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On the optimal input allocation of discrete-event systems with dynamic input sequence *
... This is a significant improvement from the state-of-the-art works where usually optimality is only shown through a numerical/simulation experiment. With this mathematical approach, the algorithm can be further applied to the similar relevant systems, as has been shown in our previous work in [4]. ...
... Communication which happens among the modeled terminal's entities uses negotiation concept of the monotonic concession protocol from [2] and [5]. To overcome gaps of negotiation models from Wooldridge those two papers, forward-backward linkage is considered in this paper, which framework can be found in [4]. The complete negotiation protocol is as follow: ...
... To show that the protocol will lead to stable (converge), condition, [2], [5], and [10] has proposed that H in the Definition 1 has to be symmetric positive definite. To make such mathematical proof, we use the framework from our previous work in [4]. ...
... This approach is chosen because it predicts the output of the model and determines the optimal control trajectory that minimizes the cost function. MPC can produce optimal global solutions to the problem of optimizing the input allocation of the DES model with dynamic input sequences [7]. This model will search for all possible solutions of a particular planning horizon. ...
Makalah ini membahas model penjadwalan dinamis dari operasi tangki bahan bakar umum dan pompa. Modelnya bersifat dinamis karena waktu kedatangan kapal diperbolehkan bervariasi. Tujuan dari studi ini adalah untuk menentukan alokasi/penjadwalan dermaga yang optimal dan rekomendasi kebijakan yang meminimalkan total waktu tunggu kapal, rasio hunian dermaga, dan biaya sewa kapal. Pemodelan Discrete-event Systems (DES) dipilih karena aperiodisitas dalam waktu kedatangan kapal dan waktu operasi asinkron di antara posisi berlabuh yang berbeda. Dua model DES dikembangkan, yaitu: (1) masalah alokasi biaya berganda (MBAP) untuk dermaga suplai dan (2) masalah alokasi dermaga sederhana (SBAP) untuk dermaga konsinyasi. Selanjutnya, digunakan model predictive control (MPC) untuk mengoptimalkan model DES, dan juga disediakan analisis matematis dari algoritma yang diusulkan. Contoh numerik memeriksa dua kasus (pasang surut dan non-pasang surut) di masing-masing model disajikan untuk menggambarkan solusi optimal. Masalah yang dihadapi adalah alokasi tambatan saat ini tidak bekerja secara efisien, yang ditunjukkan dengan rata-rata waktu tunggu kapal di dermaga pemasok (dermaga 1 dan 2) yang di atas standar (14 jam), sedangkan dermaga konsinyasi (dermaga 3) berada jauh di bawah standar.
Opacity is an important system property that is particularly relevant in the context of system security and privacy. A system is considered opaque if the predefined secret behavior of the system is not leaked to an external intruder. In this work, the opacity property is studied in the framework of labeled Petri nets (LPNs). The secret in an LPN system is characterized by a subset of reachable markings. Firstly, an opacity basis reachability graph (OBRG) containing opacity information of the system is developed to denote a system’s reachability set without computing all reachable states. Then the observer of the OBRG is computed, based on which a necessary and sufficient condition is derived to verify the opacity of the LPN system. Finally, given an LPN that does not satisfy the opacity, a maximally permissive supervisor is introduced to guarantee that the controlled system is opaque.
An asynchronous fault diagnosis problem consists in determining the occurrence of faults in a plant under the condition that a diagnosis agent, i.e., a diagnoser, is activated asynchronously with the plant. Asynchronous diagnosability is a property implying that any fault in a plant can be detected by observing a finite number of observations in the case of asynchronous activation of the diagnoser and the plant. This article studies the problem of asynchronous diagnosability enforcement in discrete event systems based on supervisory control theory, i.e., to develop a supervisor for an asynchronously undiagnosable plant such that the asynchronous diagnosability of the closed-loop system is guaranteed. Firstly, the classical definition of asynchronous diagnosability is generalized to nonlive systems since a supervisor may introduce deadlocks in a plant even if it is originally live. We then propose a structure called an
asynchronous-quiescent diagnoser
that is used for both online asynchronous diagnosis and asynchronous diagnosability determination. Finally, for a plant that is asynchronously undiagnosable, we develop a supervisor to enforce the asynchronous diagnosability based on its asynchronous-quiescent diagnoser.
We present a dynamical modeling of integrated (end-to-end) container terminal operations using finite state machine (FSM) framework where each state machine is represented by a discrete-event system (DES) formulation. The hybrid model incorporates the operations of quay cranes (QC), internal trucks (IT), and yard cranes (YC) and also the selection of storage positions in container yard (CY) and vessel bays. The QC and YC are connected by the IT in our models. As opposed to the commonly adapted modeling in container terminal operations, in which the entire information/inputs to the systems are known for a defined planning horizon, in this research we use real-time trucks, crane, and container storage operations information, which are always updated as the time evolves. The dynamical model shows that the predicted state variables closely follow the actual field data from a container terminal in Tanjung Priuk, Jakarta, Indonesia. Subsequently, using the integrated container terminal hybrid model, we proposed a model predictive algorithm (MPA) to obtain the near-optimal solution of the integrated terminal operations problem, namely the simultaneous allocation and scheduling of QC, IT, and YC, as well as selecting the storage location for the inbound and outbound containers in the CY and vessel. The numerical experiment based on the extensive Monte Carlo simulation and real dataset show that the MPA outperforms by 3-6% both of the policies currently implemented by the terminal operator and the state-of-the-art method from the current literature.
