一個新的解混合式最佳控制問題的方法

Abstract

混合系統模型是利用事件驅動與時間動動態來描述系統的特性。這樣的模型利用時間驅動動態來描述工作在製造設備間移動的情形，而當工作在機器中被處理時，物理特性的變化，則是根據時間驅動動態來陳述。當為了追求工作完成時間與完成工作時的最佳取捨，所衍生出來的最佳化控制問題在製造系統中是一個重要且困難的問題。 在本論文我們將考慮混合系統的最佳化控制問題。基於混合系統的模型，我們先對單階的製造系統作分析，並利用最佳化技巧中的對偶問題，來解決。然後，我們將工作衍生到多階製造系統上，並且利用Generalized Bender’s Decomposition的技巧與對偶的方法提供解決最佳化控制問題的策略。

Hybrid system is used to characterize systems that combine time-driven and event-driven dynamics. The framework uses event-driven dynamics to describe the movement of jobs through a manufacturing facility. While the jobs are processed by the machines, their physical characteristics undergo some transformation. Their physical characteristics change according to time-driven dynamics. The optimal control problems that arise when one attempts to trade-off demands on job completion times against the quality of the completed jogs is an important and difficult problem. This paper concerns optimal control problems of hybrid systems in manufacturing. Based on the framework of hybrid systems, we first analyze and solve a class of optimal control problems for single-stage processes. Next, we present extensions to multistage manufacturing processes for which we develop solution algorithms that make use of Generalized Bender’s Decomposition techniques and Dual method.