On a Class of Maximal Invariance Inducing Control Strategies for Large Collections of Switched Systems
On a Class of Maximal Invariance Inducing Control Strategies for Large Collections of Switched Systems
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大型切换系统集合的一类最大不变性诱导控制策略
DOI：
10.1145/3049797.3049810
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
N. Ozay
中科院分区：
文献类型：
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作者：
Petter Nilsson;N. Ozay
能够提供安全保证的现代控制综合方法通常依赖于寻找不变集。对于高维系统，计算和/或表示这些集合变得难以处理，并且经常构成计算过程的主要瓶颈。在本文中，我们转而分析研究了一个特定的高维系统，并提出了一种控制策略，我们证明了这种策略可以在可能的情况下使集合不变。控制问题——一维中具有两个模式的模式计数问题——受到恒温控制负载（tcl）调度的启发，并展示了局部安全约束和全局计数约束之间的权衡。我们从文献中改进了一种控制策略来处理异质性，并推导出该策略解决手头问题的充分条件。此外，我们还证明了问题具有解的必要条件，这意味着所提出的控制策略具有一种最优性。我们概述了更一般的问题实例，其中可以实现相同的控制策略，并给出了闭环系统满足其规范的充分（但不是必要的）条件。我们通过一个TCL调度示例来说明我们的结果。
Modern control synthesis methods that are capable of delivering safety guarantees typically rely on finding invariant sets. Computing and/or representing such sets becomes intractable for high-dimensional systems and often constitutes the main bottleneck of computational procedures. In this paper we instead analytically study a particular high-dimensional system and propose a control strategy that we prove renders a set invariant whenever it is possible to do so. The control problem---the mode-counting problem with two modes in one dimension---is inspired by scheduling of thermostatically controlled loads (TCLs) and exhibits a trade-off between local safety constraints and a global counting constraint. We improve upon a control strategy from the literature to handle heterogeneity and derive sufficient conditions for the strategy to solve the problem at hand. In addition, we show that the conditions are also necessary for the problem to have a solution, which implies a type of optimality of the proposed control strategy. We outline more general problem instances where the same control strategy can be implemented and we give sufficient (but not necessary) conditions for the closed-loop system to satisfy its specification. We illustrate our results on a TCL scheduling example.
恒定速率多模系统的优化调度
DOI：
10.1145/2185632.2185647
发表时间：
2012
期刊：
--
影响因子：
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作者：
Alur R
通讯作者：
Alur R