Direct synthesis of reduced order H controllers for a class of multivariable plants

Given an nth order, -control input, p-measured output generalized plant, this article proposes a simple, direct approach to design an output feedback H controller with order satisfying for , or for . For this purpose, the output feedback H control problem is transformed into an H state feedback problem for an augmented generalized system. A class of plants for which this transformation always exists and the ensuing controller has order as above, is identified. As a result, for such plants, the reduced order H controller gains are found just by solving a simple linear matrix inequality problem used in state feedback based H control. The efficacy of the proposed approach is studied on some benchmark examples.     

A new -gain analysis framework for discrete-time switched systems based on predictive Lyapunov function

The work proposes the pre--gain analysis framework based on the newly raised nonweighted pre--gain performance index and predictive Lyapunov function, which is devoted to nonweighted -gain analysis and relevant control of discrete-time switched systems under mode-dependent average dwell time. This also provides new ideas for other disturbance-related studies. To begin with, the predictive Lyapunov function is established for switched nonlinear systems in the sense of better reflecting future system dynamics and future external disturbances. Hence, it is achievable to develop less conservative stability and nonweighted pre--gain criteria for switched linear systems. Further, a new disturbance-output expression is devised to match with the nonweighted pre--gain, whose function is to estimate and optimize the traditional nonweighted -gain of the underlying system through discussions. Then, a solvable condition is formulated to seek the piecewise time-dependent gains of switching controller in a convex structure, ensuring the global uniform exponential stability with nonweighted pre--gain and thereby attaining much smaller non-weighted -gain. Finally, the simulation comprised of a circuit system and a numerical example manifests the impressive potential of the obtained results for the purpose of preferable disturbance attenuation performances.     

TDBF: Two-dimensional belief function

How to efficiently handle uncertain information is still an open issue. In this paper, a new method to deal with uncertain information, named as two-dimensional belief function (TDBF), is presented. A TDBF has two components, T = (), both and are classical belief functions, while is a measure of reliable of . The definition of TDBF and the discounting algorithm are proposed. Compared with the classical discounting model, the proposed TDBF is more flexible and reasonable. Numerical examples are used to show the efficiency and application of the proposed method.     

Quantum Coin Method for Numerical Integration

Light transport simulation in rendering is formulated as a numerical integration problem in each pixel, which is commonly estimated by Monte Carlo integration. Monte Carlo integration approximates an integral of a black-box function by taking the average of many evaluations (i.e. samples) of the function (integrand). For N queries of the integrand, Monte Carlo integration achieves the estimation error of . Recently, Johnston [Joh16] introduced quantum super-sampling (QSS) into rendering as a numerical integration method that can run on quantum computers. QSS breaks the fundamental limitation of the convergence rate of Monte Carlo integration and achieves the faster convergence rate of approximately which is the best possible bound of any quantum algorithms we know today [NW99]. We introduce yet another quantum numerical integration algorithm, quantum coin (QCoin) [AW99], and provide numerical experiments that are unprecedented in the fields of both quantum computing and rendering. We show that QCoin's convergence rate is equivalent to QSS's. We additionally show that QCoin is fundamentally more robust under the presence of noise in actual quantum computers due to its simpler quantum circuit and the use of fewer qubits. Considering various aspects of quantum computers, we discuss how QCoin can be a more practical alternative to QSS if we were to run light transport simulation in quantum computers in the future.     

Correlation and correlation coefficient of generalized orthopair fuzzy sets

Generalized orthopair fuzzy sets are extensions of ordinary fuzzy sets by relaxing restrictions on the degrees of support for and support against. Correlation analysis is to measure the statistical relationships between two samples or variables. In this paper, we propose a function measuring the interrelation of two -rung orthopair fuzzy sets, whose range is the unit interval . First, the correlation and correlation coefficient of -rung orthopair membership grades are presented, and their basic properties are investigated. Second, these concepts are extended to -rung orthopair fuzzy sets on discrete universes. Then, we discuss their applications in cluster analysis under generalized orthopair fuzzy environments. And, a real-world problem involving the evaluation of companies is used to illustrate the detailed processes of the clustering algorithm. Finally, we introduce the correlation and correlation coefficient of -rung orthopair fuzzy sets on both bounded and unbounded continuous universes and provide some numerical examples to substantiate such arguments.     

Research on arithmetic operations over generalized orthopair fuzzy sets

The four fundamental operations of arithmetic for real (and complex) numbers are well known to everybody and quite often used in our daily life. And they have been extended to classical and generalized fuzzy environments with the demand of practical applications. In this paper, we present the arithmetic operations, including addition, subtraction, multiplication, and division operations, over -rung orthopair membership grades, where subtraction and division operations are both defined in two different ways. One is by solving the equation involving addition or multiplication operations, whereas the other is by determining the infimum or supremum of solutions of the corresponding inequality. Not all of -rung orthopairs can be performed by the former method but by the latter method, and it is proved that the former is a special case of the latter. Moreover, the elementary properties of arithmetic operations as well as mixed operations are extensively investigated. Finally, these arithmetic operations are pointwise defined on -rung orthopair fuzzy sets in which the membership degree of each element is a -rung orthopair.     

