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**Distributed receding horizon control for multi-vehicle formation stabilization.**
*(English)*
Zbl 1103.93031

Summary: We consider the control of interacting subsystems whose dynamics and constraints are decoupled, but whose state vectors are coupled non-separably in a single cost function of a finite horizon optimal control problem. For a given cost structure, we generate distributed optimal control problems for each subsystem and establish that a distributed receding horizon control implementation is stabilizing to a neighborhood of the objective state. The implementation requires synchronous updates and the exchange of the most recent optimal control trajectory between coupled subsystems prior to each update. The key requirements for stability are that each subsystem not deviate too far from the previous open-loop state trajectory, and that the receding horizon updates happen sufficiently fast. The venue of multi-vehicle formation stabilization is used to demonstrate the distributed implementation.

### MSC:

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

93D09 | Robust stability |

93C95 | Application models in control theory |

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

### Keywords:

receding horizon control; model predictive control; distributed control; multi-vehicle formations
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\textit{W. B. Dunbar} and \textit{R. M. Murray}, Automatica 42, No. 4, 549--558 (2006; Zbl 1103.93031)

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### References:

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