•Proposes a model of multiple automated guided vehicles.•Proposes an algorithm providing their optimal work sequence minimizing a given cost.•Tackles the robustness issue pertaining their nominal and ...real performance.•Proposes a fault-tolerant control strategy for multiple automated guided vehicles.•The proposed algorithm can perform on-line with low computational burden.
An advanced control of manufacturing and transportation systems forms a prominent research field with powerful algorithms developed in the last decades. Challenges still arise, if several automated guide vehicles (AGV) have to be coordinated. This paper focuses on the modelling and fault-tolerant control of multiple AGVs. The considered application concerns a highly flexible AGV transportation system delivering product items to transfer stations at a high-storage warehouse in a manufacturing system. The research contribution concerns the development of a mathematical description of a set of multiple AGVs along with an algorithm that can generate an optimum sequence of item outlet delivery times. The proposed solution addresses both synchronization and concurrency issues, which are inevitable in this kind of multiple-vehicle systems. Apart from these issues, modelling inaccuracy is also addressed using interval analysis coupled with max-plus algebra. Subsequently, fault diagnosis and fault-tolerant control are also investigated and addressed in the proposed approach. This leads to a fault-tolerant control framework, which is based on a fusion of the predictive control and interval max-plus algebra. The distinct quality of the proposed approach is that the optimization can be carried out in a reliable way and that certain faults and modeling uncertainties can be tolerated. The paper concludes with illustrative examples, which show the performance of the proposed approach using both fault-free and faulty scenarios.
Support Vector Machines (SVMs) are one of the most popular supervised learning models to classify using a hyperplane in an Euclidean space. Similar to SVMs, tropical SVMs classify data points using a ...tropical hyperplane under the tropical metric with the max-plus algebra. In this paper, first we show generalization error bounds of tropical SVMs over the tropical projective torus. While the generalization error bounds attained via Vapnik–Chervonenkis (VC) dimensions in a distribution-free manner still depend on the dimension, we also show numerically and theoretically by extreme value statistics that the tropical SVMs for classifying data points from two Gaussian distributions as well as empirical data sets of different neuron types are fairly robust against the curse of dimensionality. Extreme value statistics also underlie the anomalous scaling behaviors of the tropical distance between random vectors with additional noise dimensions. Finally, we define tropical SVMs over a function space with the tropical metric.
•We obtain generalization error bounds of tropical SVMs via the VC dimensions.•We demonstrate that the tropical SVMs are robust against the curse of dimensionality.•We define tropical SVMs over a function space to enable the classification of curves.
We study six types of solutions (weak, strong, tolerance, control, Left-localized, and Right-localized solutions) to a two-sided interval system of max-plus linear equations with the same vector of ...variables on both sides of the equations and obtain their corresponding solvability conditions. These conditions are in the form of two-sided systems of max-plus linear inequalities which can be derived as a union of a number of interval inclusion linear systems. Therefore, we could work on the interval inclusion linear systems, instead of directly solving these six types of solutions themselves. An optimization problem with the two-sided interval system of max-plus linear constraints may be solved using the convexity of each solution set of the interval inclusion linear systems.
This paper proposes an analytical delay propagation model for single railway lines based on the max‐plus algebra theory. The scheduling measures taken by dispatchers, including re‐timing and ...re‐ordering, will be incorporated into our delay propagation model using a matrix transformation method. An analysis of delay propagation under some typical emergencies such as segment blockages and train speed limitation is performed. Numerical simulations show that the proposed train delay propagation model can predict emergency‐induced train delays under different scheduling strategies, thus may give a guidance to improve the traffic management. In the high‐speed railway train system, the scheduling measures taken by dispatchers, such as re‐timing and re‐ordering, can be formulated as a delay propagation model using a matrix transformation method.
