×

Synchronization of uncertain complex dynamical networks via adaptive control. (English) Zbl 1160.93356

Summary: Synchronization of an uncertain dynamical network with time-varying delay is investigated by means of adaptive control schemes. Time delays and uncertainties exist universally in real-world complex networks. Especially, parameters of nodes in these complex networks are usually partially or completely uncertain. Considering the networks with unknown or partially known nodes, we design adaptive controllers for the corresponding complex dynamical networks, respectively. Several criteria guaranteeing synchronization of such systems are established by employing the Lyapunov stability theorem. Analytical and numerical results show that the proposed controllers have high robustness against parameter variations including network topologies, coupling structures, and strength.

MSC:

93C40 Adaptive control/observation systems
93C41 Control/observation systems with incomplete information
93C15 Control/observation systems governed by ordinary differential equations
93D09 Robust stability
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Albert, Statistical mechanics of complex networks, Review of Modern Physics 74 pp 47– (2002)
[2] Wu, Synchronization in an array of linearly coupled dynamical systems, IEEE Transactions on Circuits and Systems I 42 (8) pp 430– (1995) · Zbl 0867.93042
[3] Pecora, Master stability function for synchronized coupled systems, Physical Review Letters 80 (10) pp 2109– (1998)
[4] Wang, Synchronization in small-world dynamical networks, International Journal of Bifurcation and Chaos 12 (1) pp 187– (2002)
[5] Wang, Synchronization in scale-free dynamical networks: robustness and fragility, IEEE Transactions on Circuits and Systems I 49 (1) pp 54– (2002) · Zbl 1368.93576
[6] Li, Synchronization in general complex dynamical networks with coupling delays, Physica A 343 pp 263– (2004)
[7] Lü, A time-varying complex dynamical network model and its controlled synchronization criteria, IEEE Transactions on Automatic Control 50 (6) pp 841– (2005) · Zbl 1365.93406
[8] Gao, New criteria for synchronization stability of general complex dynamical networks with coupling delays, Physics Letters A 360 (2) pp 263– (2006) · Zbl 1236.34069
[9] Zhou, Synchronization in general complex delayed dynamical networks, IEEE Transactions on Circuits and Systems I 53 (3) pp 733– (2006) · Zbl 1374.37056
[10] Wang, Synchronization criteria for a generalized complex delayed dynamical network model, Physica A 383 pp 703– (2007)
[11] Lu, New approach to synchronization analysis of linearly coupled ordinary differential systems, Physica D 213 (2) pp 214– (2006) · Zbl 1105.34031
[12] Czeisler, Bright light resets the human circadian pacemaker independent of the timing of the sleep-wake cycle, Science 233 pp 667– (1986)
[13] Sorrentino, Effects of the network structural properties on its controllability, Chaos 17 pp 1– (2007) · Zbl 1163.37367
[14] Peskin, Mathematical Aspects of Heart Physiology (1977)
[15] Isidori, Output regulation of nonlinear systems, IEEE Transactions on Automatic Control 35 (2) pp 131– (1990) · Zbl 0704.93034
[16] Hepburn, Error feedback and internal models on differentiable manifolds, IEEE Transactions on Automatic Control 29 (5) pp 397– (1984) · Zbl 0543.93028
[17] Huang, Stabilization on zero-error manifolds and the nonlinear servomechanism problem, IEEE Transactions on Automatic Control 37 (7) pp 1009– (1992) · Zbl 0767.93042
[18] Huijberts, Regulation and controlled synchronization for complex dynamical systems, International Journal of Robust and Nonlinear Control 10 (5) pp 363– (2000) · Zbl 1047.93540
[19] Hu, Instability and controllability of linearly coupled oscillators: eigenvalue analysis, Physical Review E 58 (4) pp 4440– (1998)
[20] Wang, Pinning control of scale-free dynamical networks, Physica A 310 (3) pp 521– (2002) · Zbl 0995.90008
[21] Li, Pinning a complex dynamical network to its equilibrium, IEEE Transactions on Circuits and Systems I 51 (10) pp 2074– (2004) · Zbl 1374.94915
[22] Li, Robust adaptive synchronization of uncertain dynamical networks, Physics Letters A 324 (2) pp 166– (2004) · Zbl 1123.93316
[23] Zhou, Adaptive synchronization of an uncertain complex dynamical network, IEEE Transactions on Automatic Control 51 (4) pp 652– (2006) · Zbl 1366.93544
[24] Li, Controlling complex dynamical networks with coupling delays to a desired orbit, Physics Letters A 359 (1) pp 42– (2006) · Zbl 1209.93136
[25] Khargonekar, Robust stabilization of uncertain linear systems: quadratic stabilizability and H control theory, IEEE Transactions on Automatic Control 35 (3) pp 356– (1990) · Zbl 0707.93060
[26] Horn, Matrix Analysis (1985) · Zbl 0576.15001 · doi:10.1017/CBO9780511810817
[27] Hale, Introduction to Functional Differential Equations (1993) · Zbl 0787.34002 · doi:10.1007/978-1-4612-4342-7
[28] Barabasiá, Emergence of scaling in random networks, Science 286 (5439) pp 509– (1999)
[29] Chua, A universal circuit for studying and generating chaos I: routes to chaos, IEEE Transactions on Circuits and Systems I 40 (10) pp 732– (1993) · Zbl 0844.58052
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.