Finite-Time Distributed Average Tracking for Second-Order Nonlinear Systems

• Published in: IEEE transaction on neural networks and learning systems Vol. 30; no. 6; pp. 1780 - 1789
• Main Authors: Zhao, Yu, Liu, Yongfang, Wen, Guanghui, Huang, Tingwen
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.06.2019; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Adaptive algorithms; Adaptive control; adaptive-gain algorithm; Algorithms; Central Processing Unit; Computer simulation; Convergence; distributed average tracking (DAT); Finite-time algorithm; Heuristic algorithms; Learning systems; Liapunov functions; Multi-agent systems; multiple signals; Nonlinear dynamical systems; nonlinear dynamics; Nonlinear systems; Reference signals; Settling; Tracking
• ISSN: 2162-237X; 2162-2388; 2162-2388
• DOI: 10.1109/TNNLS.2018.2873676

This paper studies the distributed average tracking (DAT) problem for multiple reference signals described by the second-order nonlinear dynamical systems. Leveraging the state-dependent gain design and the adaptive control approaches, a couple of DAT algorithms are developed in this paper, which are named finite-time and adaptive-gain DAT algorithms. Based on the finite-time one, the states of the physical agents in this paper can track the average of the time-varying reference signals within a finite settling time. Furthermore, the finite settling time is also estimated by considering a well-designed Lyapunov function in this paper. Compared with asymptotical DAT algorithms, the proposed finite-time algorithm not only solve finite-time DAT problems but also ensure states of physical agents to achieve an accurate average of the multiple signals. Then, an adaptive-gain DAT algorithm is designed. Based on the adaptive-gain one, the DAT problem is solved without global information. Thus, it is fully distributed. Finally, numerical simulations show the effectiveness of the theoretical results.