Computations on distributed discrete-event systems

• Authors: Kurt Ryan Rohloff;Stephane Lafortune
• Venue: Computations on distributed discrete-event systems
• Year: 2004

This thesis explores computational issues related to the control and verification of systems with distributed structure. The framework of supervisory control theory and discrete-event systems is used where system modules are modelled as sets of finite state automata whose behavior coordinates on the occurrence of common events. It is shown that in general many problems related to the supervision of these systems are PSPACE-complete. There are methods for solving these problems that are more efficient in memory than the current state-of-the-art methods, but there are most likely no time-efficient general solution methods that would aid in the study of such “large-scale” systems. This thesis explores methods for avoiding the computational difficulty of solving these problems. For decentralized control situations a new state estimator is presented that accounts for past local control actions when calculating the set of estimated system states. The new state estimator is used to develop new decentralized control protocols with a common sufficient safety condition. It is also shown that it is difficult to approximate minimal solutions to a sensor selection problem for partial observation control situations. Heuristic methods for solving this approximation problem based on a type of edge-colored graph cutting problem are then discussed. It is also shown how to convert a type of communicating controller problem into this edge-colored graph cutting problem. A notion of state permutation symmetry that defines an equivalence class for the distributed system states is introduced. A method is shown to reduce the complexity of verifying μ-calculus propositions for systems with state permutation symmetry. A special class of symmetric distributed systems is also shown that allows for an even greater reduction in the difficulty of testing several fundamental system properties. Control and verification problems related to both local and global specifications for these special systems are then explored.