Multi-Layered Abstraction-Based Controller Synthesis for Continuous-Time Systems

Kyle Hsu, R. Majumdar, Kaushik Mallik, Anne-Kathrin Schmuck
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引用次数: 56

Abstract

We present multi-layered abstraction-based controller synthesis, which extends standard abstraction-based controller synthesis (ABCS) algorithms for continuous-time control systems by simultaneously maintaining several "layers" of abstract systems with decreasing precision. The resulting abstract multi-layered controller uses the coarsest abstraction whenever this is feasible, and dynamically adjusts the precision---by moving to a more precise abstraction and back to a coarser abstraction---based on the structure of the given control problem. Abstract multi-layered controllers can be refined to controllers with non-uniform resolution using feedback refinement relations established between each abstract layer and the concrete system, resulting in a sound ABCS method. We provide multi-layered controller synthesis algorithms for reachability, safety, and generalized Büchi specifications; our approach can be generalized to any ω-regular objective. Our algorithms are complete relative to single-layered synthesis on the finest layer. We empirically demonstrate that multi-layered synthesis can outperform standard (single-layer) ABCS algorithms on a number of examples, despite the additional cost of constructing multiple abstract systems.
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基于多层抽象的连续时间系统控制器综合
我们提出了基于多层抽象的控制器综合,它扩展了连续时间控制系统的标准基于抽象的控制器综合(ABCS)算法,通过同时维持几个“层”的抽象系统,并降低精度。由此产生的抽象多层控制器在可行的情况下使用最粗略的抽象,并根据给定控制问题的结构动态调整精度——通过移动到更精确的抽象和返回到更粗略的抽象。利用各抽象层与具体系统之间建立的反馈细化关系,可以将抽象多层控制器细化为非均匀分辨率的控制器,从而形成完善的ABCS方法。我们为可达性、安全性和广义b chi规格提供多层控制器综合算法;我们的方法可以推广到任何ω-正则目标。我们的算法相对于在最细层上的单层合成是完整的。我们通过经验证明,尽管构建多个抽象系统需要额外的成本,但多层综合在许多示例上可以优于标准(单层)ABCS算法。
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Session details: Modeling and Verification Algorithms for exact and approximate linear abstractions of polynomial continuous systems Formal Controller Synthesis from Hybrid Programs Session details: Stabilization and Control Design Compositional Synthesis for Symbolic Control
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