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We present in this article a mathematical model for the traffic on a linear metro line (a metro line without junction), taking into account the train dynamics and the passenger travel demand. The train dynamics are modeled as a discrete event dynamic system, written linearly in the Max-plus algebra. The model permits an analytic derivation of phase diagrams for the train dynamics depending on the passenger travel demand. By this, the physics of traffic on linear metro lines is wholly understood and interpreted. We introduce into the model the passenger capacity of trains, and derive analytically an indicator for the passenger comfort inside the trains, as a function of the number of trains and of the level of the passenger demand. By this model, metro operators can adjust the train dwell times at platforms depending on the level of the passenger demand. They can also optimize the train frequency with respect to the number of trains, and depending on the level of the passenger demand. Furthermore, the level of the passenger comfort inside the trains can be taken as the result of a compromise between the passengers’ satisfaction, in one side, and the number of trains as well as the passenger capacity of trains, in terms of the economic criteria of the operator, in the other side.

This paper presents a generic simulation model to determine the equipment mix (quay, yard and intra-terminal transfer) for a Container Terminal Logistics Operations System (CTLOS). The simulation model for the CTLOS, a typical type of discrete event dynamic system (DEDS), consists of three sub-models: ship queue, loading-unloading operations and yard-gate operations. The simulation model is empirically applied to phase 1 of the Yangshan Deep Water Port in Shanghai. This study considers different scenarios in terms of container throughput levels, equipment utilization rates, and operational bottlenecks, and presents a sensitivity analysis to evaluate and choose reasonable equipment ratio ranges under different operational conditions.

The malfunction of the water distribution system (WDS) following severe earthquakes have significant impacts on the post-earthquake rescue. Moreover, the restoration priority of earthquake-induced pipeline damages plays an important role in improving the post-earthquake serviceability of WDS and the &ldquo, seismic resilience&rdquo, Thus, to enhance the seismic resilience of WDS, this study develops a dynamic cost-benefit method and introduces three existing methods to determine the restoration priority of pipeline damages based on a quantitative resilience evaluation framework. In this resilience evaluation framework, the restoration priority is firstly determined. Then the time-varying performance of post-earthquake WDS is modeled as a discrete event dynamic system. In this model, the system state changes after the reparation of pipeline damage, and the system performance is simulated by a hydraulic model to be consistent with the system state. In this study, this method is also tested and compared with other existing methods, and the results show that the system resilience corresponding to the restoration priority obtained by this method is close to that obtained by the global optimization method with a relative difference of less than 3%, whereas the calculation complexity is about 0.4% of the optimization model. It is concluded that this proposed method is valid.

Financial institutions are interconnected by holding debt claims against each other. A default bank may cause its creditors to default, and the risk may be further propagated to up-stream institutes (risk contagion). Such interconnection is a key contributing factor to the past worldwide financial crisis. We show that a good mechanism of default liquidation may improve the total wealth of the financial system and therefore may curb the risk contagion. We formulate this problem as a nonlinear optimization problem with constraints and propose an optimal liquidation policy to minimize the system’s loss. We show that the problem resembles a Markov decision problem (MDP) and therefore we can apply the direct-comparison based optimization approach to solve this problem. Higher order directional derivatives and some optimality properties are obtained. Furthermore, we derive an iterative algorithm which combines both the policy iteration and the gradient based approach to find a local optimal policy, and under some conditions, a global optimal policy. Our work provides a new direction in curbing the risk contagion in financial networks; and it illustrates the advantages of the direct-comparison based approach, originated in the field of discrete event dynamic system, in nonlinear optimization problems.

Electrical vehicles and renewable energy are becoming increasingly important for the green energy target and environment-friendly society. So it demands advanced infrastructures of charging stations with renewable energy, which can provide efficient charging service. This paper studies the admission control problem of electric vehicle charging with renewable energy at distributed charging station. First, to alleviate the ”curse of dimension” problem, the framework of the eventbased optimization is applied to formulate the AC problem. Second, the EV user’s satisfaction is considered when designing the reward function. By introducing the concept of the risk event, we maximize the system performance while guaranteeing the quality of service constraint. Then Lagrangian method and policy-gradient iteration method are used to get the optimal policy. Simulation experiments show the effectiveness of the proposed method.

Models with events that have small non-zero duration are considered. The goal of this paper is to propose an event simulation paradigm, different from the traditional crisp discrete event simulatio...

In this paper, we investigate the partially observed supervisor synthesis problem in the framework of fuzzy discrete-event systems (DESs). The goal is to synthesize a fuzzy supervisor such that the behavior of the closed-loop system is within a given fuzzy language. A new approach for solving this problem is proposed based on the idea of belief evolution. Specifically, we propose an algorithm that can be implemented in an online manner. We show that the proposed algorithm is both sound and complete, i.e., it effectively solves the supervisor synthesis problem. To the best of our knowledge, this is the first algorithm with such a property for fuzzy DESs, as previous works on this topic mostly focus on the supervisor existence condition rather than the supervisor synthesis problem.

A modular discrete event system is modeled by a set of module automata running synchronously. In this paper, we investigate the complexity of the verification problems of three different properties, diagnosability, predictability, and detectability, for partially-observed modular discrete event systems. We first show that deciding diagnosability for modular discrete event systems is PSPACE-complete when the number of modules is unbounded. Then we show that deciding predictability and detectability for modular discrete event systems are both PSPACE-hard problems. These results reveal that in order to verify these properties for the complete system, exploring the state space of the monolithic model may be unavoidable, in the worst case.

