互联控制系统近似抽象的组合构造
Compositional Construction of Approximate Abstractions of Interconnected Control Systems
AI总结：
本文研究了互联控制系统的近似抽象的组合构造，提出小增益条件和线性系统控制不变子空间来构建抽象，并用线性时序逻辑规范合成控制器。
摘要：
本文研究了互联控制系统的近似抽象的组合构造，提出小增益条件和线性系统控制不变子空间来构建抽象，并用线性时序逻辑规范合成控制器。
英文摘要：
We consider a compositional construction of approximate abstractions of interconnected control systems. In our framework, an abstraction acts as a substitute in the controller design process and is itself a continuous control system. The abstraction is related to the concrete control system via a so-called simulation function: a Lyapunov-like function, which is used to establish a quantitative bound between the behavior of the approximate abstraction and the concrete system. In the first part of the paper, we provide a small gain type condition that facilitates the compositional construction of an abstraction of an interconnected control system together with a simulation function from the abstractions and simulation functions of the individual subsystems. In the second part of the paper, we restrict our attention to linear control system and characterize simulation functions in terms of controlled invariant, externally stabilizable subspaces. Based on those characterizations, we propose a particular scheme to construct abstractions for linear control systems. We illustrate the compositional construction of an abstraction on an interconnected system consisting of four linear subsystems. We use the abstraction as a substitute to synthesize a controller to enforce a certain linear temporal logic specification.
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