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**Decentralized receding horizon control for large scale dynamically decoupled systems.**
*(English)*
Zbl 1104.93038

Summary: We present a detailed study on the design of decentralized receding horizon control (RHC) schemes for decoupled systems. We formulate an optimal control problem for a set of dynamically decoupled systems where the cost function and constraints couple the dynamical behavior of the systems. The coupling is described through a graph where each system is a node, and cost and constraints of the optimization problem associated with each node are only function of its state and the states of its neighbors. The complexity of the problem is addressed by breaking a centralized RHC controller into distinct RHC controllers of smaller sizes. Each RHC controller is associated with a different node and computes the local control inputs based only on the states of the node and of its neighbors. We analyze the properties of the proposed scheme and introduce sufficient stability conditions based on prediction errors. Finally, we focus on linear systems and show how to recast the stability conditions into a set of matrix semi-definiteness tests.

### MSC:

93C55 | Discrete-time control/observation systems |

93B40 | Computational methods in systems theory (MSC2010) |

93A15 | Large-scale systems |

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\textit{T. Keviczky} et al., Automatica 42, No. 12, 2105--2115 (2006; Zbl 1104.93038)

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### References:

[2] | Borrelli, F.; Baotic, M.; Bemporad, A.; Morari, M., Dynamic programming for constrained optimal control of discrete-time hybrid systems, Automatica, 41, 1, 1709-1721 (2005) · Zbl 1125.49310 |

[6] | Camponogara, E.; Jia, D.; Krogh, B. H.; Talukdar, S., Distributed model predictive control, IEEE Control Systems Magazine, 22, 1, 44-52 (2002) |

[7] | Chen, H.; Allgöwer, F., A quasi-infinite horizon nonlinear model predictive scheme with guaranteed stability, Automatica, 14, 10, 1205-1217 (1998) · Zbl 0947.93013 |

[8] | D’Andrea, R.; Dullerud, G. E., Distributed control design for spatially interconnected systems, IEEE Transactions on Automatic Control, 48, 9, 1478-1495 (2003) · Zbl 1364.93206 |

[9] | Dunbar, W. B.; Murray, R. M., Distributed receding horizon control for multi-vehicle formation stabilization, Automatica, 42, 4, 549-558 (2006) · Zbl 1103.93031 |

[10] | Jadbabaie, A.; Lin, J.; Morse, A. S., Coordination of groups of mobile autonomous agents using nearest neighbor rules, IEEE Transactions on Automatic Control, 48, 6, 988-1001 (2003) · Zbl 1364.93514 |

[12] | Keerthi, S. S.; Gilbert, E. G., Optimal infinite-horizon feedback control laws for a general class of constrained discrete-time systems: Stability and moving-horizon approximations, Journal of Optimization Theory and Applications, 57, 265-293 (1988) · Zbl 0622.93044 |

[17] | Magni, L.; De Nicolao, G.; Scattolini, R.; Allgöwer, F., Robust nonlinear model predictive control for nonlinear discrete-time systems, International Journal of Robust and Nonlinear Control, 13, 3-4, 229-246 (2003) · Zbl 1049.93030 |

[18] | Mayne, D. Q.; Rawlings, J. B.; Rao, C. V.; Scokaert, P. O.M., Constrained model predictive control: Stability and optimality, Automatica, 36, 6, 789-814 (2000) · Zbl 0949.93003 |

[23] | Sandell, N. R.; Varaiya, P.; Athans, M.; Safonov, M., Survey of decentralized control methods for large scale systems, IEEE Transactions on Automatic Control, AC-23, 2, 195-215 (1978) |

[25] | Vadigepalli, R.; Doyle III, F. J., A distributed state estimation and control algorithm for plantwide processes, IEEE Transactions on Control Systems Technology, 11, 1, 119-127 (2003) |

[26] | Wang, S.; Davison, E. J., On the stabilization of decentralized control systems, IEEE Transactions on Automatic Control, 18, 5, 473-478 (1973) · Zbl 0273.93047 |

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