Discrete event dynamic systems最新文献

Supervisor synthesis is a means to algorithmically derive a supervisory controller from a discrete-event model of a system and a requirements specification. For large systems, synthesis suffers from state space explosion. To mitigate this, synthesis can be applied to a symbolic representation of the models by using Binary Decision Diagrams (BDDs). Peak used BDD nodes and BDD operation count are introduced as deterministic and platform independent metrics to express the computational effort of a symbolic synthesis. These BDD-based metrics are useful to analyze the efficiency of the synthesis algorithm. From this analysis, modifications can be made to how BDDs are handled during synthesis, improving synthesis efficiency. We demonstrate this approach by introducing and analyzing: DCSH, a variable ordering heuristic; several edge ordering heuristics; and an approach to efficiently enforce state exclusion requirements in synthesis. These methods were recently implemented in our open source supervisory control tool: Eclipse ESCET. The analysis is based on large scale experiments of performing synthesis on a variety of models from literature. We show that: (1) by using DCSH, synthesis with high computational effort can be avoided, and generally low computational effort is required, relative to the variable ordering heuristics that were used prior to this work; (2) applying reverse-model edge order realizes relatively low synthesis effort; and (3) state exclusion requirements can efficiently be enforced by restricting edge guards prior to synthesis. While these methods reduce computational effort in practice, it should be noted that they do not affect the theoretical (worst-case) complexity of synthesis.

In this paper, a type of graph, called an extremum timed extended reachability graph, is designed to abstract the temporal specifications and represent the feasible trajectories of time Petri nets. This graph improves the timed extended reachability graph recently proposed for time Petri nets (Lefebvre. Discrete Event Dynamic Systems 29(1):31–56. (2019); Zhou et al. IEEE Trans Autom Control 67(7):3693–3698. (2022)) by replacing the earliest-firing policy with a more general policy. In detail, when a transition is preselected for the next firing, the firing can be delayed for a certain period after its minimal residual time has elapsed, rather than immediately firing once its minimal residual time has elapsed. Then, a sampled timed extended reachability graph is designed, wherein, for a transition preselected to fire next, a finite number of time points within a time interval, starting at minimal residual time and ending at maximal residual time, are selected as the firing time instants for the preselected transition. Furthermore, a special case of the sampled timed extended reachability graph, called an extremum timed extended reachability graph that details only the minimal and maximal residual times of the transitions, is also proposed. For a feasible sequence, the corresponding feasible trajectories with minimal and maximal durations are easy to compute with this graph. Thus, an end-to-end delay of a feasible sequence can be obtained by directly searching the graph. Finally, the scheduling of a typical flexible manufacturing system illustrates the advantages and applications of the proposed approach.

This paper extends the theory of diagnosability by investigating fault diagnosis in discrete event systems under sensor attacks using finite-state automata as models. It assumes that an attacker has compromised the communication channel between the system’s sensors and the diagnostic engine. While the general attack model utilized by the attacker has been previously studied in the context of supervisory control, its application to fault diagnosis remains unexplored. The attacker possesses the capability to substitute each compromised observable event with a string from an attack language. The attack model incorporates event insertion and deletion, as well as static and dynamic attacks. To formally capture the diagnostic engine’s ability to identify faults in the presence of the attacker, a novel concept called CA-diagnosability is introduced. This extends the existing notions of CA-controllability and CA-observability. A testing procedure for CA-diagnosability is developed, and its correctness is proven. Some sufficient conditions for CA-diagnosability that can be easily checked are also proposed and proved. The paper then investigates conditions under which the role of an attacker can be reverted from malicious to benevolent, that is, to help the diagnoser to diagnose faults. The paper further applies diagnosability theory to investigate conditions under which the presence of the attacker can be detected.

This paper studies a scenario in which the occurrence of one or more events in a discrete event system is subject to external restrictions which may change unexpectedly during run-time. The system is modeled as a timed event graph (TEG) and, in this context, the presence of the aforementioned external restrictions has become known as partial synchronization (PS). This phenomenon arises naturally in several applications, from manufacturing to transportation systems. We develop a formal and systematic method to compute optimal control signals for TEGs in the presence of PS, where the control objective is tracking a given output reference as closely as possible and optimality is understood in the widely-adopted just-in-time sense. The approach is based on the formalism of tropical semirings — in particular, the min-plus algebra and derived semiring of counters. We claim that our method expands modeling and control capabilities with respect to previously existing ones by tackling the case of time-varying PS restrictions, which, to the best of our knowledge, has not been dealt with before in this context.

