DIFFER Seminar: Contract theory for linear control systems

Abstract: Modern engineering systems, such as intelligent transportation systems, smart grids, smart manufacturing systems, etc., often comprise numerous interconnected components with design requirements that are becoming increasingly complex. Consequently, the development of individual components often necessitates specialized expertise and is thus handled by different (independent) teams. However, these teams rarely have the facilities to collaborate effectively, which can result in long and costly delays. This can be remedied by adopting a method for specifying design requirements that is inherently modular, i.e., that allows components to be developed independently. One such method is based on the use of contracts, a concept first introduced in computer science.

Although contract-based approaches have been developed for various system classes, they are typically restricted to systems with discrete variables evolving in discrete time. To address this limitation, we develop a contract theory for a class of (linear) dynamical control systems with continuous variables in continuous time. In particular, we define assume-guarantee contracts as specifications for the dynamic behavior of such systems. We also introduce formal notions of contract refinement and contract composition that enable the independent design of components within interconnected systems.