This paper addresses the constrained distributed optimization problem of heterogeneous linear multi-agent systems, where the agents with linear dynamics are subject to local set constraints, global nonlinear inequality constraints and heterogeneous communication delays. Agents collaborate to minimize a global objective function by communicating with their neighbors in a graph. Each agent’s decision variable is constrained in a local set. The decision variables of all agents are coupled by global inequality constraints which are modeled by nonlinear functions. To handle the heterogeneous constant communication delays, the scattering transformation between neighbors is employed. We design a new distributed control law to investigate the passivity of systems of individual agents in the presence of constraints and communication delays. Integrating the proposed control law with the scattering transformation, we prove that systems converge to the optimal solution which minimizes the global objective functions. Simulations of heterogeneous linear multi-agent systems are presented to illustrate the effectiveness of the distributed control law.

本文解决了异构线性多智能体系统的约束分布式优化问题，其中具有线性动力学的智能体受到局部集合约束、全局非线性不等式约束和异构通信延迟。代理通过与图中的邻居进行通信来协作以最小化全局目标函数。每个代理的决策变量都被约束在一个本地集合中。所有代理的决策变量通过非线性函数建模的全局不等式约束耦合。为了处理异构的恒定通信延迟，采用了邻居之间的散射变换。我们设计了一个新的分布式控制律来研究在存在约束和通信延迟的情况下个体代理系统的被动性。将提出的控制律与散射变换相结合，我们证明系统收敛到最小化全局目标函数的最优解。提出了异构线性多代理系统的仿真来说明分布式控制律的有效性。