基于非协调步长的随机网络抗干扰分布式资源分配
Disturbance-resilient Distributed Resource Allocation over Stochastic Networks using Uncoordinated Stepsizes
摘要：
研究了多智能体系统中的分布式资源分配问题，其中所有智能体在随机通信网络上合作最小化它们的费用函数之和.这个问题出现在许多实际领域，如智能电网中的经济调度，任务分配，机器人控制中的功率分配。现有的大多数工作不能收敛到最优解，如果状态偏离可行域，由于环境噪声，误操作，恶意攻击等造成的干扰，为了解决这个问题，我们提出了一种分布式偏差跟踪资源分配算法，并证明了它线性收敛到最优解与常数步长。我们进一步探讨了所提出的算法的弹性特性。最重要的是，在干扰注入和随机通信故障的情况下，算法仍然收敛到最优解。为了提高算法的收敛速度，建立了最快收敛速度的最优步长。我们还证明了该算法的线性收敛到最优解的均方，即使与不协调的步长，即，允许代理采用不同的步长。仿真结果验证了理论分析的正确性。
英文摘要：
This paper studies distributed resource allocation problem in multi-agent systems, where all the agents cooperatively minimize the sum of their cost functions with global resource constraints over stochastic communication networks. This problem arises from many practical domains such as economic dispatch in smart grid, task assignment, and power allocation in robotic control. Most of existing works cannot converge to the optimal solution if states deviate from feasible region due to disturbance caused by environmental noise, misoperation, malicious attack, etc. To solve this problem, we propose a distributed deviation-tracking resource allocation algorithm and prove that it linearly converges to the optimal solution with constant stepsizes. We further explore its resilience properties of the proposed algorithm. Most importantly, the algorithm still converges to the optimal solution under the disturbance injection and random communication failure. In order to improve the convergence rate, the optimal stepsizes for the fastest convergence rate are established. We also prove the algorithm converges linearly to the optimal solution in mean square even with uncoordinated stepsizes, i.e., agents are allowed to employ different stepsizes. Simulations are provided to verify the theoretical results.
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