An ISS self-triggered implementation of linear controllers.

*(English)*Zbl 1205.93081Summary: Nowadays control systems are mostly implemented on digital platforms and, increasingly, over shared communication networks. Reducing resources (processor utilization, network bandwidth, etc.) in such implementations increases the potential to run more applications on the same hardware. We present a self-triggered implementation of linear controllers that reduces the amount of controller updates necessary to retain stability of the closed-loop system. Furthermore, we show that the proposed self-triggered implementation is robust against additive disturbances and provide explicit guarantees of performance. The proposed technique exhibits an inherent trade-off between computation and potential savings on actuation.

##### MSC:

93C40 | Adaptive control/observation systems |

93B18 | Linearizations |

93C05 | Linear systems in control theory |

93B35 | Sensitivity (robustness) |

##### References:

[1] | Anta, A., & Tabuada, P. (2009). On the benefits of relaxing the periodicity assumption for networked control systems over can. In The 30th IEEE real-time systems symposium. |

[2] | Anta, A., & Tabuada, P. (2010). To sample or not to sample: self-triggered control for nonlinear systems. In IEEE Transactions on Automatic Control, 55(9). Arxiv preprint arXiv:0806.0709 (in press). |

[3] | Åström, K.J.; Wittenmark, B., Computer controlled systems, (1990), Prentice Hall Englewood Cliffs, NJ |

[4] | Heemels, W.P.M.H.; Sandee, J.H.; van den Bosch, P.P.J., Analysis of event-driven controllers for linear systems, International journal of control, 81, 4, 571-590, (2008) · Zbl 1152.93423 |

[5] | Hristu-Varsakelis, D.; Levine, W.S.; Alur, R.; Arzen, K.-E.; Baillieul, J.; Henzinger, T.A., Handbook of networked and embedded control systems, (2005), Birkhauser Boston |

[6] | Kellett, C.; Shim, H.; Teel, A., Further results on robustness of (possibly discontinuous) sample and hold feedback, IEEE transactions on automatic control, 49, 7, 1081-1089, (2004) · Zbl 1365.93118 |

[7] | Mazo, M. Jr., Anta, A., & Tabuada, P. (2009). On self-triggered control for linear systems: guarantees and complexity. In European control conference. |

[8] | Mazo, M. Jr., & Tabuada, P. (2009). Input-to-state stability of self-triggered control systems. In 48th IEEE conference on decision and control. |

[9] | Nesic, D.; Teel, A.R., Input-output stability properties of networked control systems, IEEE transactions on automatic control, 40, 10, 1650-1667, (2004) · Zbl 1365.93466 |

[10] | Sontag, E., () |

[11] | Tabuada, P., Event-triggered real-time scheduling of stabilizing control tasks, IEEE transactions on automatic control, 52, 9, 1680-1685, (2007) · Zbl 1366.90104 |

[12] | Velasco, M., Fuertes, J., & Marti, P. (2003). The self triggered task model for real-time control systems. In Work in progress proceedings of the 24th IEEE real-time systems symposium (pp. 67-70). |

[13] | Wang, X., & Lemmon, M. (2008). Event design in event-triggered feedback control systems. In 47th IEEE conference on decision and control. · Zbl 1228.93080 |

[14] | Wang, X.; Lemmon, M., Self-triggered feedback control systems with finite-gain L2-stability, IEEE transactions on automatic control, 45, 3, 452-467, (2009) · Zbl 1367.93354 |

[15] | Yook, J.K; Tilbury, D.M; Soparkar, N.R, Trading computation for bandwidth: reducing communication in distributed control systems using state estimators, IEEE transactions on control systems technology, 10, 4, 503-518, (2002) |

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