Anti-Delay Distributed Optimization Protocols for Multiagent Systems With Coupled Constraints

This article focuses on the constrained optimization problem for second-order multiagent systems that experience heterogeneous communication delays. Specifically, the involved agents work together to find the optimal solution of a global payoff function, which is summed by multiple strongly convex local payoff functions, with each function being exclusively owned by an individual agent. However, the feasible solutions must satisfy a coupled equality constraint, formulated by individual parameters assigned to each agent. Initially, a basic anti-delay distributed protocol is developed, which leverages a scattering transformation to enhance the generation of received information. Using the Lyapunov framework, we demonstrate that the agents coordinated by this anti-delay distributed protocol can effectively reach a consensus on the expected optimal solution, despite the presence of communication delays. In addition, we present two results that extend the basic anti-delay distributed protocol. First, we consider the scenario of lacking velocity and develop a velocity-free anti-delay distributed protocol to achieve the concerned constrained optimization objective. Next, we augment the system order and develop an anti-delay distributed optimization protocol for integrator chain multiagent systems. Finally, we confirm the anti-delay performance of the developed distributed protocols through simulations.