Postdoc: Planning for Hybrid Systems

Burdick, Joel W.加州理工学院博士后：混合系统规划（该奖项支持CES助理Milos Zefran）由离散和连续过程控制的系统被称为“混合”系统。这样的系统用连续的动力学方程来描述，这些方程的结构和/或输入根据有限自动机的状态转换而变化。由于广泛使用计算机来控制物理设备，混合系统比比皆是。成功的混合系统必须将高级规划（有限自动机过渡的规划）与低级控制（动态方程的演化）稳健地结合起来。虽然规划和控制问题已经由计算机科学家和控制理论家分别解决，但离散和连续世界的相互作用在很大程度上留给了工程师的聪明才智。随着计算机控制的物理系统的复杂性的增长，这种方法失效了，需要严格的理论来设计、构建和评估混合系统。提出的研究将探讨如何统一离散和连续模型，以帮助建立混合系统工程的基础。先前对混合系统子类的规划工作将在两个方向上扩展。首先，将最优控制框架扩展为博弈论框架，以考虑不确定性。其次，研究具有简化特性的系统的混合控制问题，如李群对称性。

97-04702 Burdick, Joel W. California Institute of Technology Postdoc: Planning for Hybrid Systems (This award supports CES associate Milos Zefran) Systems that are governed by discrete and continuous processes are known as "hybrid" systems. Such systems are described by continuous dynamical equations whose structure and/or inputs change in accordance with the state transitions of a finite automaton. Due to the widespread use of computers to control physical devices, hybrid systems abound. Successful hybrid systems must robustly combine high-level planning (planning of the finite automaton transitions) with low-level control (evolution of the dynamic equations). While the planning and control problems have been addressed separately by computer scientists and control theorists, the interaction of the discrete and continuous worlds is largely left to the ingenuity of engineers. As the complexity of the computer controlled physical systems grows, such methods break down and there is a need for rigorous theory to design, build, and evaluate hybrid systems. The proposed research will investigate how to unify discrete and continuous models to help build a foundation for hybrid system engineering. Prior work on planning for a subclass of hybrid systems will be extended in two directions. First, an optimal control framework will be extended to a game-theoretic framework so as to take uncertainty into account. Second, the hybrid control problem will be explored for systems whose dynamics exhibit some simplifying properties, such as Lie group symmetries.