Concurrencey in DES and A class of hybrid systems : theory and computation

Abstract

This thesis explains the general concurrency of discrete event systems (DES), and then extends it to hybrid systems. To this end, firstly, a theoretical extension with n-ary structure is considered for the concurrency of a group of DES in the presence of specifications. A new concept (called map) is then introduced to meet a particular class of specifications, which are based upon both events and states. The map will be used to develop the n-ary synchronous product composition to a new composition rule, called accommodating synchronous product (ASP), which can implement the mentioned class of specifications. -- Moreover, the DES concepts will be extended to a class of hybrid dynamical systems, whose concurrency is allowed to happen exclusively in the logical part. In such systems, a continuous dynamics (a physical behaviour) generates an event which then is passed to a DES to cause a transition (if any). -- In the last part, a MATLAB-based software has been developed as the testbed for the theory and algorithms described throughout the thesis. The software has been designed with the consideration of object-oriented design, vectorization, and compatibility with standard DES software. Based on its structure and a variety of different methods, it can be used for manipulating and exploring both concurrent DES and concurrent hybrid systems. Finally, the concepts presented in the thesis will be demonstrated in an extensive computational example solved by the software.