Model Decomposition of Timed Event Graphs under Partial Synchronization in Dioids (I)

Timed Event Graphs (TEGs) are a graphical model for decision free and time-invariant Discrete Event Systems (DESs). To express systems with time-variant behaviors, a new form of synchronization, called partial synchronization (PS), has been introduced for TEGs. Unlike exact synchronization, where two transitions t1,t2 can only fire if both transitions are simultaneously enabled, PS of transition t1 by transition t2 means that t1 can fire only when transition t2 fires, but t1 does not influence the firing of t2. Under some assumptions, we can show that the dynamic behavior of a TEG under PS can be decomposed into a time-variant and a time-invariant part. The time-invariant part can be interpreted as a standard TEG. Moreover, it is shown that the tools introduced for standard TEGs can be used to analyze the overall system

Model predictive control for discrete event systems with partial synchronization

In this paper, we consider discrete event systems divided in a main system and a secondary system such that the inner dynamics of each system is ruled by standard synchronizations and the interactions between both systems are expressed by partial synchronizations (i.e., event e2 can only occur when, not after, event e1 occurs) of events in the secondary system by events in the main system. The main contribution consists in adapting model predictive control, developed in the literature for (max,+)-linear systems, to the considered class of systems. This problem is solved under the condition that the performance of the main system is never degraded to improve the performance of the secondary system. Then, the optimal input is selected to respect the output reference and the remaining degrees of freedom are used to ensure just-in-time behavior. The unconstrained problem is solved in linear time with respect to the length of the prediction horizon

Weight-Balanced Timed Event Graphs to Model Periodic Phenomena in Manufacturing Systems

Timed event graphs (TEGs) are suitable to model manufacturing systems in which synchronization and delay phenomena appear. Since 1980s, TEGs are studied as a class of linear discrete event systems in idempotent semirings such as the (min,+) algebra. In this paper, we consider the class of weighted TEGs (WTEGs) that corresponds to TEGs where the edges have integer weights. By introducing nonunitary weights, WTEGs widen the class of manufacturing systems that can be modeled, especially systems with batches and duplications. Moreover, a subclass of WTEGs called weight-balanced TEGs (WB-TEGs) can be studied with the algebraic tools that stem from the theory of (min,+) linear systems. In this paper, the focus lies on some modeling issues for manufacturing systems. Besides cutting and palletization operations, it is shown that WB-TEGs are also well adapted to describe periodic routing policies and, in a symmetrical way, how to merge flows similar to a multiplexer. In order to simplify the modeling step, a class of cycloweighted TEGs (CW-TEGs) is introduced. It is an extension of WTEGs where the weights of the edges can change according to a periodic sequence. Finally, we propose some elements of modeling that can be described by CW-TEGs or equivalently with an input-output transfer relation in an appropriate idempotent semiring of operators

A sharp incisor tool for predator house mice back to the wild

The house mouse (Mus musculus domesticus), as a successful invasive species worldwide, has to forage a variety of resources. Subantarctic mice display among the most notable diet shift from the usual omnivorous–granivorous diet, relying on a larger proportion of terrestrial animal prey. In agreement, a recent study of their mandible morphology evidenced an evolution of their mandible shape to optimize incisor biting and hence seize preys. Here, the incisors themselves are the focus of a morphometric analysis combined with a 3D study of their internal structure, aiming at a comparison between subantarctic populations (Guillou island, Kerguelen archipelago) with a range of western European continental, commensal mice. The predatory foraging behavior of Guillou mice was indeed associated with a sharper bevel of the lower incisor, which appears as an efficient morphology for piercing prey. The incisor of these mice also displays a reduced pulp cavity, suggesting slower eruption counterbalancing a reduced abrasion on such soft food material. The dynamics of the ever‐growing incisor may thus allow adaptive incisor sculpting and participate to the success of mice in foraging diverse resources

Validation of the French translation-adaptation of the impact of cancer questionnaire version 2 (IOCv2) in a breast cancer survivor population

Background: The Impact of Cancer version 2 (IOCv2) was designed to assess the physical and psychosocial health experience of cancer survivors through its positive and negative impacts. Although the IOCv2 is available in English and Dutch, it has not yet been validated for use in French-speaking populations. The current study was undertaken to provide a comprehensive assessment of the reliability and validity of the French language version of the IOCv2 in a sample of breast cancer survivors. Methods: An adapted French version of the IOCv2 as well as demographic and medical information were completed by 243 women to validate the factor structure divergent/divergent validities and reliability. Concurrent validity was assessed by correlating the IOCv2 scales with measures from the SF-12, PostTraumatic Growth Inventory and Fear of Cancer Recurrence Inventory. Results: The French version of the IOCv2 supports the structure of the original version, with four positive impact dimensions and four negative impact dimensions. This result was suggested by the good fit of the confirmatory factor analysis and the adequate reliability revealed by Cronbach's alpha coefficients and other psychometric indices. The concurrent validity analysis revealed patterns of association between IOCv2 scale scores and other measures. Unlike the original version, a structure with a Positive Impact domain consisting in the IOCv2 positive dimensions and a Negative Impact domain consisting in the negative ones has not been clearly evidenced in this study. The limited practical use of the conditional dimensions Employment Concerns and Relationship Concerns, whether the patient is partnered or not, did not make possible to provide evidence of validity and reliability of these dimensions as the subsets of sample to work with were not large enough. The scores of these conditional dimensions have to be used with full knowledge of the facts of this limitation of the study. Conclusions: Integrating IOCv2 into studies will contribute to evaluate the psychosocial health experience of the growing population of cancer survivors, enabling better understanding of the multi-dimensional impact of cancer

Control and State Estimation for Max-Plus Linear Systems

Book Abstract: Max-plus linear systems theory was inspired by and originated from classical linear systems theory more than three decades ago, with the purpose of dealing with nonlinear synchronization and delay phenomena in timed discrete event systems in a linear manner. Timed discrete event systems describe many problems in diverse areas such as manufacturing, communication, or transportation networks. This monograph provides a thorough survey of current research work in max-plus linear systems. It summarizes the main mathematical concepts required for a theory of max-plus linear systems, including idempotent semirings, residuation theory, fixed point equations in the max-plus algebra, formal power series, and timed-event graphs. The authors also review some recent major achievements in control and state estimation of max-plus linear systems. These include max-plus observer design, max-plus model matching by output or state feedback and observer-based control synthesis. Control and State Estimation for Max-Plus Linear Systems offers students, practitioners, and researchers an accessible and comprehensive overview of the most important recent work in max-plus Linear Systems

Modeling and Control for Max-Plus Systems with Partial Synchronization

International audienceA max-plus system with partial synchronization is a persistent discrete event system divided into a main subsystem and a secondary subsystem where some events in the secondary subsystem can only occur when (not after) associated events in the main subsystem occur. A formal model based on max-plus recursive equations is presented for max-plus systems with partial synchronization. Furthermore, the control problem of output tracking is addressed by assigning a higher priority to the main subsystem: the performance of the main subsystem is never degraded to improve the performance of the secondary subsystem. Two different control approaches are investigated: optimal feedforward control and model predictive control. In both cases, residuation theory is applied to efficiently solve the optimization problem