Building on the line of work (Ann. Appl. Probab. 25 (2015) 2096–2133; Stochastic Process. Appl. 125 (2015) 2451–2492; Ann. Appl. Probab. 29 (2019) 89–129; Arch. Ration. Mech. Anal. 233 (2019) ...643–699; Ann. Appl. Probab. 29 (2019) 2338–2373; Finance Stoch. 23 (2019) 535–594), we continue the study of particle systems with singular interaction through hitting times. In contrast to the previous research, we (i) consider very general driving processes and interaction functions, (ii) allow for inhomogeneous connection structures and (iii) analyze a game in which the particles determine their connections strategically. Hereby, we uncover two completely new phenomena. First, we characterize the “times of fragility” of such systems (e.g., the times when a macroscopic part of the population defaults or gets infected simultaneously, or when the neuron cells “synchronize”) explicitly in terms of the dynamics of the driving processes, the current distribution of the particles’ values and the topology of the underlying network (represented by its Perron–Frobenius eigenvalue). Second, we use such systems to describe a dynamic credit-network game and show that, in equilibrium, the system regularizes, that is, the times of fragility never occur, as the particles avoid them by adjusting their connections strategically. Two auxiliary mathematical results, useful in their own right, are uncovered during our investigation: a generalization of Schauder’s fixed-point theorem for the Skorokhod space with the M1 topology, and the application of max-plus algebra to the equilibrium version of the network flow problem.
This paper reports the development and application of an interval max-plus fault-tolerant control to a seat assembly system. Such systems will undergo a profound change because novel seats for ...autonomous driving contain expanded safety systems and are more voluminous and heavy. Automated guided vehicles are a promising means of transportation in these systems, but they require dedicated and advanced control systems. This rises new challenges because such an assembly system can dispose both shared resources and redundant elements. This paper presents a fault-tolerant control framework, which allows dealing with systems containing shared resources as well as redundancies. It also overcomes the problem of uncertainties and constraints, which are inevitable in industrial reality.
•A max-plus linear dynamic equation is developed to describe the dynamic behavior of serial production systems.•A model-based event-driven performance identification method is proposed to provide a ...feedback signal.•A discrete e-MPC is established to regenerate job release time for r-WIP optimization.
Advanced technologies (e.g., distributed sensors, RFID, and auto-identification) can gather processing information (e.g., system status, uncertain machine breakdown, and uncertain job demand) accurately and in real-time. By combining this transparent, detailed, and real-time production information with production system physical properties, an intelligent event-driven feedback control can be designed to reschedule the release plan of jobs in real-time without work-in-process (WIP) explosion. This controller should obtain the operational benefits of pull (e.g., Toyota’s Kanban system) and still develop a coherent planning structure (e.g., MRPII). This paper focuses on this purpose by constructing a discrete event-driven model predictive control (e-MPC) for real-time WIP (r-WIP) optimization. The discrete e-MPC addresses three key modelling problems of serial production systems: (1) establish a max-plus linear model to describe dynamic transition behaviors of serial production systems, (2) formulate a model-based event-driven production loss identification method to provide feedback signals for r-WIP optimization, and (3) design a discrete e-MPC to generate the optimal job release plan. Based on a case from an industrial sewing machine production plant, the advantages of the discrete e-MPC are compared with the other two r-WIP control strategies: Kanban and MRPII. The results show that the discrete e-MPC can rapidly and cost-effectively reconfigure production logic. It can decrease the r-WIP without deteriorating system throughput. The proposed e-MPC utilizes the available transparent sensor data to facilitate real-time production decisions. The effort is a step forward in smart manufacturing to achieve improved system responsiveness and efficiency.
The first objective of this paper is to settle the practical problem pertaining to the modelling and identification of the production system performance, which is defined a discrete event one. For ...that purpose the Internet of Things tools are employed, which are located at each manufacturing machine. As a result, a set of time-driven data is obtained, which measure the metal processing time of the shot blasting machines. These result constitute the base for the development of the state-space model designed with fuzzy logic and max-plus algebraic paradigms. The appealing property of the processing time model is that it is designed with the experimental design strategy, and hence, a minimum number of metal plates is required for its design. It should be noted that the system considered contains concurrent machines, which are redundant, and hence, cause the need for appropriate scheduling and control. Apart from that the system has an associated economic and health-aware indicators, which express the cost of possible degradation of using them over a specified time horizon. Thus, the proposed strategy allows finding a trade-off between general performance of the entire system and these indicators. The proposed strategy is illustrated with a practical proof-of-concept production system, which clearly exhibits the benefits concerning the application of the proposed approach.
