发表机构
Georgia Institute of Technology; Florida Institute of Technology; University of Florida（佐治亚理工学院; 佛罗里达理工学院; 佛罗里达大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一个范畴论框架，通过有限链的细化关系连接不同细化级别的模型，以处理控制器设计与实现模型间无直接细化关系的问题，并给出输出失配界、闭环性能及网络提升结果，示例验证了其有效性。
AI 中文摘要
存储函数被广泛用于将控制系统与更简单的模型相关联，以进行分析和控制器设计，并用于量化当控制器在一个模型上设计但在另一个模型上实现时的模型失配。在应用中，同一物理过程的多个模型以不同的细化级别可用，而细化关系（由存储函数和关联接口组成）仅在相邻级别之间构建。因此，在用于控制器设计的模型和用于实现的模型之间，直接细化关系可能不可用。为了解决这一差距，我们考虑具有用于互连的内部端口和用于输入输出分析的外部端口的开放控制系统。我们定义了一个范畴 $\mathsf{OCS}_{\mathrm{chain}}$，其对象是开放控制系统，其态射是有限链的细化关系。使用这个范畴，我们推导了一个输出失配界和一个闭环性能结果，用于通过一系列接口细化的控制器。然后，我们定义了一个函子，将细化关系从开放控制系统转移到没有内部端口的系统。我们还开发了一个网络提升结果，表明在标准互连兼容性条件下，子系统存储函数可以组合以获得复合网络的细化关系和性能界。两个热网络示例说明了递归控制器细化和模型失配沿细化链的传播。仿真表明，即使控制器在最粗糙的模型上设计并在最精细的模型上部署，HVAC系统也能跟踪时变参考温度，误差低于 $0.2^\circ\mathrm{C}$。
英文摘要
Storage functions are widely used to relate a control system to a simpler model for analysis and controller design, and to quantify model mismatch when a controller is designed on one model but implemented on another. In applications, several models of the same physical process are available at different levels of refinement, while refinement relations, consisting of a storage function and an associated interface, are constructed only between neighboring levels. Thus, a direct refinement relation may be unavailable between the model used for controller design and the model used for implementation. To address this gap, we consider open control systems with internal ports for interconnection and external ports for input-output analysis. We define a category, $\mathsf{OCS}_{\mathrm{chain}}$, whose objects are open control systems and whose morphisms are finite chains of refinement relations. Using this category, we derive an output mismatch bound and a closed-loop performance result for controllers refined through a sequence of interfaces. We then define a functor that transfers refinement relations from open control systems to systems without internal ports. We also develop a network lifting result showing that, under standard interconnection compatibility conditions, subsystem storage functions can be combined to obtain refinement relations and performance bounds for composite networks. Two thermal network examples illustrate recursive controller refinement and the propagation of model mismatch along refinement chains. Simulations show that an HVAC system tracks a time-varying reference temperature with error below $0.2^\circ\mathrm{C}$ even when the controller is designed on the coarsest model and deployed on the finest model.
