Control from Computer Science 1

This paper presents some of the principles underlying veriication and controller synthesis techniques for discrete dynamical systems developed within Computer Science along with some ideas to extend them to continuous and hybrid systems. Hopefully, this will provide control theorists and engineers with an additional perspective of their discipline as seen by a sympathetic outsider, uncommitted to the customs and traditions of the domain. Inter-cultural experience can be frustrating but sometimes fun. 1. WHAT AM I DOING HERE? Being one of those who have chosen to study computer science partly due to an inability to understand diierential equations, I feel a bit uncomfortable to speak in this conference whose proceedings pages are full of occurrences of that terrifying R symbol. The scientiic reason for my presence here is perhaps being one of those few computer scientists interested in the so-called hybrid systems research which was supposed to bring together the Computer Science and Control communities. So let me rst speak about what I understand. 2. WHAT IS VERIFICATION? Veriication 2 like Control is concerned with a model-based design of systems. That is, we want to build something (\controller") that makes some part of the real world (the \environment" or \plant") behave in a certain desired way. Instead of using trial-and-error methods we build a mathematical model which describes the combined dy-(Veriication of Hybrid Systems). 2 The term \veriication" is used as a short approximation for the disciplines and communities interested in \model-ing, design and analysis of reactive systems" or \formal methods in system design". namics of the environment and the controller. On this model we can make \gedanken experiments", e.g. manipulation of formulae or numerical simulations , to convince ourselves that the controller indeed makes the environment behave as required. If the model is a good approximation of the real world, there is a chance that a controller validated on the model will work properly when implemented. 3 The description just given does not specify the type of dynamical models considered. In classical control these are models of continuous dynamical systems in either continuous or discrete time, and since examples of such systems appear in every decent control textbook, I will move directly to discrete systems of the type treated by the veriication community and illustrate them via an example. 2.1 The Cooee Machine Suppose we want to build a machine M which distributes various hot drinks to customers who pay …