Robust consensus tracking of double-integrator dynamics by bounded distributed control. (English) Zbl 1334.93026
Summary: This paper studies the robust consensus tracking problem of multiple second-order systems with additive disturbances and a direct communication topology. We design a continuous, bounded and distributed controller that is composed of a tracker and an uncertainty and disturbance estimator. The tracker makes the nominal closed-loop system globally asymptotically stable, while the output of uncertainty and disturbance estimator attenuates the effect of disturbances. We show that if the disturbances converge to constants, the tracking error converges asymptotically to zero, whereas for other types of disturbances, the obtained error system is small-signal \(L_\infty\) stable. Some inequalities are developed to show the relationship between the ultimate bounds of tracking errors and the design parameters. Finally, simulation results for four cases are presented to demonstrate the performance of the controller.
MSC:
| 93A14 | Decentralized systems |
| 93B35 | Sensitivity (robustness) |
| 93C10 | Nonlinear systems in control theory |
| 93C73 | Perturbations in control/observation systems |
| 93C15 | Control/observation systems governed by ordinary differential equations |
References:
| [1] | JadbabaieA, LinJ, MorseAS. Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Transactions on Automatic Control2003; 48(6):988-1001. · Zbl 1364.93514 |
| [2] | HongY, GaoL, ChengD, HuJ. Tracking control for multi‐agent consensus with an active leader and variable topology. Automatica2006; 142(7):1177-1182. · Zbl 1117.93300 |
| [3] | WangX, HongY, HuangJ, JiangZ. A distributed control approach to a robust output regulation problem for multi‐agent linear systems. IEEE Transactions on Automatic Control2010; 55(12):2891-2895. · Zbl 1368.93577 |
| [4] | ZhangH, LewisF. Adaptive cooperative tracking control of higher‐order nonlinear systems with unknown dynamics. Automatica2012; 48:1432-1439. · Zbl 1348.93144 |
| [5] | LinP, JiaYM, LiL. Distributed robust H_∞ consensus control in directed networks of agents with time‐delay. Systems & Control Letters2008; 157(8):643-653. · Zbl 1140.93355 |
| [6] | TianY, LiuC. Robust consensus of multi‐agent systems with diverse input delays and asymmetric interconnection perturbations. Automatica2009; 45:1347-1353. · Zbl 1162.93027 |
| [7] | LiZ, DuanZ, ChenG, HuangL. Consensus of multi‐agent systems and synchronization of complex networks: a unified viewpoint. IEEE Transactions on Circuits and Systems‐I2010; 57(1):213-224. · Zbl 1468.93137 |
| [8] | ZhangWL, WangZ, GuoY. Robust consensus for uncertain multi‐agent systems on directed communication topologies. The 49th IEEE Conference on Decision and Control (CDC), Atlanta, GA, Dec. 15-17, 2010; 6317-6322. |
| [9] | DasA, LewisF. Distributed adaptive control for synchronization of unknown nonlinear networked systems. Automatica2010; 146(12):2014-2021. · Zbl 1205.93045 |
| [10] | SuY, HongY, HuangJ. A result on the cooperative robust output regulation for linear uncertain multi‐agent systems. The 9th IEEE International Conference on Control and Automation, Santiago, Chile, Dec. 19-21, 2011; 639-643. |
| [11] | HuG. Robust consensus tracking of a class of second‐order multi‐agent dynamic systems. Systems & Control Letters2012; 61:134-142. · Zbl 1250.93009 |
| [12] | ZhuB, LiZ, LiuHT, GaoH. Robust second‐order tracking of multi‐vehicle systems without velocity measurements on directed communication topologies. The 2014 American Control Conference, Portland, Oregon, June 4‐6, 2014; 5414-5419. |
