Necessary and sufficient conditions for distributed averaging with state constraints

摘要

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.