This paper considers the problem on formation tracking control of second-order multi-agent systems (MASs) with communication time-varying delay. Sufficient conditions on the directed interaction topology and existence of the feedback gains to ensure the desired control are presented. Through choosing two augmented Lyapunov–Krasovskii (L–K) functionals and using some novel Wirtinger-based integral inequalities, the previously ignored information can be reconsidered and the application area of derived results can be greatly extended. Moreover, a novel constructive technique is given to compute out the controller gain by resorting to solving the achieved linear matrix inequalities (LMIs). Finally, a numerical example with comparisons and simulations is provided to illustrate the obtained results.
Issue Section:
Research Papers
Keywords:
Control theory
References
1.
Mehrabian
, A. R.
, and Khorasani
, K.
, 2015
, “Cooperative Optimal Synchronization of Networked Uncertain Nonlinear Euler-Lagrange Heterogeneous Multi-Agent Systems With Switching Topologies
,” ASME J. Dyn. Syst., Meas., Control
, 137
(4
), p. 041006
.2.
Olfati-Saber
, R.
, 2006
, “Flocking for Multi-Agent Dynamic Systems: Algorithms and Theory
,” IEEE Trans. Autom. Control
, 51
(3
), pp. 401
–420
.3.
Olfati-Saber
, R.
, and Murray
, R. M.
, 2002
, “Distributed Cooperative Control of Multiple Vehicle Formation Using Structural Potential Functions
,” IFAC Proc.
, 35
(1
), pp. 495
–500
.4.
Olfati-Saber
, R.
, and Jalalkamali
, R.
, 2012
, “Coupled Distributed Estimation and Control for Mobile Sensor Networks
,” IEEE Trans. Autom. Control
, 57
(10
), pp. 2609
–2614
.5.
Ding
, C. Y.
, Li
, J. M.
, and Li
, J. S.
, 2017
, “Distributed Optimal Consensus for Multi-Agent Systems Under Independent Position and Velocity Topology
,” ASME J. Dyn. Syst., Meas., Control
, 139
(10
), p. 101012
.6.
Olfati-Saber
, R.
, and Murray
, R. M.
, 2004
, “Consensus Problem in Networks With Switching Topology and Time-Delays
,” IEEE Trans. Autom. Control
, 49
(9
), pp. 1520
–1533
.7.
Ma
, C.
, and Zhang
, J.
, 2010
, “Necessary and Sufficient Conditions for Consensusability of Linear Multi-Agent Systems
,” IEEE Trans. Autom. Control
, 55
(5
), pp. 1263
–1268
.8.
Li
, W.
, Chen
, Z.
, and Liu
, Z.
, 2014
, “Formation Control for Nonlinear Multi-Agent Systems by Robust Output Regulation
,” Neurocomputing
, 140
, pp. 114
–120
.9.
Sun
, X.
, and Cassandras
, C. G.
, 2016
, “Optimal Dynamic Formation Control of Multi-Agent Systems in Constrained Environments
,” Automatica
, 73
, pp. 169
–179
.10.
Liu
, Y.
, and Geng
, Z.
, 2015
, “Finite-Time Formation Control for Linear Multi-Agent Systems: A Motion Planning Approach
,” Syst. Control Lett.
, 85
(9
), pp. 54
–60
.11.
Meng
, F.
, Shi
, Z.
, and Zhong
, Y.
, 2016
, “Distributed Formation Control of Singular Multi-Agent Systems
,” IEEE International Conference on Control and Automation
(ICCA
), Kathmandu, Nepal, June 1–3, pp. 915
–920
.12.
Ebihara
, Y.
, Peaucelle
, D.
, and Arzelier
, D.
, 2014
, “Efficient Convergence Rate Analysis of Multi-Agent Positive Systems Under Formation Control
,” IFAC Proc.
, 47
(3
), pp. 3790
–3796
.13.
Jafarian
, M.
, Vos
, E.
, and Persis
, C. D.
, 2015
, “Formation Control of a Multi-Agent System Subject to Coulomb Friction
,” Automatica
, 61
, pp. 253
–262
.14.
Akiyama
, K.
, Sekiguchi
, K.
, and Nonaka
, K.
, 2016
, “Robust Formation Control Applying Model Predictive Control to Multi-Agent System by Sharing Disturbance Information With UAVs
,” 55th Annual Conference of the Society of Instrument and Control Engineers
(SICE
), Tsukuba, Japan, Sept. 20–23, pp. 627
–632
.15.
Ge
, X.
, and Han
, Q. L.
, 2017
, “Distributed Formation Control of Networked Multi-Agent Systems Using a Dynamic Event-Triggered Communication Mechanism
,” IEEE Trans. Ind. Electron.