Recently, we have introduced bi-fuzzy discrete event systems (BFDESs) and established their supervisory control theory under full observations and partial observations, respectively. Compared with the models of discrete event systems and fuzzy discrete event systems, BFDESs are more satisfactory models to characterize some high-uncertainty systems. In this paper, we study the fault diagnosis problems of BFDESs. First, the framework of state-based decentralized diagnosis is introduced. Then, the notion of state-based codiagnosability is defined and a necessary and sufficient condition for state-based codiagnosability is provided. In particular, a polynomial-time algorithm for state-based codiagnosability verification and an online decentralized diagnosis method are presented. In addition, a compact state-based decentralized diagnosis framework is introduced, and the notion of state-based jointly diagnosability and its verification algorithm are proposed. Finally, the implication relationships between the two diagnosabilities are investigated.

Financial institutions are interconnected by holding debt claims against each other. The interconnection is a key contributing factor to the past worldwide financial crisis. A default bank may cause its creditors to default, and the risk may be further propagated to up-stream institutes. We study how the mechanism of default liquidation affects the total wealth of the financial system and curbs the risk contagion. We formulate this problem as a nonlinear optimization problem with equilibrium constraints and propose an optimal liquidation policy to minimize the system’s loss without changing the partition of default and non-default banks. We show that the optimization problem resembles a Markov decision problem (MDP) and therefore we can apply the direct-comparison based optimization approach to solve this problem. We derive an iteration algorithm which combines both the policy iteration and the gradient based approach. Our work provides a new direction in curbing the risk contagion in financial networks; and it illustrates the advantages of the direct-comparison based approach, which originated in the field of discrete event dynamic system, in nonlinear optimization problems.

The history of Perturbation Analysis (PA) is intimately related to that of Discrete Event Dynamic Systems (DEDS), starting with a solution of a long-standing problem in the late 1970s and continuing today with the control and optimization of Hybrid Systems and the emergence of event-driven control methods. We review the origins of the PA theory and how it became part of a broader framework for modelling, control and optimization of DEDS. We then discuss the theoretical underpinnings of Infinitesimal Perturbation Analysis (IPA) as a data-driven stochastic gradient estimation method and how it has been applied over the past few decades. We explain how IPA offers a basis for general-purpose stochastic optimization of Markovian systems through the notion of the performance potential and how it has evolved beyond DEDS and now provides a framework for control and optimization of Hybrid Systems and, more generally, event-driven methodologies.

This paper presents the design of a novel adaptive event-triggered control method based on the heuristic dynamic programming (HDP) technique for nonlinear discrete-time systems with unknown system dynamics. In the proposed method, the control law is only updated when the event-triggered condition is violated. Compared with the periodic updates in the traditional adaptive dynamic programming (ADP) control, the proposed method can reduce the computation and transmission cost. An actor-critic framework is used to learn the optimal event-triggered control law and the value function. Furthermore, a model network is designed to estimate the system state vector. The main contribution of this paper is to design a new trigger threshold for discrete-time systems. A detailed Lyapunov stability analysis shows that our proposed event-triggered controller can asymptotically stabilize the discrete-time systems. Finally, we test our method on two different discrete-time systems, and the simulation results are included.

This paper proposes a complementary discrete state space formulation of hybrid automata model in order to consider, in a systematical and visual way, internal and external influences to a hybrid system. The complemented model considers a system with hybrid states, discrete and continuous inputs, discrete and continuous outputs and internal events, all in a discrete time approximation. When various influences affect its dynamics, explosiveness and complexity of hybrid automata model is simplified using a discrete state space formulation. In order to formulate control strategies in a straightforward manner, this formulation decomposes all possible discrete influences considering the different available degrees of freedom. Using a nonlinear hybrid tank system, a modeling and hybrid control strategy formulation is shown. Systematical modeling, hybrid behavior, and control effectiveness are depicted by simulation results.

This paper treats the problem of existence of a controller for networked-timed discrete-event systems. The results are new and useful for any networked discrete-event system for which it is important that time be explicitly considered in the model. We assume that a controller (supervisor) communicates with the system to be controlled via a shared communication network. Delays and losses in communication systems and their impacts on control are investigated. Under the assumption that the delays and losses are bounded, we derive a necessary and sufficient condition for the existence of a controller. The condition is expressed as network T-controllability and network T-observability, which are defined in this paper. We apply the results to power distribution network management, and illustrate the application using a 33-node (bus) test system, where the objective is to ensure that the total substation transformer power stays within prespecified safety limits.

This technical note introduces the notion of switched Discrete Event Systems (s-DES) and investigates its representational and computational potential in (i) the description and the analysis of the underlying DES behavior, (ii) the specification of the posed control requirements, and (iii) the eventual computation of the necessary control function. More specifically, it is shown that the potential decomposition of the overall DES behavior in a well defined set of “operational modes” enables the specification of control requirements and the synthesis of the corresponding control laws in a modular and distributed manner that takes full advantage of the aforementioned decomposition. The work is motivated by the need to cope with DES operating under a number of failing modes that result from non-catastrophic failures and repairs, and also DES that might evolve their operation through a number of “stages.” Furthermore, the technical developments of the technical note and their representational and computational power are further highlighted by an application example that is drawn from the area of robot pursuit on time-varying graphs; however, due to space considerations, this example is provided in an electronic supplement to the technical note.