Hybrid Control Systems: Theory and Application

Varaiya 9417370混合系统是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进行高级监督的情况。 一个例子是自动驾驶汽车，其操纵在逻辑层面上进行规划和协调，但它们是使用确定油门、制动和转向致动器信号的连续反馈定律来执行的。 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，而不了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，但我们的知识是非常贫穷的相比，我们知道的连续时间系统和离散事件系统，孤立地考虑。 这个提议的主要目标是扩展我们对可判定或可计算混合系统的理解。 非正式地说，一个混合系统是可判定的，如果它的行为的重要问题可以回答有限的算法。 具体而言，我们建议： 1. 扩展了可判定混合系统的类; 2. 设计有限决策算法， “状态空间爆炸”问题; 3. 将这些算法应用于 自动化车辆。 我们实现这些目标的初步计划如下。 首先，我们将扩展可判定混合模型的非线性动态范围，并确定这些模型可以近似的混合系统的类别。 其次，我们将尝试正式的用户导向的细化过程，成功地包含状态空间爆炸。 第三，我们将继续验证自动车辆的混合系统控制器的设计，既作为我们的算法的测试，也作为理论发展的指导。 ***

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. ***