IEEE Transactions on Automatic Control · 2016 · 306 citations · 28 references
Mathematical ProgrammingEngineeringDistributed Ai SystemMulti-agent LearningOperations ResearchDistributed CoordinationSystems EngineeringDistributed Problem SolvingCombinatorial OptimizationMechanism DesignMulti-agent PlanningMulti-agent SystemInequality ConstraintsDistributed OptimizationDistributed Constraint OptimizationComputer ScienceMulti-agent Mechanism DesignDistributed Constrained OptimizationAdditive Objective FunctionProportional-integral Protocol
The study assumes each agent’s objective function is convex only within its local bound constraints, not requiring global convexity. The paper proposes a continuous‑time multi‑agent system for distributed constrained optimization with additive objective functions. Agents exchange output information via a proportional‑integral protocol in a continuous‑time setting to reduce communication bandwidth. The authors prove that the system converges to the optimal solution under undirected connected communication graphs, that an integral‑only protocol also converges when objectives are strictly convex, and simulations confirm the theory.
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.
28