This paper presents a discrete-event model for a mass-transit line operated with a two-service skip-stop policy while allowing for train dwell times to vary according to passengers’ demand volumes. ...The model is formulated by two mathematical constraints on the train’s travel and safe separation times that govern the train dynamics on the line. In addition, the model takes into account trains’ dwell times, which are affected by both the services offered by the operator and passenger demand. The model is written in the max-plus algebra, a mathematical framework that allows us to derive interesting analytical results, including the fundamental diagram of the line, which describes the relationship between the average train time headway (or frequency), the number of trains running on the line and the passenger travel demand. The paper also derives indicators that are capable of quantifying and, thus, assessing the impact of a skip-stop policy on passengers’ travel. Finally, the paper compares two different passenger demand profiles. Results show that long-distance passengers mainly benefit from skip-stop policies, while short-distance travelers may experience an increase in their travel time. For long-distance passengers, the increase in the waiting time is counterbalanced by the decrease in the in-vehicle time, leading to an overall decrease in total passenger travel time.
•We develop a discrete-event model for a two-service skip-stop policy.•Our model is demand-dependent, and train dwell times are calculated as a function of the skip-stop services and passenger demand.•We apply our model to a line of the Paris network.•We derive the the average train frequency of the line (fundamental diagram).•We compare two demand profiles and evaluate when the skip-stop policy is beneficial.
Artificial neural networks (ANNs) is an exponentially growing field, mainly because of its wide range of applications to everyday life such as pattern recognition or time series forecasting. In ...particular, reservoir computing (RC) arises as an optimal computational framework suited for temporal/sequential data analysis. The direct on-silicon implementation of RCs may help to minimize power and maximize processing speed, that is especially relevant in edge intelligence applications where energy storage is considerably restricted. Nevertheless, most of the RC hardware solutions present in the literature perform the training process off-chip at the server level, thus increasing processing time and overall power dissipation. Some studies integrate both learning and inference on the same chip, although these works are normally oriented to implement unsupervised learning (UL) with a lower expected accuracy than supervised learning (SL), or propose iterative solutions (with a subsequent higher power consumption). Therefore, the integration of RC systems including both inference and a fast noniterative SL method is still an incipient field. In this article, we propose a noniterative SL methodology for RC systems that can be implemented on hardware either sequentially or fully parallel. The proposal presents a considerable advantage in terms of energy efficiency (EE) and processing speed if compared to traditional off-chip methods. In order to prove the validity of the model, a cyclic echo state NN with on-chip learning capabilities for time series prediction has been implemented and tested in a field-programmable gate array (FPGA). Also, a low-cost audio processing method is proposed that may be used to optimize the sound preprocessing steps.
Finite quasi semimetrics on n can be thought of as nonnegative valuations on the edges of a complete directed graph on n vertices satisfying all possible triangle inequalities. They comprise a ...polyhedral cone whose symmetry groups were studied for small n by Deza, Dutour and Panteleeva. We show that the symmetry and combinatorial symmetry groups are as they conjectured.
Integral quasi semimetrics have a special place in the theory of tiled orders, being known as exponent matrices, and can be viewed as monoids under componentwise maximum; we provide a novel derivation of the automorphism group of that monoid. Some of these results follow from more general consideration of polyhedral cones that are closed under componentwise maximum.
This paper discusses topics in the symmetrized max-plus algebra. In this study, it will be shown the existence of eigenvalue decomposition of a symmetric matrix over symmetrized max-plus algebra. ...Eigenvalue decomposition is shown by using a function that corresponds to the symmetrized max-plus algebra with conventional algebra. The result obtained is the existence of eigenvalue decomposition of a symmetric matrix over symmetrized max-plus algebra and its application to determine eigenvalues and eigenvectors.
Recently, in a work that grew out of their exploration of interlacing polynomials, Marcus, Spielman and Srivastava 21 and Marcus 20 studied certain combinatorial polynomial convolutions. These ...convolutions preserve real-rootedness and capture expectations of characteristic polynomials of unitarily invariant random matrices, thus providing a link to free probability. We explore analogues of these types of convolutions in the setting of max-plus algebra. In this setting the max-permanent replaces the determinant, the maximum is the analogue of the expected value and real-rootedness is replaced by full canonical form. Our results resemble those of Marcus et al., however, in contrast to the classical setting we obtain an exact and simple description of all roots of the convolution of p(x) and q(x) in terms of the roots of p(x) and q(x).
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