Distributed Protocols for Constrained Optimization of Integrator Chain Multi-Agent Systems

This paper studies the constrained optimization problem of integrator chain multi-agent systems from the distributed perspective. Particularly, all the agents collaborate to find an optimal solution of a global objective function summed by multiple local ones, each of which is just convex and belongs to an individual agent. However, the potential optimal solutions are simultaneously subject to set constraint and two kinds of equality constraints, i.e., individual equality constraint and aggregate equality constraint, whereas their involved constraint parameters are privately available to individual agents. With a proper coordinate transformation, a distributed optimization protocol is synthesized by introducing proper internal dynamics. Under the Lyapunov framework, it is shown with convex theory that the synthesized distributed protocol enables the multi-agent system to achieve the concerned constrained optimization objective. An example is finally given to confirm the optimization effectiveness.