Reaching a consensus in networks of high-order integral agents under switching directed topologies

Abstract

Consensus problem of high-order integral multi-agent systems under switching directed topology is considered in this study. Depending on whether the agent’s full state is available or not, two distributed protocols are proposed to ensure that states of all agents can be convergent to a same stationary value. In the proposed protocols, the gain vector associated with the agent’s (estimated) state and the gain vector associated with the relative (estimated) states between agents are designed in a sophisticated way. By this particular design, the high-order integral multi-agent system can be transformed into a first-order integral multi-agent system. Also, the convergence of the transformed first-order integral agent’s state indicates the convergence of the original high-order integral agent’s state, if and only if all roots of the polynomial, whose coefficients are the entries of the gain vector associated with the relative (estimated) states between agents, are in the open left-half complex plane. Therefore, many analysis techniques in the first-order integral multi-agent system can be directly borrowed to solve the problems in the high-order integral multi-agent system. Due to this property, it is proved that to reach a consensus, the switching directed topology of multi-agent system is only required to be ‘uniformly jointly quasi-strongly connected’, which seems the mildest connectivity condition in the literature. In addition, the consensus problem of discrete-time high-order integral multi-agent systems is studied. The corresponding consensus protocol and performance analysis are presented. Finally, three simulation examples are provided to show the effectiveness of the proposed approach.

Keywords:

• multi-agent systems
• high-order integral agent
• linear dynamics
• switching directed topology
• consensus

Additional information

Funding

This work has been partially supported by the National Natural Science Foundation of China [grant number 61370032], [grant number 61374060], [grant number 61225017], [grant number 61333016], [grant number 61422310]; the Beijing Nova Program [grant number Z121101002512066]. This work has also been partially supported by State Key Laboratory of Intelligent Control and Decision of Complex Systems, Beijing Institute of Technology.

Notes on contributors

Long Cheng

Long Cheng received his BS degree (with honours) in control engineering from Nankai University, Tianjin, China, in July 2004 and the PhD degree (with honours) in control theory and control engineering from the Institute of Automation, Chinese Academy of Sciences, Beijing, China, in July 2009. Currently, he is an associate professor at the State Key Laboratory of Management and Control for Complex Systems, Institute of Automation, Chinese Academy of Sciences. His current research interests include coordination of multi-agent systems, neural networks, optimisation and their applications to robotics.

Hanlei Wang

Hanlei Wang received his BS degree in mechanical engineering from Shijiazhuang Railway Institute, China, in 2004, MS degree in mechanical engineering from Harbin Institute of Technology, China, in 2006, and PhD degree in control theory and control engineering from Beijing Institute of Control Engineering, China Academy of Space Technology, China, in 2009. He joined Beijing Institute of Control Engineering as an engineer in 2009. Since 2011, he has been a senior engineer in Beijing Institute of Control Engineering. His research interests include robotics, spacecraft, networked systems, teleoperation, and nonlinear control.

Zeng-Guang Hou

Zeng-Guang Hou received his BE and ME degrees in electrical engineering from Yanshan University (formerly, Northeast Heavy Machinery Institute), Qinhuangdao, China, in 1991 and 1993, respectively, and PhD degree in electrical engineering from Beijing Institute of Technology, Beijing, China, in 1997. He is now a professor in the State Key Laboratory of Management and Control for Complex Systems, Institute of Automation, Chinese Academy of Sciences. His current research interests include neural networks, optimisation algorithms, robotics, and intelligent control systems.

Min Tan

Min Tan received his BS degree in control engineering from Tsinghua University, Beijing, China, in 1986 and the PhD degree in control theory and control engineering from the Institute of Automation, Chinese Academy of Sciences, Beijing, in 1990. He is a professor in the State Key Laboratory of Management and Control for Complex Systems, Institute of Automation, Chinese Academy of Sciences. His research interests include advanced robot control, multi-robot systems, biomimetic robots, and manufacturing systems.