This paper proposes two nonlinear dynamics to solve constrained distributed optimization problem for resource allocation over a multi-agent network. In this setup, coupling constraint refers to resource-demand balance which is preserved at all-times. The proposed solutions can address various model nonlinearities, for example, due to quantization and/or saturation. Further, it allows to reach faster convergence or to robustify the solution against impulsive noise or uncertainties. We prove convergence over weakly connected networks using convex analysis and Lyapunov theory. Our findings show that convergence can be reached for general sign-preserving odd nonlinearity. We further propose delay-tolerant mechanisms to handle general bounded heterogeneous time-varying delays over the communication network of agents while preserving all-time feasibility. This work finds application in CPU scheduling and coverage control among others. This paper advances the state-of-the-art by addressing (i) possible nonlinearity on the agents/links, meanwhile handling (ii) resource-demand feasibility at all times, (iii) uniform-connectivity instead of all-time connectivity, and (iv) possible heterogeneous and time-varying delays. To our best knowledge, no existing work addresses contributions (i)-(iv) altogether. Simulations and comparative analysis are provided to corroborate our contributions.

翻译：本文提出了两种非线性动力学方法，用于解决多智能体网络资源分配中的约束分布式优化问题。在该框架下，耦合约束指资源-需求平衡需始终维持。所提方案能够处理多种模型非线性，例如由量化及/或饱和效应引发的非线性。此外，该方法可实现更快的收敛速度，或增强解决方案对脉冲噪声及不确定性的鲁棒性。我们利用凸分析与李雅普诺夫理论，证明了在弱连通网络下的收敛性。研究结果表明，对于一般符号保持的奇非线性函数，均可实现收敛。进一步地，我们提出了延迟容忍机制，以应对智能体通信网络中一般有界异构时变延迟，同时保证全时可行性。该工作可应用于CPU调度、覆盖控制等领域。本文通过解决以下问题推进了现有研究：(i) 智能体/链路上可能存在的非线性，(ii) 资源-需求的全时可行性，(iii) 统一连通性而非全时连通性，以及 (iv) 可能的异构时变延迟。据我们所知，目前尚无工作能同时解决上述(i)-(iv)项贡献。我们提供仿真实验与对比分析以验证所提方法的有效性。