| [13] | ZhuB, LiuHT, LiZ. Robust distributed attitude synchronization of multiple three‐DOF experimental helicopters. Control Engineering Practice2015; 36:87-99. |
| [14] | KhooS, XieL, ManZ. Robust finite‐time consensus tracking algorithm for multirobot systems. IEEE Transaction on Mechatronics2009; 14(2):219-228. |
| [15] | CaoY, RenW. Distributed coordinated tracking with reduced interaction via a variable structure apporach. IEEE Transactions on Automatic Control2012; 57(1):33-48. · Zbl 1369.93012 |
| [16] | RenW. On consensus algorithms for double‐integrator dynamics. IEEE Transactions on Automatic Control2008; 53(6):1503-1509. · Zbl 1367.93567 |
| [17] | AbdessameudA, TayebiA. On consensus algorithms for double‐integrator dynamics without velocity measurements and with input constraints. Systems & Control Letters2010; 59:812-821. · Zbl 1217.93009 |
| [18] | AbdessameudA, TayebiA. On consensus algorithms design for double‐integrator dynamics. Automatica2013; 49:253-260. · Zbl 1257.93002 |
| [19] | ZhuB, SunW, MengC. Position tracking of multi double‐integrator dynamics by bounded distributed control without velocity measurements. The 2013 American Control Conference (ACC), Washington, DC, USA, June 17‐19, 2013; 4039-4044. |
| [20] | TaloleaSE. Robust input‐output linearisation using uncertainty and disturbance estimation. International Journal of Control2010; 82(10):1794-1803. · Zbl 1178.93039 |
| [21] | KupermanA, ZhongQC. Robust control of uncertain nonlinear systems with state delays based on an uncertainty and disturbance estimator. International Journal of Robust and Nonlinear Control2011; 21(1):79-92. · Zbl 1207.93027 |
| [22] | DeshpandeVS, PhadkeSB. Control of uncertain nonlinear systems using an uncertainty and disturbance estimator. Journal of Dynamic Systems, Measurement and Control2012; 134(2):024501 (7 pages). |
| [23] | Aguinaga‐RuizE, Zavala‐RioA, SantibanezV, ReyesF. Global trajectory tracking through static feedback for robot manipulators with input saturations. The 47th IEEE Conference on Decision and Control, Cancun, Mexico, 2008; 3516-3522. |
| [24] | Aguinaga‐RuizE, Zavala‐RioA, SantibanezV, ReyesF. Global trajectory tracking through static feedback for robot manipulators with bounded inputs. IEEE Transactions on Control Systems Technology2009; 17(4):934-944. |
| [25] | QuZ. Cooperative Control of Dynamical Systems: Applications to Autonomous Vehicles. Springer‐Verlag: London, 2009. · Zbl 1171.93005 |
| [26] | YuW, ChenG, CaoM, KurthsJ. Second‐order consensus for multi‐agent systems with directed topologies and nonlinear dynamics. IEEE Transactions on Systems, Man and Cybernetics, Part B2010; 40:881-891. |
| [27] | SuH, ChenG, WangX, LinZ. Adaptive second‐order consensus of networked mobile agents with nonlinear dynamics. Automatica2011; 47:368-375. · Zbl 1207.93006 |
| [28] | KhalilHK. Nonlinear Systems (3rd edition). Prentice Hall: Upper Saddle River, NJ, 2002. · Zbl 1003.34002 |
| [29] | PengY, VrancicD, HanusR. Anti‐Windup, bumpless, and conditioned transfer techniques for PID controllers. IEEE Control Systems Magazine1996; 16(4):48-57. |
| [30] | AstromKJ, HagglundT. Automatic Tuning of PID Controllers. Instrument Society of American: Research Triangle Park, N.C., 1988 |
| [31] | CampoPJ, MorariIM. Robust control of processes subject to saturation nonlinearities. Computers and Chemical Engineering1990; 114(4):343-358. |
| [32] | VisioliA. Practical PID Control. Springer‐Verlag: London, 2006. · Zbl 1122.93032 |
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