Analysis and synthesis of discrete-event regulator systems
Kevin M. Passino, Panos J. Antsaklis · 1989
A event (DES) is a dynamical whose evolution in time develops as a result of the occurrence of physical events at possibly irregular time intervals. Some examples include manufacturing and traffic systems. The properties of such can be improved using control-theoretic techniques by exploiting feedback. The controller, here a regulator, is connected to the DES and utilized to achieve certain design objectives that characterize the DESs behavior. Several control problems are addressed for the subsequent discrete event regulator system (DERS). We introduce costs for events to occur and a performance index which depends on the event costs. With this, we formulate an optimal regulator synthesis that can be solved by constructing a regulator that produces optimal allowable DES behavior for a given plant. The theory of the heuristic search algorithm called A* is extended and adapted to solve the regulator synthesis problem for a class of DERS. It is explained how certain Artificial Intelligence planning systems can be studied in a DES setting and the results of this dissertation are applied to such examples. Next, we study the possibility of utilizing a temporal logic approach to DERS analysis. We use a temporal language with formulas that can characterize, for instance, control-theoretic design objectives analogous to stability. We show that for a certain DERS there exists an effective algorithm for deciding whether or not DES design objectives stated in our temporal language are true or not for a given plant and regulator. A synthesis result follows. The proofs are based on the fact that although the regulator may not generate ultimately periodic strings it can be safely assumed to do so. In addition to the above results, the advancement of time and timing issues in DESs are discussed at length. Also, an Input/Output Petri net is introduced to simplify the DES modelling process and it is shown to be a special case of the plant model used to develop the above results.