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Distributed Receding Horizon Control with Applications to Multi-Vehicle Formation Stabilization

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William B. Dunbar and Richard M. Murray

Submitted, *Automatica*

We consider the control of interacting subsystems whose dynamics and constraints
are uncoupled, but whose state vectors are coupled non-separably in a single centralized
cost function of a finite horizon optimal control problem. For a given centralized
cost structure, we generate distributed optimal control problems for each subsystem
and establish that the distributed receding horizon implementation is asymptotically
stabilizing. The communication requirements between subsystems with coupling in the
cost function are that each subsystem obtain the previous optimal control trajectory of
those subsystems at each receding horizon update. The key requirements for stability
are that each distributed optimal control not deviate too far from the previous optimal
control, and that the receding horizon updates happen sufficiently fast. The theory is
applied in simulation for stabilization of a formation of vehicles.

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Richard Murray
(murray@cds. caltech.edu)