Stochastic Network Calculus is a probabilistic method to compute performance bounds in networks, such as end-to-end delays. It relies on the analysis of stochastic processes using formalism of (Deterministic) Network Calculus. However, unlike the deterministic theory, the computed bounds are usually very loose compared to the simulation. This is mainly due to the intensive use of the Boole’s inequality. On the other hand, analyses based on martingales can achieve tight bounds, but until now, they have not been applied to sequences of servers. In this paper, we improve the accuracy of Stochastic Network Calculus by combining this martingale analysis with a recent Stochastic Network Calculus results based on the Pay-Multiplexing-Only-Once property, well-known from the Deterministic Network calculus. We exhibit a non-trivial class of networks that can benefit from this analysis and compare our bounds with simulation.

The aim of this paper is the analysis of the property of the relaxed structurally boundedness of the unobservable subnet of the Petri net which brings a condition guaranteeing the finitude of all possible sequence lengths in the context of an on-line estimation in Partially Observable Petri Nets relevant to a sliding horizon or a receding horizon starting from the initial marking. Based on specific invariants defined over the real numbers, the approach focuses on an offline structural analysis, that is, the determination of the parts of the unobservable subnet where an online estimation for any criterion can be made. The decomposition-composition technique is based on a block triangular form obtained with any technique. The composition of the substructures leads to a propagation of the relaxed structurally boundedness property through the structure. The study of a large-scale manufacturing system shows that the direct treatment of the large system system can be avoided and that the triangular form brings a sequential treatment allowing a computation based on smaller systems independently of the resolution of the complete system.

This work deals with the control problem of Discrete Event Systems (DESs) modelled by Timed Event Graphs (TEGs) and subject to Generalized Marking Constraints (GMCs). The aim of this paper is to propose an algebraic methodology for the determination of control laws in the form of state feedback, guaranteeing the satisfaction of marking specifications expressed by weighted inequalities in the Min-Plus algebra. The resultant controller can be represented by marked and timed control places, connected to the initial TEG model. The role of the established feedback is to limit the number of tokens in weighted paths for partially observable TEGs. In order to illustrate and show the interest of these current studies, we applied the suggested control method to a machine of filling bottles with liquid.

The min-plus algebra is a commutative semiring with two operations: addition (varvec{a} oplus varvec{b := min (a,b)}) and multiplication (varvec{a} otimes varvec{b := a + b}). In this paper, we discuss a min-plus algebraic counterpart of matrix diagonalization in conventional linear algebra. Due to the absence of subtraction in the min-plus algebra, few matrices admit such a canonical form. Instead, we consider triangulation of min-plus matrices in terms of algebraic eigenvectors, which is an extended concept of usual eigenvectors. We deal with two types of min-plus matrices: strongly diagonally dominant (SDD) and nearly diagonally dominant (NDD) matrices. For an SDD matrix, the roots of the characteristic polynomial coincide with its diagonal entries. On the other hand, for an NDD matrix, the roots except for the maximum one appear in diagonal entries. We show that SDD matrices admit upper triangulation whose diagonal entries are algebraic eigenvalues, while NDD matrices admit block upper triangulation. We exhibit applications of triangulation of min-plus matrices to traffic flow models.

Two types of simulations and four types of bisimulations for weighted finite automata over the complete max-plus semiring we define as solutions of particular systems of matrix inequations. We provide a procedure that either decides that there is a simulation or bisimulation of a given type between two automata, and outputs the greatest one, or decides that no simulation or bisimulation of that type exists. The procedure is iterative and does not have to end in a finite number of steps. Certain conditions under which this procedure must terminate in a finite number of steps are described in a slightly more general context in Stamenković et al. (Discrete Event Dynamic Systems, 32:1–25, 2022). We also propose a modification of this procedure which, in case there is no simulation or bisimulation of a given type between two max-plus automata, detects this in finitely many steps and faster than the original procedure. In the same case, that modification also finds a natural number such that containment or equivalence is valid for all input words of length less than that number. For max-plus automata with non-negative weights, we point out the differences that occur when the above mentioned procedure is applied over the complete max-plus semiring, and when it is applied over its non-negative part with minus infinity added.

In this work, we consider D/D/S series queues characterized by deterministic interarrival and service times, with a single multi-server bottleneck stage. When the arrival rate is greater than the bottleneck capacity—for a temporary window of time—the derivation of cycle time is not immediately clear, and warrants a formal proof.