Hierarchy is a tool that has been applied to improve the scalability of solving planning problems modeled using Supervisory Control Theory. In the work of Hill and Lafortune (2016), the notion of cost equivalence was employed to generate an abstraction of the supervisor that, with additional conditions, guarantees that an optimal plan generated on the abstraction is also optimal when applied to the full supervisor. Their work is able to improve their abstraction by artificially giving transitions zero cost based on the sequentially-dependent ordering of events. Here, we relax the requirement on a specific ordering of the dependent events, while maintaining the optimal relationship between upper and lower levels of the hierarchy. This present paper also extends the authors’ work (Vilela and Hill 2020) where we developed a new notion of equivalence based on cost equivalence and weak bisimulation that we term priced-observation equivalence. This equivalence allows the supervisor abstraction to be generated compositionally. This helps to avoid the explosion of the state space that arises from having to first synthesize the full supervisor before the abstraction can be applied. Here, we also show that models with artificial zero-cost transitions can be created compositionally employing the new relaxed sequential dependence definition. An example cooperative robot control application is used to demonstrate the improvements achieved by the compositional approach to abstraction proposed by this paper.

层次结构是一种工具，用于提高解决使用监督控制理论建模的规划问题的可扩展性。在 Hill 和 Lafortune（2016）的工作中，成本等价的概念被用来生成监督者的抽象，在附加条件下，保证在抽象上生成的最优计划在应用于完整监督者时也是最优的。他们的工作能够通过基于事件的顺序相关排序人为地给予转换零成本来改进他们的抽象。在这里，我们放宽了对依赖事件的特定顺序的要求，同时保持层次结构的上层和下层之间的最佳关系。本文还扩展了作者的工作（Vilela 和 Hill 2020），我们在成本等价和弱互模拟的基础上提出了一种新的等价概念，我们称之为定价观察等价。这种等价性允许以组合方式生成主管抽象。这有助于避免由于在应用抽象之前必须首先综合完整的监督程序而导致的状态空间爆炸。在这里，我们还表明，可以使用新的宽松顺序依赖定义组合地创建具有人工零成本转换的模型。使用示例协作机器人控制应用程序来演示本文提出的组合抽象方法所实现的改进。