The control of large-scale cyber-physical systems requires optimal distributed policies relying solely on limited communication with neighboring agents. However, computing stabilizing controllers for nonlinear systems while optimizing complex costs remains a significant challenge. Neural Networks (NNs), known for their expressivity, can be leveraged to parametrize control policies that yield good performance. However, NNs' sensitivity to small input changes poses a risk of destabilizing the closed-loop system. Many existing approaches enforce constraints on the controllers' parameter space to guarantee closed-loop stability, leading to computationally expensive optimization procedures. To address these problems, we leverage the framework of port-Hamiltonian systems to design continuous-time distributed control policies for nonlinear systems that guarantee closed-loop stability and finite $\mathcal{L}_2$ or incremental $\mathcal{L}_2$ gains, independent of the optimzation parameters of the controllers. This eliminates the need to constrain parameters during optimization, allowing the use of standard techniques such as gradient-based methods. Additionally, we discuss discretization schemes that preserve the dissipation properties of these controllers for implementation on embedded systems. The effectiveness of the proposed distributed controllers is demonstrated through consensus control of non-holonomic mobile robots subject to collision avoidance and averaged voltage regulation with weighted power sharing in DC microgrids.

翻译：大规模信息物理系统的控制需要仅依赖与相邻智能体有限通信的最优分布式策略。然而，在优化复杂成本的同时为非线性系统计算镇定控制器仍然是一个重大挑战。神经网络以其强大的表达能力著称，可用于参数化能产生良好性能的控制策略。然而，神经网络对微小输入变化的敏感性可能导致闭环系统失稳。许多现有方法通过对控制器参数空间施加约束来保证闭环稳定性，但这导致了计算成本高昂的优化过程。为解决这些问题，我们利用端口-哈密顿系统框架，为非线性系统设计连续时间分布式控制策略，这些策略能保证闭环稳定性及有限的$\mathcal{L}_2$或增量$\mathcal{L}_2$增益，且与控制器优化参数无关。这消除了在优化过程中约束参数的必要性，从而允许使用基于梯度方法等标准技术。此外，我们讨论了能在嵌入式系统实现中保持这些控制器耗散特性的离散化方案。所提出的分布式控制器的有效性通过以下两个案例得到验证：受避碰约束的非完整移动机器人一致性控制，以及直流微电网中具有加权功率共享的平均电压调节。