Stubborn state estimation for nonlinear distributed parameter systems subject to measurement outliers

In this article, the state estimation problem is investigated for a class of distributed parameter systems (DPSs). In order to estimate the state of DPSs, we give a partition of spatial interval with a finite sequence and, on each subinterval, one sensor is placed to receive the measurements from the DPS. Due to the unexpected environment changes, the measurements will probably contain some outliers. To eliminate the effects of the possibly occurring outliers, we construct a stubborn state estimator where the innovation is constrained by a saturation function. By using Lyapunov functional, Wirtinger inequality and piecewise integration, some sufficient conditions are obtained under which the resulting estimation error system is exponentially stable and the performance requirement is satisfied. According to the obtained analysis results, the desired state estimator is designed in terms of the solution to a set of matrix inequalities. Finally, a numerical simulation example is given to verify the effectiveness of the proposed state estimation scheme.     

Linear-time algorithms for eliminating claws in graphs

Since many -complete graph problems are polynomial-time solvable when restricted to claw-free graphs, we study the problem of determining the distance of a given graph to a claw-free graph, considering vertex elimination a measure. Claw-free Vertex Deletion (CFVD) consists of determining the minimum number of vertices to be removed from a graph such that the resulting graph is claw-free. Although CFVD is -hard in general and recognizing claw-free graphs is still a challenge, where the current best deterministic algorithm for a graph G consists of performing executions of the best algorithm for matrix multiplication, we present linear-time algorithms for CFVD on weighted block graphs and weighted graphs with bounded treewidth. Furthermore, we show that this problem on forests can be solved in linear time by a simpler algorithm, and we determine the exact values for full k-ary trees. On the other hand, we show that CFVD is -hard even when the input graph is a split graph. We also show that the problem is hard to be approximated within any constant factor better than 2, assuming the unique games conjecture.     

Linguistic-induced ordered weighted averaging operator for multiple attribute group decision-making

To solve the problems of making decision with uncertain and imprecise information, Zadeh proposed the concept of Z-number as an ordered pair, the first component of which is a restriction of variable, and the second one is a measure of reliability of the first component. But the decision-makers’ confidence in decision-making was neglected. In this paper, firstly, we present a new method to evaluate and rank -numbers based on the operations of trapezoidal Type 2 fuzzy numbers and generalized trapezoidal fuzzy numbers. Then, linguistic-induced ordered weighted averaging operator and linguistic combined weighted averaging aggregation operator are developed to solve multiple attribute group decision-making problems. And we analyze the main properties of them by utilizing some operational laws of fuzzy linguistic variables. Finally, a numerical example is provided to illustrate the rationality of the proposed method.     

Mixed coordination mechanisms for scheduling games on hierarchical machines

In this paper, we study scheduling games under mixed coordination mechanisms on hierarchical machines. The two scheduling policies involved are ‐ and ‐, where ‐ (resp., ‐) policy sequences jobs in nondecreasing order of their hierarchies, and jobs of the same hierarchy in nonincreasing (resp., nondecreasing) order of their processing times. We first show the existence of a Nash equilibrium. Then we present the price of anarchy and the price of stability for the games with social costs of minimizing the makespan and maximizing the minimum machine load. All the bounds given in this paper are tight.     

Fast vision‐based autonomous detection of moving cooperative target for unmanned aerial vehicle landing

We propose a fast and effective method, fast target detection (FTD), to detect the moving cooperative target for the unmanned aerial vehicle landing, and the target is composed of double circles and a cross. The purpose of our strategy is to land on the target. The FTD method needs to detect the target at the high and low heights. At the high height, the target appears completely and stably in the camera field. The FTD method can detect the circle and cross to rapidly reach the target center, named cross and circle–FTD (). To detect the cross, we propose a slope distance equation to obtain the distance between two slopes. The proposed slopes cluster method, based on the distance equation and K‐means, is used to determine the cross center. At the low height, the target appears incompletely and unstably. Therefore, FTD methods detect only the cross, named cross–FTD (). We extract the cross features ( CFs) based on line segments. Then, four CFs are combined based on graph theory. Experiments on our four datasets show that FTD has rapid speed and good performance. (Our method is implemented in C++ and is available at https://github.com/Li-Zhaoxi/UAV-Vision-Servo .) On the Mohamed Bin Zayed International Robotics Challenge datasets made we constructed, detects the target from a image approximately per pipeline with F‐measure and tracks target approximately per pipeline with F‐measure. detects centers from a image at approximately per image with F‐measure.     

Sparse control for continuous-time systems

In this survey article, we give a comprehensive review of sparse control for continuous-time systems, called maximum hands-off control. The maximum hands-off control is the optimal control, for which we introduce fundamental properties such as necessary conditions, existence, and equivalence to the optimal control. We also show an efficient numerical computation algorithm for the maximum hands-off control based on the time discretization and ADMM (alternating direction method of multipliers). A numerical example is shown with an available MATLAB program.     

