Modares Mechanical Engineering

Modares Mechanical Engineering

Formation Tracking of Fractional-Order Multi-Agent Systems by Using Robust Sliding Mode Approach

Authors
Vahid Momeni 1
Mahdi Sojoodi
Vahid Johari Majd 2
1 Control Eng.,Electrical and Computer Eng Faculty, Tarbiat Mdares University
2 Control Dep.,Electrical and Computer Eng Faculty, tarbiat Moadres University
Abstract
The main purpose of this paper is to the distributed formation tracking for fractional order multi agent systems with the leader-follower approach. First, it discusses the Lyapunov candidate function used to check the stability of the controlled system. The introduced candidate function is based on the properties of the matrix representing the desired system graph of the system. In this phase, the Lyapunov direct method is used to determine the stability of fractional order systems. Then, using sliding mode control, a decentralized controller design for tracking in fractional multi agent systems is presented in which it introduces and verifies the introduced control inputs. In the model, the input system is also considered as a disturbance type, and the control efficiency designed in turbulence mode is shown. In this section, it is shown that the controller introduced in the previous section has a desirable efficiency due to the sliding mode control. In the second section, the stability of the system, such as the first section, is investigated. at the end of this paper, several simulation examples are developed for controlling the performance of the controller.
Keywords
Formation tracking
Multi agent systems
Distributed Control
Sliding mode control
Fractional order systems

Subjects

[1] Y. Xu, W. Liu, and J. Gong, “Stable multi-agent-based load shedding algorithm for power systems,” IEEE Trans. Power Syst., vol. 26, no. 4, pp. 2006–2014, 2011.
[2] G. Xiong and S. Kishore, “Second Order Distributed Consensus Time Synchronization Algorithm for Wireless Sensor Networks,” IEEE GLOBECOM 2008 - 2008 IEEE Glob. Telecommun. Conf., vol. 2009, pp. 1–5, 2008.
[3] F. Xiao, L. Wang, J. Chen, and Y. Gao, “Finite-time formation control for multi-agent systems,” Automatica, vol. 45, no. 11, pp. 2605–2611, 2009.
[4] L. Zhao, Y. Jia, J. Yu, and J. Du, “H??? sliding mode based scaled consensus control for linear multi-agent systems with disturbances,” Appl. Math. Comput., vol. 292, pp. 375–389, 2017.
[5] A. Amini, A. Azarbahram, and M. Sojoodi, “$$H_{infty }$$ H ∞ Consensus of nonlinear multi-agent systems using dynamic output feedback controller: an LMI approach,” Nonlinear Dyn., vol. 85, no. 3, pp. 1865–1886, 2016.
[6] A. Mahmood and Y. Kim, “Decentrailized formation flight control of quadcopters using robust feedback linearization,” J. Franklin Inst., vol. 354, no. 2, pp. 852–871, 2017.
[7] S. M. Kang and H. S. Ahn, “Design and Realization of Distributed Adaptive Formation Control Law for Multi-Agent Systems with Moving Leader,” IEEE Trans. Ind. Electron., vol. 63, no. 2, pp. 1268–1279, 2016.
[8] L. Han, X. Dong, Q. Li, and Z. Ren, “Formation-containment control for second-order multi-agent systems with time-varying delays,” Neurocomputing, vol. 218, pp. 439–447, 2016.
[9] X. Dong and G. Hu, “Time-varying formation control for general linear multi-agent systems with switching directed topologies,” Automatica, vol. 73, pp. 47–55, 2016.
[10] J. Li and J. Li, “Adaptive iterative learning control for coordination of second‐order multi‐agent systems,” Int. J. Robust Nonlinear Control, vol. 24, no. 18, pp. 3282–3299, 2014.
[11] W. Ren, “Consensus strategies for cooperative control of vehicle formations,” IET Control Theory Appl., vol. 1, no. 2, pp. 505–512, 2007.
[12] H. M. Guzey, T. Dierks, and S. Jagannathan, “Hybrid consensus-based formation control of agents with second order dynamics,” Proc. Am. Control Conf., vol. 2015–July, pp. 4386–4391, 2015.
[13] J. Seo, Y. Kim, S. Kim, and A. Tsourdos, “Consensus-based reconfigurable controller design for unmanned aerial vehicle formation flight,” Proc. Inst. Mech. Eng. Part G J. Aerosp. Eng., vol. 226, no. 7, pp. 817–829, 2012.
[14] Y. Cao, Y. Li, W. Ren, and Y. Q. Chen, “Distributed coordination algorithms for multiple fractional-order systems,” Proc. IEEE Conf. Decis. Control, pp. 2920–2925, 2008.
[15] Y. Cao and W. Ren, “Distributed formation control for fractional-order systems: Dynamic interaction and absolute/relative damping,” Syst. Control Lett., vol. 59, no. 3–4, pp. 233–240, 2010.
[16] C. Song, J. Cao, and Y. Liu, “Robust consensus of fractional-order multi-agent systems with positive real uncertainty via second-order neighbors information,” Neurocomputing, vol. 165, pp. 293–299, 2015.
[17] J. Chen, Z. H. Guan, T. Li, D. X. Zhang, M. F. Ge, and D. F. Zheng, “Multiconsensus of fractional-order uncertain multi-agent systems,” Neurocomputing, vol. 168, pp. 698–705, 2015.
[18] C. Yin, Y. Chen, and S. Zhong, “Fractional-order sliding mode based extremum seeking control of a class of nonlinear systems,” Automatica, vol. 50, no. 12, pp. 3173–3181, 2014.
[19] Y. Li, Y. Chen, and I. Podlubny, “Stability of fractional-order nonlinear dynamic systems: Lyapunov direct method and generalized Mittag-Leffler stability,” Comput. Math. with Appl., vol. 59, no. 5, pp. 1810–1821, 2010.
[20] W. Ren and Y. Cao, Distributed coordination of multi-agent networks: emergent problems, models, and issues. Springer Science & Business Media, 2010.
Modares Mechanical Engineering
Volume 18, Issue 8
December 2018
Pages 30-36