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. ***
