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**Cooperative adaptive control for synchronization of second-order systems with unknown nonlinearities.**
*(English)*
Zbl 1227.93006

Summary: This paper studies synchronization to a desired trajectory for multi-agent systems with second-order integrator dynamics and unknown nonlinearities and disturbances. The agents can have different dynamics and the treatment is for directed graphs with fixed communication topologies. The command generator or leader node dynamics is also nonlinear and unknown. Cooperative tracking adaptive controllers are designed based on each node maintaining a neural network parametric approximator and suitably tuning it to guarantee stability and performance. A Lyapunov-based proof shows the ultimate boundedness of the tracking error. A simulation example with nodes having second-order Lagrangian dynamics verifies the performance of the cooperative tracking adaptive controller.

### MSC:

93A14 | Decentralized systems |

93C40 | Adaptive control/observation systems |

93C10 | Nonlinear systems in control theory |

92B20 | Neural networks for/in biological studies, artificial life and related topics |

### Keywords:

cooperative control; multi-agent system; nonlinear adaptive control; Lyapunov stability; neural network
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\textit{A. Das} and \textit{F. L. Lewis}, Int. J. Robust Nonlinear Control 21, No. 13, 1509--1524 (2011; Zbl 1227.93006)

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### References:

[1] | Kuramoto, International Symposium on Mathematical Problems in Theoretical Physics pp 420– (1975) |

[2] | Tsitsiklis JN Problems in decentralized decision making and computation 1984 |

[3] | Ren, Distributed Consensus in Multi-vehicle Cooperative Control: Theory and Applications (2008) · Zbl 1144.93002 |

[4] | Ren W Beard RW Atkins EM A survey of consensus problems in multi-agent coordination |

[5] | Olfati-Saber, Consensus and cooperation in networked multi-agent systems, Proceedings of the IEEE 95 pp 215– (2007) · Zbl 1376.68138 |

[6] | Ren, Information consensus in multivehicle cooperative control, IEEE Control Systems Magazine 27 pp 71– (2007) |

[7] | Olfati-Saber, Consensus problems in networks of agents with switching topology and time-delays, IEEE Transaction of Automatic Control 49 pp 1520– (2004) · Zbl 1365.93301 |

[8] | Fax, Information flow and cooperative control of vehicle formations, IEEE Transactions on Automatic Control 49 pp 1465– (2004) · Zbl 1365.90056 |

[9] | Ren, Consensus seeking in multiagent systems under dynamically changing interaction topologies, IEEE Transactions on Automatic Control 50 pp 655– (2005) · Zbl 1365.93302 |

[10] | Jadbabaie, Coordination of groups of mobile autonomous agents using nearest neighbor rules, IEEE Transactions on Automatic Control 48 pp 988– (2003) · Zbl 1364.93514 |

[11] | Jiang T Baras J Graph algebraic interpretation of trust establishment in autonomic networks 2009 |

[12] | Spanos DP Olfati-Saber R Murray RM Dynamic consensus on mobile networks 2005 |

[13] | Lu, A time-varying complex dynamical network model and its controlled synchronization criteria, IEEE Transactions on Automatic Control 50 pp 841– (2005) · Zbl 1365.93406 |

[14] | Wang, Pinning control of scale-free dynamical networks, Physica A 310 pp 521– (2002) · Zbl 0995.90008 |

[15] | Li, Pinning a complex dynamical network to its equilibrium, IEEE Transactions on Circuits and Systems 51 pp 2074– (2004) · Zbl 1374.94915 |

[16] | Li, Consensus of multi-agent systems and synchronization of complex networks: a unified viewpoint, IEEE Transactions on Circuits and Systems Part I: Regular Papers 57 (1) pp 213– (2010) |

[17] | Ren, High-order and model reference consensus algorithms in cooperative control of multivehicle systems, Journal of Dynamic Systems, Measurement and Control 129 pp 678– (2007) |

[18] | Zhu, On the general consensus protocol of multi-agent systems with double-integrator dynamics, Linear Algebra and its Applications 431 pp 701– (2009) · Zbl 1165.93022 |

[19] | Khoo, Robust finite-time consensus tracking algorithm for multirobot systems, IEEE Transaction on Mechatronics 14 pp 219– |

[20] | Bo, Second-order consensus in networks of agents with delayed dynamics, Journal of Natural Sciences 14 pp 158– (2009) |

[21] | Yang W Bertozzi AL Wang X |

[22] | Su H Wang X |

[23] | Seo, Consensus of high-order linear systems using dynamic output feedback compensator: low gain approach, Automatica 45 pp 2659– (2009) · Zbl 1180.93005 |

[24] | Chopra, Advances in Robot Control pp 107– (2006) |

[25] | Hornik, Multilayer feedforward networks are universal approximations, Neural Networks 20 pp 359– (1989) · Zbl 1383.92015 |

[26] | Qu, Cooperative Control of Dynamical Systems: Applications to Autonomous Vehicles (2009) · Zbl 1171.93005 |

[27] | Lewis, Neural Network Control of Robot Manipulators and Nonlinear Systems (1999) |

[28] | Lewis, Multilayer neural net robot controller with guaranteed tracking performance, IEEE Transactions of Neural Networks 7 pp 388– (1996) |

[29] | Narendra, Adaptive Control of Dynamical Systems Using Neural Networks (1992) |

[30] | Narendra, Identification and control of dynamical systems using neural networks, IEEE Transaction of Neural Networks 1 pp 4– (1990) |

[31] | Chen, Adaptive control of nonlinear systems using neural networks, International Journal of Control 55 pp 1299– (1992) · Zbl 0759.93046 |

[32] | Polycarpou, Stable adaptive neural control scheme for nonlinear systems, IEEE Transactins on Automatic Control 41 pp 447– (1996) · Zbl 0846.93060 |

[33] | Hou, Decentralized robust adaptive control for the multiagent system consensus problem using neural networks, IEEE Transactions on Systems, Man and Cybernetics, Part B: Cybernetics 39 (3) pp 636– (2009) |

[34] | Das, Distributed adaptive control for synchronization of unknown nonlinear networked systems, Automatica (2009) |

[35] | Horn, Matrix Analysis (1994) |

[36] | Ge, Stable Adaptive Neural Network Control (1998) |

[37] | Stone, The generalized Weierstrass approximation theorem, Mathematics Magazine 21 pp 167– (1948) |

[38] | Khalil, Nonlinear Systems (1996) |

[39] | Ge, Adaptive neural control of uncertain MIMO nonlinear systems, IEEE Transactions of Neural Networks 15 pp 674– (2004) |

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