Volumen 31 (2021): Heft 3 (September 2021)

Linear systems described by fractional differential equations (FDEs) with variable coefficients involving Riemann–Liouville and Caputo derivatives are examined in the paper. For these systems, a solution of the initial-value problem is derived in terms of the generalized Peano–Baker series and a time-optimal control problem is formulated. The optimal control problem is treated from the convex-analytical viewpoint. Necessary and sufficient conditions for time-optimal control similar to that of Pontryagin’s maximum principle are obtained. Theoretical results are supported by examples.

This paper proposes novel forecasting models for fractional-order chaotic oscillators, such as Duffing’s, Van der Pol’s, Tamaševičius’s and Chua’s, using feedforward neural networks. The models predict a change in the state values which bears a weighted relationship with the oscillator states. Such an arrangement is a suitable candidate model for out-of-sample forecasting of system states. The proposed neural network-assisted weighted model is applied to the above oscillators. The improved out-of-sample forecasting results of the proposed modeling strategy compared with the literature are comprehensively analyzed. The proposed models corresponding to the optimal weights result in the least mean square error (MSE) for all the system states. Further, the MSE for the proposed model is less in most of the oscillators compared with the one reported in the literature. The proposed prediction model’s out-of-sample forecasting plots show the best tracking ability to approximate future state values.

A wide variety of approaches for set-valued simulation, parameter identification, state estimation as well as reachability, observability and stability analysis for nonlinear discrete-time systems involve the propagation of ellipsoids via nonlinear functions. It is well known that the corresponding image sets usually possess a complex shape and may even be nonconvex despite the convexity of the input data. For that reason, domain splitting procedures are often employed which help to reduce the phenomenon of overestimation that can be traced back to the well-known dependency and wrapping effects of interval analysis. In this paper, we propose a simple, yet efficient scheme for simultaneously determining outer and inner ellipsoidal range enclosures of the solution for the evaluation of multi-dimensional functions if the input domains are themselves described by ellipsoids. The Hausdorff distance between the computed enclosure and the exact solution set reduces at least linearly when decreasing the size of the input domains. In addition to algebraic function evaluations, the proposed technique is—for the first time, to our knowledge—employed for quantifying worst-case errors when extended Kalman filter-like, linearization-based techniques are used for forecasting confidence ellipsoids in a stochastic setting.

Multiple criteria decision making (MCDM) problems in practice may simultaneously contain both redundant and incomplete information and are difficult to solve. This paper proposes a new decision-making approach based on soft set theory to solve MCDM problems with redundant and incomplete information. Firstly, we give an incomplete soft set a precise definition. After that, the binary relationships of objects in an incomplete soft set are analyzed and some operations on it are provided. Next, some definitions regarding the incomplete soft decision system are also given. Based on that, an algorithm to solve MCDM problems with redundant and incomplete information based on an incomplete soft set is presented and illustrated with a numerical example. The results show that our newly developed method can be directly used on the original redundant and incomplete data set. There is no need to transform an incomplete information system into a complete one, which may lead to bad decision-making due to information loss or some unreliable assumptions about the data generating mechanism. To demonstrate its practical applications, the proposed method is applied to a problem of regional food safety evaluation in Chongqing, China.

Fuzzy inference using the conjunctive approach is very popular in many practical applications. It is intuitive for engineers, simple to understand, and characterized by the lowest computational complexity. However, it leads to incorrect results in the cases when the relationship between a fact and a premise is undefined. This article analyses the problem thoroughly and provides several possible solutions. The drawbacks of uncertainty in the conjunctive approach are presented using fuzzy inference based on a fuzzy truth value, first introduced by Baldwin (1979c). The theory of inference is completed with a new truth function named 0-undefined for two-valued logic, which is further generalized into fuzzy logic as α-undefined. Eventually, the proposed modifications allow altering existing implementations of conjunctive fuzzy systems to interpret the undefined state, giving adequate results.

Neuro-fuzzy systems have proved their ability to elaborate intelligible nonlinear models for presented data. However, their bottleneck is the volume of data. They have to read all data in order to produce a model. We apply the granular approach and propose a granular neuro-fuzzy system for large volume data. In our method the data are read by parts and granulated. In the next stage the fuzzy model is produced not on data but on granules. In the paper we introduce a novel type of granules: a fuzzy rule. In our system granules are represented by both regular data items and fuzzy rules. Fuzzy rules are a kind of data summaries. The experiments show that the proposed granular neuro-fuzzy system can produce intelligible models even for large volume datasets. The system outperforms the sampling techniques for large volume datasets.