Observer-based consensus control for multi-agent systems with measurement noises and external disturbances

This study presents a distributed observer-based consensus control for general linear multi-agent systems under measurement noises and external disturbances. By using the state linear transformation with the matrix constructed from the incidence matrix of a virtual chained directed spanning tree, we transform the observer-based consensus problem into an asymptotic stability problem of a corresponding augmented linear system. The augmented linear system consists of the reduced-order system deduced from dynamic equations of the agents and state estimation error system. Based on asymptotic stability of the augmented linear system, we present some sufficient conditions in terms of linear matrix inequalities for the existence of the distributed observer-based consensus controller. Finally, the effectiveness of the proposed approach is illustrated by a numerical example.     

New logarithmic operational laws and their aggregation operators for Pythagorean fuzzy set and their applications

The aim of this paper is to develop some new logarithm operational laws (LOL) with real number base for the Pythagorean fuzzy sets. Some properties of LOL have been studied and based on these, various weighted averaging and geometric operators have been developed. Then, we utilized it to solve the decision-making problems. The validity of the proposed method is demonstrated with a numerical example and compared the results with the several existing approaches result. Finally, the influences of logarithmic operation and the selection of the logarithmic base in practice are discussed.     

Stabilization of the planar vertical take-off and landing using nonlinear feedback control

This article presents a new control strategy for the well-known problem of the planar vertical take-off and landing. The total thrust is computed using a nonlinear feedback compensation so that the altitude reaches the desired altitude. The horizontal position x is then controlled by choosing the orientation angle as a smooth saturation function of x and . A proof of convergence is presented using a Lyapunov approach. The proposed control strategy is successfully tested in numerical simulations.     

Resource provisioning in collaborative fog computing for multiple delay-sensitive users

Fog computing is an emerging paradigm that supplies storage, computation, and networking resources between traditional cloud data centers and end devices. This article focuses on the resource provisioning problem in collaborative fog computing for multiple delay-sensitive users. Our goal is to implement a resource provisioning strategy for network operators to minimize the total monetary cost by considering the deadline and capacity constraints. Two scenarios are considered: unlimited-processor fog nodes (UPFN) and limited-processor fog nodes (LPFN). In either scenario, we prove that the resource provisioning problem is NP-hard. First, we consider the UPFN scenario that the processors of fog nodes are unlimited and users' requests can be ideally processed in parallel. Two algorithms are proposed which greedily delete fog nodes based on the local or global collaborative influences until there is no feasible provisioning to guarantee the deadline of users. Then we extend the resource provisioning problem to a more realistic and complicated scenario LPFN in which the scheduling delay cannot be ignored. Two types of tasks are considered. One is the arbitrarily divided tasks, and a near-optimal solution bounded by has been found. m is the number of fog nodes, and is the upper bound on the Lipschitz constant of the delay function. Another one is the application-driven tasks, and we propose a heuristic algorithm. Extensive experiments validate the efficiency of the proposed algorithms.     

Constrained shortest path tour problem: models,valid inequalities,and Lagrangian heuristics

The constrained shortest path tour problem (CSPTP) is an NP‐hard combinatorial optimization problem defined on a connected directed graph , where V is the set of nodes and A is the set of nonnegative weighted arcs. Given two distinct nodes , an integer value , and node disjoint subsets , , the CSPTP aims at finding the shortest trail from s to t while visiting at least one node in every subset , in this order. In this paper, we perform a comparative analysis between two integer programming (IP) models for the problem. We also propose valid inequalities and a Lagrangian‐based heuristic framework. Branch‐and‐bound algorithms from the literature, as well as a metaheuristic approach, are used for comparison. Extensive computational experiments carried out on benchmark data sets show the effective use of valid inequalities and the quality of bounds obtained by the Lagrangian framework. Because benchmark instances do not require a great computational effort of IP models in the sense that their optimality is reached at the root node of the CPLEX branch‐and‐cut search tree, we introduce new challenging CSPTP instances for which our solution approaches outperform existing ones for the problem.     

Structural Analogy from a Single Image Pair

The task of unsupervised image‐to‐image translation has seen substantial advancements in recent years through the use of deep neural networks. Typically, the proposed solutions learn the characterizing distribution of two large, unpaired collections of images, and are able to alter the appearance of a given image, while keeping its geometry intact. In this paper, we explore the capabilities of neural networks to understand image structure given only a single pair of images, and . We seek to generate images that are structurally aligned: that is, to generate an image that keeps the appearance and style of , but has a structural arrangement that corresponds to . The key idea is to map between image patches at different scales. This enables controlling the granularity at which analogies are produced, which determines the conceptual distinction between style and content. In addition to structural alignment, our method can be used to generate high quality imagery in other conditional generation tasks utilizing images and only: guided image synthesis, style and texture transfer, text translation as well as video translation. Our code and additional results are available in https://github.com/rmokady/structural-analogy/