论文标题
与马尔可夫开关的互连随机系统的组成控制器合成
Compositional Controller Synthesis for Interconnected Stochastic Systems with Markovian Switching
论文作者
论文摘要
在这项工作中，我们提出了一种组成方案，用于与马尔可夫开关信号的互连离散时间随机系统合成安全控制器。我们提出的方法是基于针对各个子系统计算的所谓控制存储证书的概念，该概念可以通过利用它可以合成互连系统的状态反馈控制器，以在有限的时间范围内执行安全规范。为此，我们采用了一个方（SOS）优化方法来搜索每个开关子系统的多个存储证书，同时合成其相应的安全控制器。然后，我们利用耗散理论根据基于单个子系统的存储证书为互连系统的组合构成屏障证书。提出的耗散型组成条件可以利用互连拓扑结构，并独立于子系统的数量或成就来实现。最终，我们采用了构造的屏障证书，并根据互连系统在有限的时间范围内到达某些不安全区域的概率上量化了上限。我们将结果应用于200个房间的室温网络，并在接受多个存储证书的同时，带有Markovian交换信号。我们在组合上合成安全控制器，以将每个房间的温度保持在舒适区域，以在有限的时间范围内保持。
In this work, we propose a compositional scheme for the safety controller synthesis of interconnected discrete-time stochastic systems with Markovian switching signals. Our proposed approach is based on a notion of so-called control storage certificates computed for individual subsystems, by leveraging which, one can synthesize state-feedback controllers for interconnected systems to enforce safety specifications over finite time horizons. To do so, we employ a sum-of-squares (SOS) optimization approach to search for multiple storage certificates of each switching subsystem while synthesizing its corresponding safety controller. We then utilize dissipativity theory to compositionally construct barrier certificates for interconnected systems based on storage certificates of individual subsystems. The proposed dissipativity-type compositional conditions can leverage the structure of the interconnection topology and be fulfilled independently of the number or gains of subsystems. We eventually employ the constructed barrier certificate and quantify upper bounds on the probability that the interconnected system reaches certain unsafe regions in a finite time horizon. We apply our results to a room temperature network of 200 rooms with Markovian switching signals while accepting multiple storage certificates. We compositionally synthesize safety controllers to maintain the temperature of each room in a comfort zone for a bounded time horizon.
