Synchronisation of uncertain chaotic systems via fuzzy-regulated adaptive optimal control approach

ABSTRACT

This study investigates the adaptive synchronisation of uncertain chaotic systems with unmodelled nonlinearities, dynamic mismatch, parametric perturbations, and external disturbances. A fuzzy-regulated adaptive optimal control (FRAOC) scheme is derived to realise chaotic synchronisation under both structure and parameter uncertainties. In the proposed scheme, the uncertain chaotic dynamics is firstly captured and estimated using a self-organising learning algorithm in an online fuzzy rule database. Based on the complicated and uncertain chaotic information, control strategy is adaptively regulated and configured in the form of weighting matrix for the subsequent optimal controller by the use of fuzzy logic inference. An adaptive optimal controller is then developed, so that its control behaviour and performance are adaptively adjusted for the chaotic synchronisation and compound uncertainty compensation. A supervisory compensator with recursive adaptation law is also designed to attenuate the residual compensation error and guarantee the synchronisation stability. Chaotic synchronisation convergence using the proposed approach can be mathematically ensured and speeded up with satisfactory robustness. Simulation results also demonstrate the effectiveness of the proposed control method in comparison with robust quadratic optimal control based on linear matrix inequality approach.

KEYWORDS:

• Uncertain chaotic synchronisation
• self-organising learning algorithm
• fuzzy logic regulation
• adaptive optimal control
• recursive adaptation compensation

Additional information

Funding

The supports of the National Natural Science Foundation of China [grant number 51805531], [grant number 51675470], the Natural Science Foundation of Jiangsu Province (BK20150200), and the Priority Academic Program Development of Jiangsu Higher Education Institutions are gratefully acknowledged.

Notes on contributors

Haiyun Zhang

Haiyun Zhang (Ph.D.) received his Bachelor’s and Doctor’s degree from the College of Mechanical Engineering of Zhejiang University, Hangzhou, China in 2009 and 2014, respectively. He is currently a Postdoctor at Robotics Institute of Zhejiang University, China. His research interests include Robotics, Mechatronic systems and control, Optimal control and optimality methods, Adaptive theory and applications. His research has received the support from Natural Science Foundation of Jiangsu Province, National Natural Science Foundation of China, etc.

Deyuan Meng

Deyuan Meng received the B. Eng. and M. Eng. degrees from China University of Mining and Technology, Xuzhou, China, in 2003 and 2006, respectively, and the Ph.D degree in mechatronic control engineering from Zhejiang University, Hangzhou, China, in 2013. He is currently an associate professor with the Department of Mechatronic Engineering, China University of Mining and Technology, China. His research interests include servo control of pneumatic systems, adaptive and robust control, and MRI-compatible robots.

Jin Wang

Jin Wang is currently an associate professor at the College of Mechanical Engineering, Zhejiang University, China. He gained his B.Sc. and Ph.D. in Mechanical Engineering of Zhejiang University, China, in 2003 and 2008, respectively. His research interests include design automation and optimization, industrial robotic offline planning, industrial robot intelligent control, and multi-robot coordinated control and application, etc.

Guodong Lu

Guodong Lu is currently a professor at the College of Mechanical Engineering, Zhejiang University, China. He is the Deputy Director of Engineering and Computer Graphics Institute at Zhejiang University. He received his B.Sc., M.Sc. and Ph.D. from Zhejiang University, china, in 1983, 1990 and 2000, respectively. His research interests include CAD/CAM, robotic offline planning, and robotics technology and application, etc.