Supervisory Control of Fuzzy Discrete Event Systems: A Formal Approach

Fuzzy {\it discrete event systems} (DESs) were proposed recently by Lin and Ying [19], which may better cope with the real-world problems with fuzziness, impreciseness, and subjectivity such as those in biomedicine. As a continuation of [19], in this paper we further develop fuzzy DESs by dealing with supervisory control of fuzzy DESs. More specifically, (i) we reformulate the parallel composition of crisp DESs, and then define the parallel composition of fuzzy DESs that is equivalent to that in [19]; {\it max-product} and {\it max-min} automata for modeling fuzzy DESs are considered; (ii) we deal with a number of fundamental problems regarding supervisory control of fuzzy DESs, particularly demonstrate controllability theorem and nonblocking controllability theorem of fuzzy DESs, and thus present the conditions for the existence of supervisors in fuzzy DESs; (iii) we analyze the complexity for presenting a uniform criterion to test the fuzzy controllability condition of fuzzy DESs modeled by max-product automata; in particular, we present in detail a general computing method for checking whether or not the fuzzy controllability condition holds, if max-min automata are used to model fuzzy DESs, and by means of this method we can search for all possible fuzzy states reachable from initial fuzzy state in max-min automata; also, we introduce the fuzzy $n$-controllability condition for some practical problems; (iv) a number of examples serving to illustrate the applications of the derived results and methods are described; some basic properties related to supervisory control of fuzzy DESs are investigated. To conclude, some related issues are raised for further consideration

Supervisory Control of Fuzzy Discrete Event Systems

In order to cope with situations in which a plant's dynamics are not precisely known, we consider the problem of supervisory control for a class of discrete event systems modelled by fuzzy automata. The behavior of such discrete event systems is described by fuzzy languages; the supervisors are event feedback and can disable only controllable events with any degree. The concept of discrete event system controllability is thus extended by incorporating fuzziness. In this new sense, we present a necessary and sufficient condition for a fuzzy language to be controllable. We also study the supremal controllable fuzzy sublanguage and the infimal controllable fuzzy superlanguage when a given pre-specified desired fuzzy language is uncontrollable. Our framework generalizes that of Ramadge-Wonham and reduces to Ramadge-Wonham framework when membership grades in all fuzzy languages must be either 0 or 1. The theoretical development is accompanied by illustrative numerical examples.Comment: 12 pages, 2 figure

State-Based Control of Fuzzy Discrete Event Systems

To effectively represent possibility arising from states and dynamics of a system, fuzzy discrete event systems as a generalization of conventional discrete event systems have been introduced recently. Supervisory control theory based on event feedback has been well established for such systems. Noting that the system state description, from the viewpoint of specification, seems more convenient, we investigate the state-based control of fuzzy discrete event systems in this paper. We first present an approach to finding all fuzzy states that are reachable by controlling the system. After introducing the notion of controllability for fuzzy states, we then provide a necessary and sufficient condition for a set of fuzzy states to be controllable. We also find that event-based control and state-based control are not equivalent and further discuss the relationship between them. Finally, we examine the possibility of driving a fuzzy discrete event system under control from a given initial state to a prescribed set of fuzzy states and then keeping it there indefinitely.Comment: 14 double column pages; 4 figures; to be published in the IEEE Transactions on Systems, Man, and Cybernetics--Part B: Cybernetic

Observability and Decentralized Control of Fuzzy Discrete Event Systems

Fuzzy discrete event systems as a generalization of (crisp) discrete event systems have been introduced in order that it is possible to effectively represent uncertainty, imprecision, and vagueness arising from the dynamic of systems. A fuzzy discrete event system has been modelled by a fuzzy automaton; its behavior is described in terms of the fuzzy language generated by the automaton. In this paper, we are concerned with the supervisory control problem for fuzzy discrete event systems with partial observation. Observability, normality, and co-observability of crisp languages are extended to fuzzy languages. It is shown that the observability, together with controllability, of the desired fuzzy language is a necessary and sufficient condition for the existence of a partially observable fuzzy supervisor. When a decentralized solution is desired, it is proved that there exist local fuzzy supervisors if and only if the fuzzy language to be synthesized is controllable and co-observable. Moreover, the infimal controllable and observable fuzzy superlanguage, and the supremal controllable and normal fuzzy sublanguage are also discussed. Simple examples are provided to illustrate the theoretical development.Comment: 14 pages, 1 figure. to be published in the IEEE Transactions on Fuzzy System

Multiobjective strategies for New Product Development in the pharmaceutical industry

