Design of the state predictive model following control system with time-delay.

*(English)*Zbl 1167.93346Summary: Time-delay systems exist in many engineering fields such as transportation systems, communication systems, process engineering and, more recently, networked control systems. It usually results in unsatisfactory performance and is frequently a source of instability, so the control of time-delay systems is practically important. In this paper, a design of the state predictive model following control system with time-delay is discussed. The bounded property of the internal states for the control is given, and the utility of this control design is guaranteed. Finally, examples are given to illustrate the effectiveness of the proposed method, and state predictive control techniques are applied to congestion control synthesis problems for a transmission control protocol/active queue management (TCP/AQM) network.

##### MSC:

93B51 | Design techniques (robust design, computer-aided design, etc.) |

93C15 | Control/observation systems governed by ordinary differential equations |

93D99 | Stability of control systems |

68M12 | Network protocols |

##### Keywords:

state predictive control; time-delay; model following control system (MFCS); TCP/AQM network; congestion control##### References:

[1] | Alevisakis, G. and Seborg, D. E. (1974). Control of multivariable systems containing time delays using a multivariable Smith predictor, Chemical Engineering Science 29(3): 373-380. |

[2] | Akiyama, T., Hattori, H. and Okubo, S. (1998). Design of the model following control system with time delays, Transactions of the Institute of Electrical Engineers of Japan 118(4): 497-510. |

[3] | Azuma, T., Fujita, T. and Fujita, M. (2005a). Congestion control for TCP/AQM networks using state predictive control, IEEE Transactions on Electronics, Information and Systems 125c(9): 1491-1496. |

[4] | Azuma, T., Fujita, T. and Fujita, M. (2005b). A design of state predictive H \infty congestion controllers for TCP/AQM networks, Transactions of the Institute of Systems, Control and Information Engineers 18(10): 373-375. |

[5] | Azuma, T., Fujita, T. and Fujita, M. (2005c). Experimental verification of stabilizing congestion controllers using the network testbed, Proceedings of the 2005 American Control Conference, Portland, OR, USA, pp. 1841-1846. |

[6] | Chiasson, J. and Loiseau, J. J. (2007). Applications of Time Delay Systems, Springer-Verlag, Berlin. · Zbl 1110.93003 |

[7] | Gu, Y., Towsley, D., Hollot, C. V. and Zhang, H. (2007). Congestion control for small buffer high speed networks, Proceedings of IEEE Infocom, Anchorage, AK, USA. |

[8] | Hollot, C. V., Misra, V., Towsley, D. and Gong, W. (2001a). On designing improved controllers for AQM routers supporting TCP flows, Proceedings of IEEE Infocom, Anchorage, AK, USA. · Zbl 1364.93279 |

[9] | Hollot, C. V., Misra, V., Towsley, D. and Gong, W. (2001b). A control theoretic analysis of RED, Proceedings of IEEE Infocom, Anchorage, AK, USA. |

[10] | Hollot, C. V., Misra, V., Towsley, D. and Gong, W. (2002). Analysis and design of controllers for AQM routers supporting TCP flows, IEEE Transactions on Automatic Control 47(6): 945-959. · Zbl 1364.93279 |

[11] | Kim, B. K. and Bien, Z. (1981). Design of a time-optimal feedback controller for systems with delay in control, IEEE Transactions on Industrial Electronics and Control Instrumentation 28(1): 28-36. |

[12] | Mascolo, S. (2000). Smith’s principle for congestion control in high-speed daata networks, IEEE Transactions on Automatic Control 45(2): 358-364. · Zbl 0964.90007 |

[13] | Misra, V., Gong, W. and Towsley, D. (2000). Fluid-based analysis of network of AQM routers supporting TCP flows with an aplication to RED, Proceedings of ACM SIGCOMM, Stockholm, Sweden. |

[14] | Okubo, S. (1985). A design of nonlinear model following control system with disturbances, Transactions of the Society of Instrument and Control Engineers 21(8): 792-799. |

[15] | Okubo, S. (1992). Nonlinear model following control system using stable zero assignment, Transactions of the Society of Instrument and Control Engineers 28(8): 939-946. |

[16] | Watanabe, K. and Ito, M. (1981). A process-model control for linear system with delay, IEEE Transactions on Automatic Control 26(6): 1261-1269. · Zbl 0471.93035 |

[17] | Wood, R. K. and Berry, M. W. (1973). Terminal composition control of a binary distillation control, Chemical Engineering Science 28(12): 1707-1717. |

[18] | Zhang, H. S. and Xie, L. H. (2007). Control and Estimation of Systems with Input/Output Delays, Springer-Verlag, Berlin. · Zbl 1117.93003 |

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