, 64
(10
), pp. 8118
–8127
.16.
Qin
, L.
, He
, X.
, and Zhou
, D.
, 2017
, “Distributed Proportion-Integration-Derivation Formation Control for Second-Order Multi-Agent Systems With Communication Time Delays
,” Neurocomputing
, 267
, pp. 271
–282
.17.
Dong
, X.
, Xi
, J.
, and Lu
, G.
, 2014
, “Formation Control for High-Order Linear Time-Invariant Multi-Agent Systems With Time Delays
,” IEEE Trans. Control Network Syst.
, 1
(3
), pp. 232
–240
.18.
Xiao
, Q.
, Wang
, Y. N.
, and Mao
, J. X.
, 2014
, “Nonlinear Control for Multi-Agent Formations With Delays in Noisy Environments
,” Acta Autom. Sin.
, 40
(12
), pp. 2959
–2967
.19.
Gonzalez
, A.
, and Aranda
, M.
, 2017
, “Time Delay Compensation Based on Smith Predictor in Multi-Agent Formation Control
,” IFAC-PaperOnline
, 50
(1
), pp. 11645
–11651
.20.
Li
, P.
, Qin
, K. Y.
, and Pu
, H. P.
, 2017
, “Distributed Robust Time-Varying Formation Control for Multiple Unmanned Aerial Vehicles Systems With Time-Delay
,” IEEE Chinese Control and Decision Conference
(CCDC
), Chongqing, China, May 28–30, pp. 1539
–1544
.21.
Mahmood
, A.
, and Kim
, Y.
, 2015
, “Leader-Following Formation Control of Quadcopters With Heading Synchronization
,” Aerosp. Sci. Technol.
, 47
, pp. 68
–74
.22.
Ding
, Y.
, Wei
, C.
, and Bao
, S.
, 2014
, “Decentralized Formation Control for Multiple UAVs Based on Leader-Following Consensus With Time-Varying Delays
,” IEEE Chinese Automation Congress
(CAC
), Changsha, China, Nov. 7–8, pp. 426
–431
.23.
Luo
, H. F.
, and Peng
, S. G.
, 2017
, “Formation Control for Nonlinear Multi-Agent Systems With Diverse Time-Varying Delays and Uncertain Topologies
,” IEEE Chinese Control and Decision Conference
(CCDC
), Chongqing, China, May 28–30, pp. 1730
–1736
.24.
Li
, W.
, Chen
, Z.
, and Liu
, Z.
, 2014
, “Robust H∞ Formation Control for Multi-Agent Systems With Nonlinear Dynamics and Time-Varying Delay
,” IEEE Chinese Control Conference
(CCC
), Nanjing, China, July 28–30, pp. 1144
–1149
.25.
Xue
, D.
, Yao
, J.
, and Wang
, J.
, 2013
, “Formation Control of Multi-Agent Systems With Stochastic Switching Topology and Time-Varying Communication Delays
,” IET Control Theory Appl.
, 7
(13
), pp. 1689
–1698
.26.
Haeri
, M.
, and Khani
, F.
, 2017
, “Constrained Tracking Control for Nonlinear Systems
,” ISA Trans.
, 70
, pp. 64
–72
.27.
Mu
, C.
, Sun
, C.
, and Wang
, D.
, 2017
, “Adaptive Tracking Control for a Class of Continuous-Time Uncertain Nonlinear Systems Using the Approximate Solution of HJB Equation
,” Neurocomputing
, 260
, pp. 432
–442
.28.
Xue
, L.
, Zhang
, W.
, and Lin
, Y.
, 2016
, “Global Output Tracking Control for High-Order Stochastic Nonlinear Systems With SISS Inverse Dynamics and Time-Varying Delays
,” J. Franklin Inst.
, 353
(13
), pp. 3249
–3270
.29.
Hua
, C. C.
, Li
, Y. F.
, and Li
, H. G.
, 2016
, “Decentralized Output Feedback Adaptive NN Tracking Control of Interconnected Nonlinear Time-Delay Systems With Prescribed Performance
,” Neurocomputing
, 174
, pp. 885
–896
.30.
Pan
, H.
, Sun
, W.
, and Jing
, X.
, 2017
, “Adaptive Tracking Control for Active Suspension Systems With Non-Ideal Actuators
,” J. Sound Vib.
, 399
, pp. 2
–20
.31.
Deng
, K. B.
, Wang
, R. X.
, and Li
, C. L.
, 2016
, “Tracking Control for a Ten-Ring Chaotic System With an Exponential Nonlinear Term
,” Int. J. Light Electron Opt.
, 130
, pp. 576
–583
.32.
