A pursuit–evasion problem with a constraint on the distance between objects

A trajectory pursuit–evasion problem is considered under constraints on the velocities of the counteracting objects and on the distance between them. This level of the model study brings the tactical capabilities of designed pilotless aircraft closer to the tactical capabilities of the existing piloted aircraft, which is an important problem of modern aircraft engineering. An approach that allows obtaining exact solutions in specific parametric situations is proposed.     

Improved stability of a class of switched neutral systems via Lyapunov–Krasovskii functionals and an average dwell-time scheme

This article is concerned with the stability analysis for a class of switched neutral systems with mixed time-varying delays. The upper bound of derivative of the discrete time-varying delay is not restricted to one. A delay-dependent criterion of exponential stability under switching signals with an average dwell time is developed by employing free weighting matrices. The criterion is given in the form of linear matrix inequality. A state decay estimation for the switched system is explicitly given by considering the individual rate of decay of state for each subsystem. Two simulation examples are given to illustrate the effectiveness of the proposed method.     

Method of predicting the position of the energy center of the image of a laser beam using a parallel–hierarchical network

This paper presents a prediction method using a parallel–hierarchical (PH) network and hyperbolic smoothing of empirical data. The average prediction error is 0.55% for the developed method and 1.62% for neural networks; therefore, this method is more efficient as applied to real-time systems than traditional neural networks due to the use of the PH network and hyperbolic smoothing in implementing the operation of predicting the positions of energy centers of laser beam spot images for optical communication systems.     

Distance localization of the moving object by applying the Karhunen–Loeve transform to ultra-wideband impulse signals

The possibility of applying the first principal component of the Karhunen–Loeve transform to localize reflections from a moving object on the time axis by sondaging with an ultra-wideband locator is studied.     

Automated process planning method to machine A B-Spline free-form feature on a mill–turn center

In this paper, we present a methodology for automating the process planning and NC code generation for a widely encountered class of free-form features that can be machined on a 3-axis mill–turn center. The free-form feature family that is considered is that of extruded protrusions whose cross-section is a closed, periodic B-Spline curve. In this methodology, for machining a part with B-Spline protrusion located at the free end, the part is first rough turned to the maximum profile diameter of the B-Spline, followed by rough profile cutting and finish profiling with axially mounted end mill tools. The identification and sequencing of machining volumes is completely automated, as is the generation of actual NC code. The approach supports both convex and non-convex profiles. In the case of non-convex profiles, the process planning algorithm ensures that there is no gouging of the work piece by the tool. The algorithm also identifies when sections of the tool path lie outside the work piece and utilizes rapid traverses in these regions to reduce cutting time. This methodology presents an integrated turn–mill process planning where by making the process fully automated from design with no user intervention making the overall process planning efficient. The algorithm was tested on several examples and test parts using the unmodified NC code obtained from the implementation were run on a Moriseiki mill–turn center. The parts that were produced met the dimensional specifications of the desired part.     

The key theorem and the bounds on the rate of uniform convergence of learning theory on Sugeno measure space

In the 1970s, Vapnik[1―3] proposed the Statistical Learning Theory (SLT), which deals mainly with the statistical learning principles when samples are limited. SLT is an im- portant development and supplement of traditional statistics, whose kernel idea …     

Counting critical formations on the circle: algebraic–geometric and Morse-theoretic bounds

In this work, we analyze the critical points of potential functions on the torus arising in decentralized formation shape control of multiagent systems on the unit circle. A rotation symmetry of the potential function allows to reduce the analysis to a reduced function on a lower-dimensional torus. We show that these reduced potential functions are generically Morse functions. Lower bounds on the number of critical points of the reduced potential are obtained by Morse-theoretic arguments. For trees, precise information on the number of critical points is obtained. We use algebraic–geometric methods to determine upper bounds on the number of critical points of the reduced potentials. Our approach is applicable both to standard formation control potential functions and potential functions arising from the Kuramoto model of coupled oscillators with identical natural frequencies.     