We discuss the possibility of reaching consensus in finite time using only
linear iterations, with the additional restrictions that the update matrices
must be stochastic with positive diagonals and consistent with a given graph
structure. We show that finite-time average consensus can always be achieved
for connected undirected graphs. For directed graphs, we show some necessary
conditions for finite-time consensus, including strong connectivity and the
presence of a simple cycle of even length.
This paper establishes global convergence for a class of adaptive control algorithms applied to discrete time multi-input multi-output deterministic linear systems. It is shown that the algorithms will ensure that the system inputs and outputs remain bounded for all time and that the output tracking error converges to zero.
We discuss an old distributed algorithm for reaching consensus that has received a fair amount of recent attention. In this algorithm, a number of agents exchange their values asynchronously and form weighted averages with (possibly outdated) values possessed by their neighbors. We overview existing convergence results, and establish some new ones, for the case of unbounded intercommunication intervals.
The problem of the optimal control of systems accurately
represented with a logical discrete-event system (DES) model is
formulated and solved for the deterministic case. The given DES model P
is thought of as characterizing the valid dynamical behavior of the
physical plant. Another DES model A represents design objectives which
specify the allowable DES behavior which is `contained in' the valid
behavior. Assuming that the allowable behavior can be attained, a
controller can be constructed which will select a sequence of inputs
that results in allowable plant behavior. The authors consider the case
where there is another part of the design objectives which indicates
that not only should the controller choose the plant inputs so that the
plant behavior is allowable, but it should also, in some sense, be
optimal. It is within this context that they formulate an optimal
controller synthesis problem, i.e. how to construct a controller to
achieve optimal allowable DES behavior. Their solution to this problem
utilizes results from the theory of heuristic search to help overcome
problems with computational complexity often encountered with logical
DES models
Introduction to Discrete Event Systems is a comprehensive introduction to the field of discrete event systems, offering a breadth of coverage that makes the material accessible to readers of varied backgrounds. The book emphasizes a unified modeling framework that transcends specific application areas, linking the following topics in a coherent manner: language and automata theory, supervisory control, Petri net theory, Markov chains and queueing theory, discrete-event simulation, and concurrent estimation techniques. Distinctive features of the second edition include: •more detailed treatment of equivalence of automata, event diagnosis, and decentralized event diagnosis •expanded treatment of centralized and decentralized control of partially-observed systems •new sections on timed automata with guards (in the Alur-Dill formalism) and hybrid automata •an introduction to hybrid systems •updated coverage of discrete event simulation, including new software tools available •recent developments in sensitivity analysis for discrete event systems as well as hybrid systems This textbook is valuable to advanced-level students and researchers in a variety of disciplines where the study of discrete event systems is relevant: control, communications, computer engineering, computer science, manufacturing engineering, operations research, and industrial engineering. © 2008 Springer Science+Business Media, LLC. All rights reserved.
We consider dynamical systems which are driven by external
“events” that occur asynchronously. It is assumed that the
event rates are fixed, or at least they can be bounded on any time
period of length T. Such systems are becoming increasingly important in
control due to the very rapid advances in digital systems, communication
systems, and data networks. Examples of asynchronous systems include,
control systems in which signals are transmitted over an asynchronous
network, parallelized numerical algorithms, and queuing networks. We
present a Lyapunov-based theory for asynchronous dynamical systems and
show how Lyapunov functions and controllers can be constructed for such
systems by solving linear matrix inequality (LMI) and bilinear matrix
inequality (BMI) problems. Examples are also presented that demonstrate
the effectiveness of the approach in analyzing practical systems
This paper establishes global convergence for a class of adaptive control algorithms applied to discrete-time multiinput multioutput deterministic linear systems. It is shown that the algorithms will ensure that the systems inptus and outputs remain bounded for all time and that the output tracking error converges to zero.
