The computational complexity of decentralized discrete-event control problems

Abstract

Computational complexity results are obtained for decentralized discrete-event system problems. These results generalize the earlier work of Tsitsiklis, who showed that for centralized supervisory control problems under partial observation, solution existence is decidable in polynomial time for a special type of problem but becomes computationally intractable for the general class. As in the case of centralized control, there is no polynomial-time algorithm for producing supervisor solutions.

Incremental verification of Co-observability in discrete-event systems

“…The property of co-observability was introduced in [15], and a verification algorithm was introduced in [14]. The following is the definition of co-observability adapted from [15], [1].…”

Decentralized control of discrete-event systems when supervisors observe particular event occurrences

“…Although our construction of the modified M-machine derives from the construction in [7] and [8], it is considerably more complexto a degree that makes it a nontrivial extension of the work in [7] and [8]. In particular, in the construction of the transition function of the standard M-machine, there are three possible transitions that can lead out of a state, depending on values of certain strings sσ, s σ, and s σ, and one has to consider four possible combinations for every transition that could emanate from a state (namely, the binary possibilities of the event σ being in or not being in each of Σ 1 ,o and Σ 2 ,o ).…”

“…Given G = (Σ, Q G , δ G , q 0 ) and E = (Σ, Q E , δ E , q 0 ), we construct an automatonM (G, E), which is similar to M in [7] and [8], and which we will refer to as a modified M-machine. There is only one marked state, which is denoted by d, and called the dump state.…”

“…In [7] and [8], a nondeterministic finite automaton, which we call an M-machine, is constructed to check coobservability. The M-machine traces all the possible sequences ambiguous to supervisors, then checks if those sequences violate the property of co-observability of L(E) with respect to G. In this section, we will modify the structure of the M-machine so that it will check state-based co-observability.…”

Decentralized Diagnosis of Discrete Event Systems using Unconditional and Conditional Decisions

“…Since NF-DIAG is equivalent to F-DIAG, verification algorithms for F-DIAG, including diagnosers [2] and verifiers [18], can be used to verify NF-DIAG as well. We are particularly interested in the verifier approach because it has polynomial computational complexity and can be easily generalized to decentralized settings [11,19]. Online diagnosis of the absence of faults can be done by diagnosers.…”