Location matters,especially for non-salient features–An eye-tracking study on the effects of web object placement on different types of websites

Users have clear expectations of where web objects are located on a web page. Studies conducted with manipulated, fictitious websites showed that web objects placed according to user expectations are found faster and remembered more easily. Whether this is also true for existing websites has not yet been examined. The present study investigates the relation between location typicality and efficiency in finding target web objects in online shops, online newspapers, and company web pages. Forty participants attended a within-subject eye-tracking experiment. Typical web object placement led to fewer fixations and participants found target web objects faster. However, some web objects were less sensitive to location typicality, if they were more visually salient and conformed to user expectations in appearance. Placing web objects at expected locations and designing their appearance according to user expectations facilitates orientation, which is beneficial for first impressions and the overall user experience of websites.     

An HPC hybrid parallel approach to the experimental analysis of Fermat’s theorem extension to arbitrary dimensions on heterogeneous computer systems

The Journal of Supercomputing - In this work, we consider the empirical, computational, study of the generalized Fermat’s last theorem conjecture recently proposed using Minkowski norms...     

A Rejoinder to Notes on a ‘Constructive Proof of the Existence of a Collateral Equilibrium’

This rejoinder contains a few remarks on my paper published in this journal with the title ‘A Constructive Proof of the Existence of Collateral Equilibrium for a Two-Period Exchange Economy Based on a Smooth Interior-Point Path’ and Ragupathy and Velupillai’s notes on a ‘Constructive Proof of the Existence of Collateral Equilibrium’ published recently in the same journal.     

Evasion of a moving object from detection by a system of observers: Sensor–maneuvering search means

Consideration was given to planning the optimal evasion trajectory of a moving object from the system of observers consisting of a sensor and initial and terminal points of the route. An optimization criterion was proposed. The optimal trajectory and the speed mode of the moving object were determined for sector and ring—the two zones of search for the maneuvering search means.     

Iterative solution of a class of linear equations with application to reconstruction of three-dimensional object arrays†

An iterative algorithm baaed on probabilistic estimation is described for obtaining the minimum-norm solution of a very large, consistent, linear system of equations AX = g where A is an (m × n) matrix with non-negative elements, x and g are respectively (n × 1) and (m × 1) vectors with positive components.

This algorithm will find application in the reconstruction of three-dimensional object arrays from projections and in several other areas.     

Analysis of a Multiobjective Evolutionary Algorithm on the 0–1 knapsack problem

Multiobjective Evolutionary Algorithms (MOEAs) are increasingly being used for effectively solving many real-world problems, and many empirical results are available. However, theoretical analysis is limited to a few simple toy functions. In this work, we select the well-known knapsack problem for the analysis. The multiobjective knapsack problem in its general form is NP-complete. Moreover, the size of the set of Pareto-optimal solutions can grow exponentially with the number of items in the knapsack. Thus, we formalize a (1+ε)$(1+\epsilon )$-approximate set of the knapsack problem and attempt to present a rigorous running time analysis of a MOEA to obtain the formalized set. The algorithm used in the paper is based on a restricted mating pool with a separate archive to store the remaining population; we call the algorithm a Restricted Evolutionary Multiobjective Optimizer (REMO). We also analyze the running time of REMO on a special bi-objective linear function, known as LOTZ (Leading Ones : Trailing Zeros), whose Pareto set is shown to be a subset of the knapsack. An extension of the analysis to the Simple Evolutionary Multiobjective Optimizer (SEMO) is also presented. A strategy based on partitioning of the decision space into fitness layers is used for the analysis.     

Nonlinear observer of the thermal loads applied to the helium bath of a cryogenic Joule–Thompson cycle

In this paper, a nonlinear observer of the thermal loads applied to the helium bath of a cryogenic refrigerator is proposed. The thermal loads represent a time-varying thermal disturbance expected to take place in future tokamaks refrigerators such as those used in the cooling systems for the International Thermonuclear Experimental Reactor (ITER) or the Japan Torus-60 Super Advanced (JT-60SA). The proposed observer can serve as a monitoring tool for cryogenic operators and/or in observer-based advanced control strategies. The observer is based on a part of the nonlinear model of the refrigerator. The paper details how the physical model of the Joule–Thompson cycle is obtained and the structure of the observer and validates its performance using experimental data.     

