinese University of Hong Kong, Hong Kong, in 2004. From 2004 to 2006, he was a research fellow in the Department of Electrical and Computer Engineering, National University of Singapore, Singapore. Since December in 2006, he has been with the Department of Automation, Xiamen University, Xiamen, China, where he is currently a professor. Dr. Lan is a member of Technical Committee on Control Theory, Chinese Associate of Automation, and the vice-president of Fujian Association of Automation. He is also serving as an associate editor for the Transactions of the Institute of Measurement and Control. His research interests include nonlinear control theory and applications, intelligent control technology, and robust and optimal control.