State Based Control of Timed Discrete Event Systems using Binary ...

Chapter 5. BDD based implementation 35[30], which is many times faster and smaller in the sense of memory usage than TCT.STCT does not need an exhaustive list of the entire state space and thus is able to achievea performance far beyond that of TCT.For a timed model this complexity problem is more critical, because as we saw in the previoussection state explosion is much faster in untimed models than timed ones. Clearlyfor large systems an exhaustive list of the entire state space cannot be used.5.3 Converting ATG to TTGConstructing the TTG from the ATG of the TDES is based on the definition of δ(q, σ).Actually we should find the reachable states of the TDES. As we saw in chapter 2, eachstate of the TDES has two kinds of component: activity and timer of each event. Thuseach state would be an n + 1 tuple, where n is the number of events in the system.The natural way to find these states is to start from the initial state q 0 = (a 0 , {t σ,0 |σ ∈Σ act }) where⎧⎪⎨ u σ ,t σ,0 =⎪⎩ l σ ,if σ ∈ Σ speif σ ∈ Σ remand find the reachable states by the rules given in the definition of δ. In this method,we should go through all the states and check the conditions to find the next states inthe graph. If the time bounds of events are big, the number of states will be much bigger.Using this exhaustive search method would not be efficient and fast. Additionally,using the tables for storing these states would be much too memory-consuming. Insteadwe convert the rules for defining the transitions in TDES to logical operations that canbe applied to predicates. By these logical operations, all the possible transitions in thesystem which satisfy the rules, can be found in the form of predicate. After finding thetransition predicates, the reachable states can be found by applying suitable logical operationsas we will discuss later.