Two-Grid Mixed Finite-Element Approximations to the Navier–Stokes Equations Based on a Newton-Type Step

A two-grid scheme to approximate the evolutionary Navier–Stokes equations is introduced and analyzed. A standard mixed finite element approximation is first obtained over a coarse mesh of size H at any positive time \(T>0\). Then, the approximation is postprocessed by means of solving a steady problem based on one step of a Newton iteration over a finer mesh of size \(h<H\). The method increases the rate of convergence of the standard Galerkin method in one unit in terms of H and equals the rate of convergence of the standard Galerkin method over the fine mesh h. However, the computational cost is essentially the cost of approaching the Navier–Stokes equations with the plain Galerkin method over the coarse mesh of size H since the cost of solving one single steady problem is negligible compared with the cost of computing the Galerkin approximation over the full time interval (0, T]. For the analysis we take into account the loss of regularity at initial time of the solution of the Navier–Stokes equations in the absence of nonlocal compatibility conditions. Some numerical experiments are shown.     

Boosting the decay of solutions of the linearised Korteweg-de Vries–Burgers equation to a predetermined rate from the boundary

The aim of this article is to extend recent results on the boundary feedback controllability of the Korteweg-de Vries equation to the Korteweg-de Vries–Burgers equation which is posed on a bounded domain. In the first part of the paper, it is proven that all the sufficiently small solutions can be steered to zero at any desired exponential rate by means of a suitably constructed boundary feedback controller. In the second part, an observer is proposed when a type of boundary measurement is available while there is no full access to the medium.     

Identification of Wiener–Hammerstein models: Two algorithms based on the best split of a linear model applied to the SYSID'09 benchmark problem

This paper describes the identification of Wiener–Hammerstein models and two recently suggested algorithms are applied to the SYSID'09 benchmark data. The most difficult step in the identification process of such block-oriented models is to generate good initial values for the linear dynamic blocks so that local minima are avoided. Both of the considered algorithms obtain good initial estimates by using the best linear approximation (BLA) which can easily be estimated from data. Given the BLA, the two algorithms differ in the way the dynamics are separated into two linear parts. The first algorithm simply considers all possible splits of the dynamics. Each of the splits is used to initialize one Wiener–Hammerstein model using linear least-squares and the best performing model is selected. In the second algorithm, both linear blocks are initialized with the entire BLA model using basis function expansions of the poles and zeros of the BLA. This gives over-parameterized linear blocks and their order is decreased in a model reduction step. Both algorithms are explained and their properties are discussed. They both give good, comparable models on the benchmark data.     

Fuzzy tuning control approach to perform cooperative object manipulation by a rigid–flexible multibody robot

We study cooperative object manipulation control of rigid–flexible multibody systems in space. During such tasks, flexible members like solar panels may get vibrated. Which in turn may lead to some oscillatory disturbing forces on other subsystems and consequently produce errors in the motion of the end-effectors of the cooperative manipulating arms. Therefore, to design and develop capable model-based controllers for such complicated systems, deriving a dynamics model is required. However, due to practical limitations and real-time implementation, the system dynamics model should require low computations. So, first, to obtain a precise compact dynamics model, the rigid–flexible interactive dynamics modeling (RFIM) approach is briefly introduced. Using this approach, the system is virtually partitioned into two rigid and flexible portions, and a convenient model for control purposes is developed. Next, a fuzzy tuning manipulation control (FTMC) algorithm is developed for a simple conceptual model for cooperative object manipulation. In fact, a suitable setup is designed for practical implementation of this controller. After that, a wheeled mobile robot (WMR) system with flexible appendages is considered as a practical case that necessitates delicate force exertion by several end-effectors to move an object along a desired path. The WMR system contains two cooperative manipulators, appended with two flexible solar panels. To reveal the merits of the developed model-based controller, the maneuver is deliberately planned such that flexible modes of solar panels get stimulated due to arms motion. The obtained results show an effective performance of the proposed approach as will be discussed.