Liu
, Y.
, and Zhang
, H.
, 2016
, “ADP Based Optimal Tracking Control for a Class of Linear Discrete-Time System With Multiple Delays
,” J. Franklin Inst.
, 353
(9
), pp. 2117
–2136
.33.
Weiwei
, Q.
, Bing
, H. E.
, and Liu
, G.
, 2016
, “Robust Model Predictive Tracking Control of Hypersonic Vehicles in the Presence of Actuator Constraints and Input Delays
,” J. Franklin Inst.
, 353
(17
), pp. 4351
–4367
.34.
Hu
, J.
, Cao
, J.
, and Yuan
, K.
, 2016
, “Cooperative Tracking for Nonlinear Multi-Agent Systems With Hybrid Time-Delayed Protocol
,” Neurocomputing
, 171
, pp. 171
–178
.35.
Han
, L.
, Dong
, X. W.
, and Li
, Q.
, 2017
, “Formation Tracking Control for Time-Delayed Multi-Agent Systems With Second-Order Dynamics
,” Chin. J. Aeronautics
, 30
(1
), pp. 348
–357
.36.
Dong
, X. W.
, Zhou
, Y.
, and Ren
, Z.
, 2016
, “Time-Varying Formation Tracking for Second-Order Multi-Agent Systems Subjected to Switching Topologies With Application to Quadrotor Formation Flying
,” IEEE Trans. Ind. Electron.
, 64
(6
), pp. 5014
–5024
.37.
Han
, L.
, Dong
, X. W.
, and Yi
, K.
, 2017
, “Circular Formation Tracking Control for Time-Delayed Second-Order Multi-Agent Systems With Multiple Leaders
,” IEEE Guidance, Navigation and Control Conference
(CGNCC
), Nanjing, China, Aug. 12–14, pp. 1648
–1653
.38.
Ge
, M. F.
, Guan
, Z. H.
, and Yang
, C.
, 2016
, “Time-Varying Formation Tracking of Multiple Manipulators Via Distributed Finite-Time Control
,” Neurocomputing
, 202
, pp. 20
–26
.39.
Wang
, P.
, Li
, C.
, and Sun
, Y.
, 2016
, “State Feedback Control for Formation Keeping in Elliptical Orbits With Unknown Relative Perturbations
,” IEEE Chinese Control Conference
(CCC
), Chengdu, China, July 27–29, pp. 5660
–5665
.40.
Zeng
, H.
, He
, Y.
, and Wu
, M.
, 2015
, “New Results on Stability Analysis for Systems With Discrete Distributed Delay
,” Automatica
, 63
, pp. 189
–192
.41.
Liu
, Y.
, Ju
, H. P.
, and Guo
, B. Z.
, 2016
, “Results on Stability of Linear Systems With Time Varying Delay
,” IET Control Theory Appl.
, 11
(1
), pp. 129
–134
.42.
Park
, M.
, Kwon
, O.
, Park
, J. H.
, and Lee
, S.
, 2015
, “Stability of Time-Delay Systems Via Wirtinger-Based Double Integral Inequality
,” Automatica
, 55
, pp. 204
–208
.43.
Park
, P.
, Lee
, W.
, and Lee
, S. Y.
, 2016
, “Auxiliary Function-Based Integral Inequalities for Quadratic Functions and Their Applications to Time-Delay Systems
,” J. Franklin Inst.
, 352
(4
), pp. 1378
–1396
.44.
Hua
, C. C.
, Wu
, S. S.
, Yang
, X.
, and Guan
, X. P.
, 2017
, “Stability Analysis of Time-Delay Systems Via Free-Matrix-Based Double Integral Inequality
,” Int. J. Syst. Sci.
, 48
(2
), pp. 257
–263
.45.
Zhang
, C. K.
, Jiang
, L.
, Wu
, M.
, and Zeng
, H. B.
, 2016
, “Stability Analysis of Systems With Time-Varying Delay Via Relaxed Integral Inequalities
,” Syst. Control Lett.
, 92
, pp. 52
–61
.46.
Shen
, M. Q.
, Yan
, S.
, and Zhang
, G. M.
, 2016
, “A New Approach to Event-Triggered Static Output Feedback Control of Networked Control Systems
,” ISA Trans.
, 65
(4
), pp. 468
–474
.47.
Li
, T.
, Wang
, T.
, Song
, A. G.
, and Fei
, S. M.
, 2010
, “Delay-Derivative-Dependent Stability for Delayed Neural Networks With Unbounded Distributed Delay
,” IEEE Trans. Neural Networks
, 21
, pp. 1365
–1371
.Copyright © 2018 by ASME
You do not currently have access to this content.
