Cooperative optimal preview tracking control of discrete-time multi-agent systems

LU Yan-rong; LIAO Fu-cheng; REN Jin-ming; FU Hai-long; SHENG Chao-yi

doi:10.13374/j.issn2095-9389.2018.02.015

Volume 40 Issue 2

Feb. 2018

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Article Navigation > Chinese Journal of Engineering > 2018 > 40(2): 241-251

LU Yan-rong, LIAO Fu-cheng, REN Jin-ming, FU Hai-long, SHENG Chao-yi. Cooperative optimal preview tracking control of discrete-time multi-agent systems[J]. Chinese Journal of Engineering, 2018, 40(2): 241-251. doi: 10.13374/j.issn2095-9389.2018.02.015

Citation:

LU Yan-rong, LIAO Fu-cheng, REN Jin-ming, FU Hai-long, SHENG Chao-yi. Cooperative optimal preview tracking control of discrete-time multi-agent systems[J]. Chinese Journal of Engineering, 2018, 40(2): 241-251. doi: 10.13374/j.issn2095-9389.2018.02.015

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Cooperative optimal preview tracking control of discrete-time multi-agent systems

doi: 10.13374/j.issn2095-9389.2018.02.015

School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China

Received Date: 2017-06-01

Abstract

Abstract

This study investigated the cooperative optimal preview tracking problem of discrete-time multi-agent systems under the assumption of the communication topology containing a directed spanning tree. First, a state augmentation technique was used to convert the cooperative preview tracking problem into a global optimal regulation problem of an augmented system. Second, by resorting to relative conclusions about the discrete-time linear quadratic regulation theory, an optimal controller was obtained, which can guarantee the asymptotic stability of the closed-loop augmented system. Moreover, a global optimal preview controller was provided in order for the original system to achieve the tracking consensus. Finally, the simulation results not only verified the effectiveness of the designed controller, but also indicated that it is critical for accurately tracking the reference signal to moderately increase the preview length.
- multi-agent systems,
- cooperative tracking,
- preview control,
- algebraic Riccati equation

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References(34)

References

[1]	Lynch N A. Distributed Algorithms. San Francisco:Morgan Kaufmann, 1996
[2]	Olfati-Saber R, Murray R M. Consensus problems in networks of agents with switching topology and time-delays. IEEE Trans Autom Control, 2004, 49(9):1520
[3]	Ren W, Atkins E. Distributed multi-vehicle coordinated control via local information exchange. Int J Robust Nonlinear Control, 2007, 17(10-11):1002
[4]	Ren W. On consensus algorithms for double-integrator dynamics. IEEE Trans Autom Control, 2008, 53(6):1503
[5]	Wang J H, Cheng D Z, Hu X M. Consensus of multi-agent linear dynamic systems. Asian J Control, 2008, 10(2):144
[6]	Seo J H, Shim H, Back J. Consensus of high-order linear systems using dynamic output feedback compensator:low gain approach. Automatica, 2009, 45(11):2659
[7]	Yang X R, Liu G P. Consensus of descriptor multi-agent systems via dynamic compensators. IET Control Theory Appl, 2014, 8(6):389
[8]	Li Z K, Duan Z S, Chen G R. Dynamic consensus of linear multi-agent systems. IET Control Theory Appl, 2011, 5(1):19
[9]	Li Z K, Duan Z S, Chen G R. On H_∞ and H₂ performance regions of multi-agent systems. Automatica, 2011, 47(4):797
[10]	Chen Y, Lü J H, Lin Z. Consensus of discrete-time multi-agent systems with transmission nonlinearity. Automatica, 2013, 49(6):1768
[11]	Yang T, Meng Z, Dimarogonas D V, et al. Global consensus for discrete-time multi-agent systems with input saturation constraints. Automatica, 2014, 50(2):499
[12]	Qin J, Gao H, Yu C. On discrete-time convergence for general linear multi-agent systems under dynamic topology. IEEE Trans Autom Control, 2014, 59(4):1054
[13]	Xiao F, Wang L. Consensus protocols for discrete-time multi-agent systems with time-varying delays. Automatica, 2008, 44(10):2577
[14]	Cortés J. Distributed algorithms for reaching consensus on general functions. Automatica, 2008, 44(3):726
[15]	Hong Y, Chen G, Bushnell L. Distributed observers design for leader-following control of multi-agent networks. Automatica, 2008, 44(3):846
[16]	Hu J, Feng G. Distributed tracking control of leader-follower multi-agent systems under noisy measurement. Automatica, 2011, 46(8):1382
[17]	Zhu W, Cheng D. Leader-following consensus of second-order agents with multiple time-varying delays. Automatica, 2010, 46(12):1994
[18]	Ni W, Cheng D. Leader-following consensus of multi-agent systems under fixed and switching topologies. Syst Control Lett, 2010, 59(3-4):209
[19]	Wang X H, Xu D B, Hong Y G. Consensus control of nonlinear leader-follower multi-agent systems with actuating disturbances. Syst Control Lett, 2014, 73:58
[20]	Cao Y C, Ren W. Distributed coordinated tracking with reduced interaction via a variable structure approach. IEEE Trans Autom Control, 2012, 57(1):33
[21]	Hać A. Optimal linear preview control of active vehicle suspension. Vehicle Syst Dyn, 1992, 21(1):167
[22]	Shimmyo S, Sato T, Ohnishi K. Biped walking pattern generation by using preview control based on three-mass model. IEEE Trans Ind Electron, 2013, 60(11):5137
[23]	Katayama T, Ohki T, Inoue T, et al. Design of an optimal controller for a discrete-time system subject to previewable demand. Int J Control, 1985, 41(3):677
[24]	Kojima A, Ishijima S. LQ preview synthesis optimal control and worst case analysis. IEEE Trans Autom Control, 1999, 44(2):352
[25]	Liao F C, Takaba K, Katayama T, et al. Design of an optimal preview servomechanism for discrete-time systems in a multirate setting. Dyn Contin Discrete Impuls Syst Ser B, 2003, 10(5):727
[26]	Moelja A A, Meinsma G. H₂-optimal control of systems with multiple i/o delays:time domain approach. Automatica, 2005, 41(7):1229
[27]	Moelja A A, Meinsma G. H₂ control of preview systems. Automatica, 2006, 42(6):945
[28]	Takaba K. Robust servomechanism with preview action for polytopic uncertain systems. Int J Robust Nonlinear Control, 2000, 10(2):101
[29]	Li L, Liao F. C Parameter-dependent preview control with robust tracking performance. IET Control Theory Appl, 2017, 11(1):38
[30]	Wang D, Liao F C, Tomizuka M. Adaptive preview control for piecewise discrete-time systems using multiple models. Appl Math Model, 2016, 40(23-24):9932
[31]	Liao F C, Lu Y R, Liu H Y. Cooperative optimal preview tracking control of continuous-time multi-agent systems. Int J Control, 2016, 89(10):2019
[32]	Horn R A, Johnson C R. Matrix Analysis. Cambridge, MA:Cambridge University Press, 1990
[35]	You K Y, Xie L H. Coordination of discrete-time multi-agent systems via relative output feedback. Int J Robust Nonlinear Control, 2011, 21(13):1587
[36]	You K Y, Li Z K, Xie L H. Consensus condition for linear multi-agent systems over randomly switching topologies. Automatica, 2013, 49(10):3125