Contract theory for linear control systems

Modern engineering systems, such as intelligent transportation systems, smart grids, smart manufacturing systems, etc., often comprise a large number of interconnected components. The design requirements for the components of such systems are becoming increasingly complex. Consequently, the development of components usually requires specialized expertise and is, thus, handled by different (independent) teams. But independent teams seldom have the facilities to collaborate effectively, which can cause long and costly delays. This can be avoided by adopting a method for specifying design requirements that is inherently modular, i.e., that allows components to be considered independently. One such method is based on using so-called contracts, first introduced in the field of computer science. While contract theories have been developed for various system classes, these are generally restricted to systems with discrete variables evolving in discrete time.

Motivated by this, in this thesis, we develop a contract theory for a class of dynamical control systems with continuous variables in continuous time. In particular, we introduce notions of implementation, refinement, and conjunction, which allow us to express, compare, and combine specifications using contracts. Furthermore, we introduce two notions of contract composition, which, together with the notion of refinement, enable the independent design of components within interconnected systems.