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•Development and deployment of IoT structure.•Development of a metal processing machine model for manufacturing prediction.•Improvement of the Takagi–Sugeno model quality with an optimal experimental design.•Development of health-aware economic control strategy for the entire metal processing system.
This study addresses the problem of scheduling tank trucks at a fuel distribution terminal. The plant was modeled in the max-plus algebra, applying machine learning to determine process times. With ...this model, and based on a just-in-time approach, we have developed a predictive controller with two operation modes. This control system aims to prevent the excess of tank trucks inside the loading yard, thus achieving a better flow, efficiency, and safety in the process. Next, we have investigated the case study of a realistic and representative fuel distribution terminal, developing a simulator to enable a performance comparison between the proposed algorithms and the current heuristic. There was a 42.7% reduction in the work-in-progress (WIP) and 41.4% in the lead time, while productivity suffered a 2.8% loss. Bearing in mind, however, that there is flexibility in parametrization to mitigate this loss of productivity. In doing so, the reductions in WIP and lead time are slightly lower, at 34.7% for both metrics. The results show that the proposed control system can contribute significantly to improving the company’s performance indicators.
•Model predictive control and max-plus algebra applied to a scheduling problem.•A pre-trained neural network provides the process times for the max-plus model.•Optimizing the sequencing and timing of entry through switching max-plus-linear systems.•Notes on the implementation and performance analysis of the control strategies.
This paper considers max-consensus of a discrete-time multi-agent system (MAS) in directed random networks. Interactions among agents in the MAS are probabilistic and independent with each other. By ...using max-plus algebra and random theory, a sufficient and necessary condition is given for achieving max-consensus of the MAS. Moreover, we demonstrate that the max-consensus in four probabilistic senses (almost surely, in probability, expectation and mean square) is equivalent when expected graph is strongly connected. This ensures that max-consensus can be achieved in multi-agent systems even if random failures occur in the communication network, which is of practical importance in the fields of wireless sensor networks and distributed computing. A simulation example is presented to illustrate the effectiveness of theoretical results.
The energy-saving potential of original equipment manufacturers (OEMs) for electronic products is substantial owing to the huge market size of assembling industry in China. A semi-automatic ...electronic assembly line (SAEAL) for smart-phones is introduced, and its digital twin (DT) enabled energy-saving platform is developed as the hardware foundation. We propose a stochastic dynamics model via max-plus algebra to characterize the spatio-temporal nature of state transition, which provides dynamical opportunity windows for further energy-saving control strategy. Accordingly, model linearization is conducted to obtain linear state and output equations. Then, a model predictive control (MPC) approach for energy saving optimization is provided to determine the optimal start-stop control signal. The dynamics modeling and MPC approach have been applied and verified in the case of assembly line. The results show that the optimization approach could reach a proportion of 49% for the equipment sleep time of total running time and save a considerable amount of energy for normal production of OEMs.
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•A digital twin prototype system of smart-phone assembly line is developed as the testing platform for energy-saving control.•The assembling behaviors of assembly line are depicted by linear state equations via max-plus semiring algebra.•A spatio-temporal dynamics model is provided to evaluate the system performance based on max-plus semiring algebra.•An energy-saving MPC approach is proposed to determine the start-stop control sequences of automatic machines.•The equipment’s sleeping time can reach a proportion of 49% of total running time without production efficiency loss.
The paper concerns fault-tolerant control of a real battery assembly system which is under a pilot implementation at RAFI GmbH Company (one of the leading electronic manufacturing service providers ...in Germany). The proposed framework is based on an interval analysis approach, which along with max-plus algebra, allows describing uncertain discrete event system such as the production one being considered in this paper. Having a mathematical system description, a model predictive control-based fault tolerant strategy is developed which can cope with both processing, transportation and mobile robot faults. In particular, it enables tolerating (up to some degree) the influence of these faults on the overall system performance. As a result, a novel robust predictive fault-tolerant strategy is developed that is applied to the advanced battery assembly system. The final part of the paper shows the implementation and experimental validation of the proposed strategy. The proposed approach is tested against single as well as simultaneous faults concerning processing, transportation and mobile robots.
•An automated battery assembly system is designed.•A mathematical framework for describing uncertain production system is proposed.•A robust fault-tolerant control algorithm is proposed and applied to the battery assembly system.•The proposed approach is able to deal with simultaneous processing and mobile robot faults.•A comprehensive experimental study was realized in order to expose the performance of the proposed approach.
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