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.ud
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机译：我们考虑相互作用子系统的控制，这些子系统的动力学和约束条件是不耦合的，但是其状态向量在有限范围的最优控制问题的单个集中成本函数中是不可分离地耦合的。对于给定的集中成本结构，我们为每个子系统生成分布式最优控制问题，并确定分布式后退范围的实现是渐近稳定的。具有成本函数耦合的子系统之间的通信要求是，每个子系统在每个后退水平更新时都获得这些子系统的先前最佳控制轨迹。稳定性的关键要求是每个分散的最优控制与先前的最优控制之间的偏差不应太大，并且后退的水平更新必须足够快地发生。该理论在模拟中用于稳定车辆编队。 ud
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