Symbolic Computation of Nonblocking Control Function for Timed Discrete Event Systems

In this paper, we symbolically compute a minimally restrictive nonblocking supervisor for timed discrete event systems, in the supervisory control theory context. The method is based on Timed Extended Finite Automata, which is an augmentation of extended finite automata (EFAs) by incorporating discrete time into the model. EFAs are ordinary automaton extended with discrete variables, guard expressions and action functions. To tackle large problems all computations are based on binary decision diagrams (BDDs). The main feature of this approach is that the BDD-based fixed-point computations is not based on “tick” models that have been commonly used in this area, leading to better performance in many cases. As a case study, we effectively computed the minimally restrictive nonblocking supervisor for a well-known production cell

Time-optimal control of large-scale systems of systems using compositional optimization

Optimization of industrial processes such as manufacturing cells can have great impact on their performance. Finding optimal solutions to these large-scale systems is, however, a complex problem. They typically include multiple subsystems, and the search space generally grows exponentially with each subsystem. In previous work we proposed Compositional Optimization as a method to solve these type of problems. This integrates optimization with techniques from compositional supervisory control, dividing the optimization into separate sub-problems. The main purpose is to mitigate the state explosion problem, but a bonus is that the individual sub-problems can be solved using parallel computation, making the method even more scalable. This paper further improves on compositional optimization with a novel synchronization method, called partial time-weighted synchronization (PTWS), that is specifically designed for time-optimal control of asynchronous systems. The benefit is its ability to combine the behaviour of asynchronous subsystems without introducing additional states or transitions. The method also reduces the search space further by integrating an optimization heuristic that removes many non-optimal or redundant solutions already during synchronization. Results in this paper show that compositional optimization efficiently generates global optimal solutions to large-scale realistic optimization problems, too big to solve when based on traditional monolithic models. It is also shown that the introduction of PTWS drastically decreases the total search space of the optimization compared to previous work