Reliability, efficiency and generalization are basic evaluation criteria for a vehicle automated driving system. This paper proposes an automated driving decision-making method based on the Wasserstein generative adversarial imitation learning–deep deterministic policy gradient (WGAIL–DDPG(λ)). Here the exact reward function is designed based on the requirements of a vehicle’s driving performance, i.e., safety, dynamic and ride comfort performance. The model’s training efficiency is improved through the proposed imitation learning strategy, and a gain regulator is designed to smooth the transition from imitation to reinforcement phases. Test results show that the proposed decision-making model can generate actions quickly and accurately according to the surrounding environment. Meanwhile, the imitation learning strategy based on expert experience and the gain regulator can effectively improve the training efficiency for the reinforcement learning model. Additionally, an extended test also proves its good adaptability for different driving conditions.

In the present paper, we concentrate on basic concepts connected with the theory of queueing systems with random volume customers and a sectorized unlimited memory buffer. In such systems, the arriving customers are additionally characterized by a non-negative random volume vector. The vector’s indications can be understood as the sizes of portions of information of a different type that are located in the sectors of memory space of the system during customers’ sojourn in it. This information does not change while a customer is present in the system. After service termination, information immediately leaves the buffer, releasing its resources. In analyzed models, the service time of a customer is assumed to be dependent on his volume vector characteristics, which has influence on the total volume vector distribution. We investigate three types of such queueing systems: the Erlang queueing system, the single-server queueing system with unlimited queue and the egalitarian processor sharing system. For these models, we obtain a joint distribution function of the total volume vector in terms of Laplace (or Laplace–Stieltjes) transforms and formulae for steady-state initial mixed moments of the analyzed random vector, in the case when the memory buffer is composed of two sectors. We also calculate these characteristics for some practical case in which the service time of a customer is proportional to the customer’s length (understood as the sum of the volume vector’s indications). Moreover, we present some numerical computations illustrating theoretical results.

A linear combination of Gaussian components is known as a Gaussian mixture model. It is widely used in data mining and pattern recognition. In this paper, we propose a method to estimate the parameters of the density function given by a Gaussian mixture model. Our proposal is based on the Gini index, a methodology to measure the inequality degree between two probability distributions, and consists in minimizing the Gini index between an empirical distribution for the data and a Gaussian mixture model. We will show several simulated examples and real data examples, observing some of the properties of the proposed method.

The shape-from-shading (SFS) technique uses the pattern of shading in images in order to obtain 3D view information. By virtue of their ease of implementation, linearization-based SFS algorithms are frequently used in the literature. In this study, Fourier coefficients of central differences obtained from gray-level images are employed, and two basic linearization-based algorithms are combined. By using the functionally generated surfaces and 3D reconstruction datasets, the hybrid algorithm is compared with linearization-based approaches. Five different evaluation metrics are applied on recovered depth maps and the corresponding gray-level images. The results on defective sample surfaces are also included to show the effect of the algorithm on surface reconstruction. The proposed method can prevent erroneous estimates on object boundaries and produce satisfactory 3D reconstruction results in a low number of iterations.

In recent years, there has been a highly competitive pressure on industrial production. To keep ahead of the competition, emerging technologies must be developed and incorporated. Automated visual inspection systems, which improve the overall mass production quantity and quality in lines, are crucial. The modifications of the inspection system involve excessive time and money costs. Therefore, these systems should be flexible in terms of fulfilling the changing requirements of high capacity production support. A coherent defect detection model as a primary application to be used in a real-time intelligent visual surface inspection system is proposed in this paper. The method utilizes a new approach consisting of nested autoencoders trained with defect-free and defect injected samples to detect defects. Making use of two nested autoencoders, the proposed approach shows great performance in eliminating defects. The first autoencoder is used essentially for feature extraction and reconstructing the image from these features. The second one is employed to identify and fix defects in the feature code. Defects are detected by thresholding the difference between decoded feature code outputs of the first and the second autoencoder. The proposed model has a 96% detection rate and a relatively good segmentation performance while being able to inspect fabrics driven at high speeds.

Tennis, as one of the most popular individual sports in the world, holds an important role in the betting world. There are two main categories of bets: pre-match betting, which is conducted before the match starts, and live betting, which allows placing bets during the sporting event. Betting systems rely on setting sports odds, something historically done by domain experts. Setting odds for live betting represents a challenge due to the need to follow events in real-time and react accordingly. In tennis, hierarchical models often stand out as a popular choice when trying to predict the outcome of the match. These models commonly leverage a recursive approach that aims to predict the winner or the final score starting at any point in the match. However, recursive expressions inherently contain computational complexity which hinders the efficiency of methods relying on them. This paper proposes a more resource-effective alternative in the form of a combinatorial approach based on a binomial distribution. The resulting accuracy of the combinatorial approach is identical to that of the recursive approach while being vastly more efficient when considering the execution time, making it a superior choice for live betting in this domain.