Control Synthesis for Large Collections of Systems with Mode-Counting Constraints
Control Synthesis for Large Collections of Systems with Mode-Counting Constraints
复制标题
具有模式计数约束的大型系统集合的控制综合
DOI：
10.1145/2883817.2883831
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发表时间：
2016
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
给定一个大的同构交换系统集合，我们考虑一类新的安全约束，称为模式计数约束，它对处于特定模式的系统数量施加限制。我们提出了一种方法来合成按构造正确的交换协议，以随着时间的推移强制执行这些约束。我们的方法从构建单个系统模型的近似双类似抽象开始。然后，我们证明了集合的聚合行为可以用一个线性系统来表示，这个线性系统的系统矩阵是由抽象的转移图诱导出来的。最后，将带模式计数约束的控制综合问题简化为过渡图上的循环分配问题。该方法的一个显著特征是其可扩展性；计算复杂度与所涉及的系统数量无关。我们在协调大量恒温控制负载的问题上说明了这种方法，同时确保在任何给定时间从电网中提取电力的负载数量有一个界限。
Given a large homogeneous collection of switched systems, we consider a novel class of safety constraints, called mode-counting constraints, that impose restrictions on the number of systems that are in a particular mode. We propose an approach for synthesizing correct-by-construction switching protocols to enforce such constraints over time. Our approach starts by constructing an approximately bisimilar abstraction of the individual system model. Then, we show that the aggregate behavior of the collection can be represented by a linear system, whose system matrices are induced by the transition graph of the abstraction. Finally, the control synthesis problem with mode-counting constraints is reduced to a cycle assignment problem on the transition graph. One salient feature of the proposed approach is its scalability; the computational complexity is independent of the number of systems involved. We illustrate this approach on the problem of coordinating a large collection of thermostatically controlled loads while ensuring a bound on the number of loads that are extracting power from the electricity grid at any given time.