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**Averaging approach to distributed convex optimization for continuous-time multi-agent systems.**
*(English)*
Zbl 1389.93002

Summary: Recently, distributed convex optimization has received much attention by many researchers. Current research on this problem mainly focuses on fixed network topologies, without enough attention to switching ones. This paper specially establishes a new technique called averaging-base approach to design a continuous-time distributed algorithm for convex optimization problem under switching topology. This idea of using averaging was proposed in our earlier works for the consensus problem of multi-agent systems under switching topology, and it is further developed in this paper to gain further insight into the distributed optimization algorithm. Key techniques are used, such as two-time-scale analysis and asymptotic expansions for the solutions of the backward equation or Liouville equation. Important results are obtained, including weak convergence of our algorithm to the optimal solution.

### MSC:

93A10 | General systems |

60J75 | Jump processes (MSC2010) |

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

93C35 | Multivariable systems, multidimensional control systems |