A Multi-Agent System With a Proportional-Integral Protocol for Distributed Constrained Optimization

This technical note presents a continuous-time multi-agent system for distributed optimization with an additive objective function composed of individual objective functions subject to bound, equality, and inequality constraints. Each individual objective function is assumed to be convex in the region defined by its local bound constraints only without the need to be globally convex. All agents in the system communicate using a proportional-integral protocol with their output information instead of state information to reduce communication bandwidth. It is proved that all agents with any initial state can reach output consensus at an optimal solution to the given constrained optimization problem, provided that the graph describing the communication links among agents is undirected and connected. It is further proved that the system with only integral protocol is also convergent to the unique optimal solution if each individual objective function is strictly convex. Simulation results are presented to substantiate the theoretical results.