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Necessary and Sufficient Conditions for Distributed Averaging with State Constraints

机译：具有状态约束的分布平均的必要和充分条件

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Distributed averaging algorithms for multi-agent systems have recently gained a significant amount of interest. In many cases, maximizing the convergence rate of these algorithms leads to rapid changes in the system's state, which may not be desirable or physically possible. This paper derives necessary and sufficient conditions to guarantee that the states of the system are always contained within a polytopic region during the convergence process. These constraints prevent sudden or steep changes in the state variables. In addition to providing these conditions, we provide a convex design for the controller that can achieve the fastest convergence while satisfying the constraints. The design problem is formulated as a semi-definite program (SDP) which can be solved using any standard interior-point method SDP solver, and the solution can thus be efficiently computed.
机译：多种子体系统的分布式平均算法最近获得了大量的兴趣。在许多情况下，最大化这些算法的收敛速率导致系统状态的快速变化，这可能是不可取的或物理的。本文推出了必须和充分的条件，以保证在收敛过程中始终包含系统的状态始终包含在多粒子区域内。这些约束防止状态变量突然或陡峭变化。除了提供这些条件外，我们还为控制器提供了一个凸面设计，可以实现最快的收敛，同时满足约束。设计问题作为半定程序（SDP）配制，可以使用任何标准内部点方法SDP求解器来解决，因此可以有效地计算解决方案。

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