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首页> 外文期刊>Automatic Control, IEEE Transactions on >Separable and Localized System-Level Synthesis for Large-Scale Systems
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Separable and Localized System-Level Synthesis for Large-Scale Systems

机译：大型系统的可分离和局部系统级综合

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摘要

A major challenge faced in the design of large-scale cyber-physical systems, such as power systems, the Internet of Things or intelligent transportation systems, is that traditional distributed optimal control methods do not scale gracefully, neither in controller synthesis nor in controller implementation, to systems composed of a large number (e.g., on the order of billions) of interacting subsystems. This paper shows that this challenge can now be addressed by leveraging the recently introduced system-level approach (SLA) to controller synthesis. In particular, in the context of the SLA, we define suitable notions of separability for control objective functions and system constraints such that the global optimization problem (or iterate update problems of a distributed optimization algorithm) can be decomposed into parallel subproblems. We then further show that if additional locality (i.e., sparsity) constraints are imposed, then these subproblems can be solved using local models and local decision variables. The SLA is essential to maintain the convexity of the aforementioned problems under locality constraints. As a consequence, the resulting synthesis methods have$O(1)$complexity relative to the size of the global system. We further show that many optimal control problems of interest, such as (localized) LQR and LQG,$mathcal {H}_2$optimal control with joint actuator and sensor regularization, and (localized) mixed$mathcal {H}_2/mathcal {L}_1$optimal control problems, satisfy these notions of separability, and use these problems to explore tradeoffs in performance, actuator, and sensing density, and average versus worst-case performance for a large-scale power inspired system.
机译：大型网络物理系统（例如电力系统，物联网或智能交通系统）的设计面临的主要挑战是，传统的分布式最优控制方法在控制器综合和控制器实现方面均无法正常扩展。到由大量（例如，数十亿个）交互子系统组成的系统。本文表明，现在可以通过利用最近引入的系统级方法（SLA）进行控制器综合来解决这一挑战。特别地，在SLA的上下文中，我们为控制目标函数和系统约束定义了适当的可分离性概念，以便可以将全局优化问题（或分布式优化算法的迭代更新问题）分解为并行子问题。然后，我们进一步表明，如果施加了附加的局部性（即稀疏性）约束，则可以使用局部模型和局部决策变量来解决这些子问题。 SLA对于在局部性约束下保持上述问题的凸性至关重要。结果，所得的合成方法具有 n <在线公式xmlns：mml = “ http：//www.w3.org/1998/Math/MathML ” xmlns：xlink = “ http：// www。 w3.org/1999/xlink"> $ O（1）$ n相对于全局系统大小的复杂性。我们进一步显示了许多感兴趣的最佳控制问题，例如（本地化的）LQR和LQG， n $ mathcal {H} _2 $ 最优控制，带有联合执行器和传感器正则化，以及（本地化）混合 n <内联公式xmlns：mml = “ http：//www.w3.org/1998/Math/MathML ” xmlns： xlink = “ http：//www.w3.org/1999/xlink ”> $ 数学{H} _2 / mathcal {L} _1 $ < / tex-math> 最优控制问题，满足这些可分离性的概念，并使用这些问题来探索性能，执行器和传感密度以及大规模与平均与最坏情况下的性能之间的权衡动力启发系统。

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