Symbolic control techniques aim to satisfy complex logic specifications. A critical step in these techniques is the construction of a symbolic (discrete) abstraction, a finite-state system whose behaviour mimics that of a given continuous-state system. The methods used to compute symbolic abstractions, however, require knowledge of an accurate closed-form model. To generalize them to systems with unknown dynamics, we present a new data-driven approach that does not require closed-form dynamics, instead relying only the ability to evaluate successors of each state under given inputs. To provide guarantees for the learned abstraction, we use the Probably Approximately Correct (PAC) statistical framework. We first introduce a PAC-style behavioural relationship and an appropriate refinement procedure. We then show how the symbolic abstraction can be constructed to satisfy this new behavioural relationship. Moreover, we provide PAC bounds that dictate the number of data required to guarantee a prescribed level of accuracy and confidence. Finally, we present an illustrative example.
翻译:核心控制技术旨在满足复杂的逻辑规格。这些技术的一个关键步骤是构建一个象征性(分解)抽象,一个模仿特定连续状态系统的有限状态系统,其行为仿照一个特定连续状态系统。然而,计算符号抽象的方法需要精确的封闭式模型知识。为了将其推广到不为人知的动态系统,我们提出了一个新的数据驱动方法,它并不要求闭式动态,而只是依赖根据给定投入对每个国家的继任者进行评估的能力。为了为所学的抽象提供保障,我们首先采用了“准准正确”统计框架。我们采用了PAC型的行为关系和适当的改进程序。然后我们展示了如何构建象征性抽象的抽象以满足这一新的行为关系。此外,我们提供了PAC型的界限,它决定了保证规定的准确度和信任度所需的数据数量。最后,我们举了一个示例。