Multi-agent systems are widely studied due to its ability of solving complex tasks in many fields, especially in deep reinforcement learning. Recently, distributed optimization problem over multi-agent systems has drawn much attention because of its extensive applications. This paper presents a projection-based continuous-time algorithm for solving convex distributed optimization problem with equality and inequality constraints over multi-agent systems. The distinguishing feature of such problem lies in the fact that each agent with private local cost function and constraints can only communicate with its neighbors. All agents aim to cooperatively optimize a sum of local cost functions. By the aid of penalty method, the states of the proposed algorithm will enter equality constraint set in fixed time and ultimately converge to an optimal solution to the objective problem. In contrast to some existed approaches, the continuous-time algorithm has fewer state variables and the testification of the consensus is also involved in the proof of convergence. Ultimately, two simulations are given to show the viability of the algorithm.

由于多智能体系统能够解决许多领域中的复杂任务，尤其是在深度强化学习中，因此能够被广泛研究。近来，由于其广泛的应用，在多智能体系统上的分布式优化问题引起了很多关注。本文提出了一种基于投影的连续时间算法，用于求解多主体系统上具有等式和不等式约束的凸分布优化问题。这种问题的显着特征在于，具有私有本地成本函数和约束的每个代理只能与其邻居通信。所有代理商都旨在合作优化局部成本函数之和。借助惩罚方法，该算法的状态将在固定时间内进入等式约束集，最终收敛为目标问题的最优解。与某些现有方法相比，连续时间算法具有较少的状态变量，并且共识的证明也涉及收敛性的证明。最终，给出了两个仿真以显示该算法的可行性。