A discrete event system (DES) is a dynamic system that evolves in
accordance with the abrupt occurrence, at possibly unknown irregular
intervals, of physical events. Such systems arise in a variety of
contexts ranging from computer operating systems to the control of
complex multimode processes. A control theory for the logical aspects of
such DESs is surveyed. The focus is on the qualitative aspects of
control, but computation and the related issue of computational
complexity are also considered. Automata and formal language models for
DESs are surveyed
In this paper, we study the problem of integrated berth and quay crane allocation (I-BCAP) in general seaport container terminals and propose the model predictive allocation (MPA) algorithm and preconditioning methods for solving the I-BCAP. First, we propose a dynamical modeling framework based on discrete-event systems (DESs), which describes the operation of a berthing process with multiple discrete berthing positions and multiple quay cranes. Second, based on the discrete-event model, we propose the MPA algorithm for solving the I-BCAP using the model predictive control (MPC) principle with a rolling event horizon. The validation and performance evaluation of the proposed modeling framework and allocation method are done using: 1) extensive Monte Carlo simulations with realistically generated datasets; 2) real dataset from a container terminal in Tanjung Priuk port, located in Jakarta, Indonesia; and 3) real life field experiment at the aforementioned container terminal. The numerical simulation results show that our proposed MPA algorithm can improve the efficiency of the process where the total handling and waiting cost is reduced by approximately 6%-9% in comparison with the commonly adapted method of first-come first-served (FCFS) (for the berthing process) combined with the density-based quay cranes allocation (DBQA) strategy. Moreover, the proposed method outperforms the state-of-the-art hybrid particle swarm optimization (HPSO)-based and genetic algorithm (GA)-based method proposed in the recent literature. The real life field experiment shows an improvement of about 6% in comparison with the existing allocation method used in the terminal.
We study in this paper a dynamic berth and quay cranes allocation strategy in general seaport container terminals. We develop a dynamical model that describes the operation of berthing process with multiple discrete berthing positions and multiple quay cranes. Based on the proposed model, we develop a dynamic allocation strategy using the model predictive control (MPC) paradigm. The proposed strategy is evaluated using real data from a container terminal in Indonesia. The simulation results show that the MPC-based allocation strategy can improve the efficiency of the process where the total handling and waiting cost is reduced by approximately 20% in comparison to the commonly adapted method of first-come first-served (FCFS) (for the berthing process) combined with the density-based quay cranes allocation strategy.
Technical report bds:01-01 MPC for discrete-event systems with soft and hard synchronisation constraints * B. De Schutter and T.J.J. van den Boom If you want to cite this report, please use the following reference instead: B. De Schutter and T.J.J. van den Boom, "MPC for discrete-event systems with soft and hard synchronisation constraints, Abstract Discrete-event systems with only synchronisation and no concurrency, also known as timed event graphs or (max,+)-linear systems, have been studied by several authors. The syn-chronisation constraints that arise in these discrete-event systems are hard, i.e., they cannot be broken under any circumstance. In this paper we consider a more extended class of discrete-event systems with both hard and soft synchronisation constraints, i.e., if necessary, some synchronisation conditions may be broken, but then a penalty is in-curred. We show how the model predictive control (MPC) framework, which is a very popular controller design method in the process industry, can be extended to this class of discrete-event systems. In general, the MPC control design problem for discrete-event systems with soft and hard synchronisation constraints leads to a nonlinear non-convex optimisation problem. We show that the optimal MPC strategy can also be computed using an extended linear complementarity problem.
Inventory control for the management of multi-item multi-echelon distribution chains is addressed in a two-level hierarchical framework motivated by strategic and tactical points of view. Toward this end, a discrete-time dynamic model is presented together with various types of constraints to describe a generic distribution chain in detail. As to the strategic level, a worst-case approach is proposed to set up a stock replenishment policy by using the uncertain information available on long-term predictions of customers' demands. The solution of the resulting min-max problem is obtained by using a branch-and-bound algorithm to select policy parameters such as safety stocks and delivery cycle times of goods. The online decisions on the transportation of goods are made at the tactical level instead. In order to accomplish such a task, an approach based on model predictive control is proposed to exploit recent, more reliable, short-term predictions of the demands. Simulation results are presented to show the effectiveness and potential of the proposed methodology.
Scheduling trains in a railway network is a fundamental operational problem in the railway industry. A local feedback-based travel advance strategy is developed using a discrete event model of train advances along lines of the railway. This approach can quickly handle perturbations in the schedule and is shown to perform well on three time-performance criteria while maintaining the local nature of the strategy. If the local strategy leads to a deadlock, a capacity check algorithm is applied that prevents deadlock, but requires additional nonlocal information. Extensions to the strategy are developed for networks with double-track sections and with variable train characteristics and priorities.
A discrete-event system is a system whose behavior can be described by means of a set of time-consuming activities, performed according to a prescribed ordering. Events correspond to starting or ending some activity. An analogy between linear systems and a class of discrete-event systems is developed. Following this analogy, such discrete-event systems can be viewed as linear, in the sense of an appropriate algebra. The periodical behavior of closed discrete-event systems, i.e., involving a set of repeatedly performed activities, can be totally characterized by solving an eigenvalue and eigenvector equation in this algebra. This problem is numerically solved by an efficient algorithm which basically consists of finding the shortest paths from one node to all other nodes in a graph. The potentiality of this approach for the performance evaluation of flexible manufacturing systems is emphasized; the case of a flowshop-like production process is analyzed in detail.
Discrete-time multivariable adaptive control
- V I Norkin
- G C Pflug
- A Ruszczyński
Discrete-time multivariable adaptive control
- norkin