Hybrid Control Systems: Theory and Application

混合系统是由离散事件系统监督连续时间系统的模型。这些模型特别适用于描述计算机或人类符号处理系统对连续过程提供高层次监督的情况。一个例子是自动驾驶汽车，它的操作在逻辑层面上是计划和协调的，但它们是使用连续的反馈律来执行的，这些反馈律决定了油门、刹车和转向执行器的信号。另一个例子是我们每天使用“常识”规则来成功地控制复杂的过程，如微波炉、汽车和复印机，而不理解控制这些过程行为的物理和工程原理。混合系统的研究开始受到重视，但与我们对连续时间系统和离散事件系统的了解相比，我们的知识非常贫乏，孤立地考虑。本提案的主要目标是扩展我们对可决定或可计算混合系统的理解。非正式地说，如果一个混合系统的行为的重要问题可以用有限的算法来回答，那么它就是可决定的。具体而言，我们建议：1。扩展可决定混合系统的类别；2. 设计有限决策算法，衰减“状态空间爆炸”问题；3. 将这些算法应用于自动驾驶车辆的控制问题。我们实现这些目标的初步计划如下。首先，我们将扩展可决定混合模型的非线性动力学范围，并确定这些模型可以近似的混合系统的类别。其次，我们将尝试形式化用户导向的改进程序，该程序成功地包含了状态空间爆炸。第三，我们将继续验证自动驾驶车辆混合系统控制器的设计，这既是对我们算法的测试，也是对理论发展的指导。＊＊＊

Varaiya 9417370 Hybrid systems are models in which a discrete event system supervises a continuous time system. These models are especially appropriate for describing situations in which a computer or human symbol-processing system provides high level supervision of a continuous process. One example is an automated vehicle whose maneuvers are planned and coordinated at a logical level, but they are executed using continuous feedback laws that determine the throttle, braking and steering actuator signals. Another example is our daily use of "common sense" rules to successfully control sophisticated processes such as microwave ovens, automobiles and copying machines, without understanding the physical and engineering principles that govern the behavior of those processes. The study of hybrid systems is beginning to receive serious attention, but our knowledge is very poor compared with what we know about continuous time systems and discrete event systems, considered in isolation. The primary goal of this proposal is to extend our understanding of decidable or computable hybrid systems. Informally, a hybrid system is decidable if important questions of its behavior can be answered by finite algorithms. Specifically, we propose to: 1. Extend the class of decidable hybrid systems; 2. Design finite decision algorithms that attenuate the "state space explosion" problem; 3. Apply those algorithms to problems of control of automated vehicles. Our initial plan for meeting these objectives are as follows. First, we will extend the range of nonlinear dynamics of the decidable hybrid models and determine the class of hybrid systems these models can approximate. Second, we will attempt to formalize the user-directed refinement procedure which succeeded in containing the state space explosion. Third, we shall continue to verify the design of hybrid system controllers for automated vehicles both as a test of our algor ithms and as a guide to theory development. ***