New Product Development (NPD) constitutes a challenging problem in the pharmaceutical industry, due to the characteristics of the development pipeline. Formally, the NPD problem can be stated as follows: select a set of R&D projects from a pool of candidate projects in order to satisfy several criteria (economic profitability, time to market) while coping with the uncertain nature of the projects. More precisely, the recurrent key issues are to determine the projects to develop once target molecules have been identified, their order and the level of resources to assign. In this context, the proposed approach combines discrete event stochastic simulation (Monte Carlo approach) with multiobjective genetic algorithms (NSGAII type, Non-Sorted Genetic Algorithm II) to optimize the highly combinatorial portfolio management problem. In that context, Genetic Algorithms (GAs) are particularly attractive for treating this kind of problem, due to their ability to directly lead to the so-called Pareto front and to account for the combinatorial aspect. This work is illustrated with a study case involving nine interdependent new product candidates targeting three diseases. An analysis is performed for this test bench on the different pairs of criteria both for the bi- and tricriteria optimization: large portfolios cause resource queues and delays time to launch and are eliminated by the bi- and tricriteria optimization strategy. The optimization strategy is thus interesting to detect the sequence candidates. Time is an important criterion to consider simultaneously with NPV and risk criteria. The order in which drugs are released in the pipeline is of great importance as with scheduling problems

Multiobjective strategies for New Product Development in the pharmaceutical industry

New Product Development (NPD) constitutes a challenging problem in the pharmaceutical industry, due to the characteristics of the development pipeline. Formally, the NPD problem can be stated as follows: select a set of R&D projects from a pool of candidate projects in order to satisfy several criteria (economic profitability, time to market) while coping with the uncertain nature of the projects. More precisely, the recurrent key issues are to determine the projects to develop once target molecules have been identified, their order and the level of resources to assign. In this context, the proposed approach combines discrete event stochastic simulation (Monte Carlo approach) with multiobjective genetic algorithms (NSGAII type, Non-Sorted Genetic Algorithm II) to optimize the highly combinatorial portfolio management problem. In that context, Genetic Algorithms (GAs) are particularly attractive for treating this kind of problem, due to their ability to directly lead to the so-called Pareto front and to account for the combinatorial aspect. This work is illustrated with a study case involving nine interdependent new product candidates targeting three diseases. An analysis is performed for this test bench on the different pairs of criteria both for the bi- and tricriteria optimization: large portfolios cause resource queues and delays time to launch and are eliminated by the bi- and tricriteria optimization strategy. The optimization strategy is thus interesting to detect the sequence candidates. Time is an important criterion to consider simultaneously with NPV and risk criteria. The order in which drugs are released in the pipeline is of great importance as with scheduling problems

Operational Risk Management using a Fuzzy Logic Inference System

Operational Risk (OR) results from endogenous and exogenous risk factors, as diverse and complex to assess as human resources and technology, which may not be properly measured using traditional quantitative approaches. Engineering has faced the same challenges when designing practical solutions to complex multifactor and non-linear systems where human reasoning, expert knowledge or imprecise information are valuable inputs. One of the solutions provided by engineering is a Fuzzy Logic Inference System (FLIS). Despite the goal of the FLIS model for OR is its assessment, it is not an end in itself. The choice of a FLIS results in a convenient and sound use of qualitative and quantitative inputs, capable of effectively articulating risk management's identification, assessment, monitoring and mitigation stages. Different from traditional approaches, the proposed model allows evaluating mitigation efforts ex-ante, thus avoiding concealed OR sources from system complexity build-up and optimizing risk management resources. Furthermore, because the model contrasts effective with expected OR data, it is able to constantly validate its outcome, recognize environment shifts and issue warning signals.Operational Risk, Fuzzy Logic, Risk Management Classification JEL:G32, C63, D80

Integration of a failure monitoring within a hybrid dynamic simulation environment

The complexity and the size of the industrial chemical processes induce the monitoring of a growing number of process variables. Their knowledge is generally based on the measurements of system variables and on the physico-chemical models of the process. Nevertheless this information is imprecise because of process and measurement noise. So the research ways aim at developing new and more powerful techniques for the detection of process fault. In this work, we present a method for the fault detection based on the comparison between the real system and the reference model evolution generated by the extended Kalman filter. The reference model is simulated by the dynamic hybrid simulator, PrODHyS. It is a general object-oriented environment which provides common and reusable components designed for the development and the management of dynamic simulation of industrial systems. The use of this method is illustrated through a didactic example relating to the field of Chemical Process System Engineering