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.     

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.     

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.     

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.     

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.     

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.     

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.     

An iterative approach for the discrete‐time dynamic control of Markov jump linear systems with partial information

The , and mixed dynamic output feedback control of Markov jump linear systems in a partial observation context is studied through an iterative approach. By partial information, we mean that neither the state variable x(k) nor the Markov chain θ(k) are available to the controller. Instead, we assume that the controller relies only on an output y(k) and a measured variable coming from a detector that provides the only information of the Markov chain θ(k). To solve the problem, we resort to an iterative method that starts with a state‐feedback controller and solves at each iteration a linear matrix inequality optimization problem. It is shown that this iterative algorithm yields to a nonincreasing sequence of upper bound costs so that it converges to a minimum value. The effectiveness of the iterative procedure is illustrated by means of two examples in which the conservatism between the upper bounds and actual costs is significantly reduced.     

Hidden Markov model based filtering for singular semi-Markov jump systems

This article investigates the hidden Markov model based filter design problem for the singular semi-Markov jump systems (SSMJSs). The considered semi-Markov process is a generalization of Markov process, which can eliminate the restriction on the exponential distribution of sojourn time. Besides, the hidden Markov model based filter is introduced to tackle the asynchronous phenomenons occurred between the system modes and filter modes. To ensure the stochastic stability of the SSMJSs and derive solvable filter parameters, a filter design technic is constructed. First, the direct evolution of the states between two arbitrary close time instants is constructed from the filtering error system according to slow-fast decomposition, sufficient conditions are then proposed based on the consistent projector of the filtering error system and the constructed direct state evolution. Second, a new linear decoupling strategy is presented to deal with the coupled terms under the established stability conditions, which further derives the desired hidden Markov model based filter parameters. A numerical example is given to illustrate the effectiveness of the proposed method.     

Optimal linear combination of sensors and actuators to enforce an interior conic open‐loop system

This paper presents techniques to linearly combine the sensor measurements and/or actuator inputs of a linear time‐invariant system to obtain a new system that is interior conic with prescribed bounds. In the optimal sensor combination problem, a desired system output is defined, and in the optimal actuator combination problem, a desired system input is defined, along with a frequency bandwidth in which the desired system input or output should be matched. The simultaneous optimal sensor and actuator combination problem includes desired system outputs and inputs. In all cases, the weighted or norm of the difference between the system with linearly combined sensors or actuators and the desired system is minimized while rendering the new system interior conic with prescribed bounds. The weighting transfer matrix used in the ‐ or ‐optimization problem is determined by the frequency bandwidth of interest. The individual sensor and actuator combination methods involve linear matrix inequality constraints and are posed as convex optimization problems, whereas the combined sensor and actuator method is an iterative procedure composed of convex optimization steps. Numerical examples illustrate superior tracking performance with the proposed sensor and actuator combination techniques over comparable techniques in the literature when implemented with a simple feedback controller. Robust asymptotic stability of the closed‐loop system to plant uncertainty is demonstrated in the numerical examples.     

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.     

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.     

PAS: A new powerful and simple quantum computing simulator

In recent years, many researchers have been using CPU for quantum computing simulation. However, in reality, the simulation efficiency of the large-scale simulator is low on a single node. Therefore, striving to improve the simulator efficiency on a single node has become a serious challenge that many researchers need to solve. After many experiments, we found that much computational redundancy and frequent memory access are important factors that hinder the efficient operation of the CPU. This paper proposes a new powerful and simple quantum computing simulator: PAS (power and simple). Compared with existing simulators, PAS introduces four novel optimization methods: efficient hybrid vectorization, fast bitwise operation, memory access filtering, and quantum tracking. In the experiment, we tested the QFT (quantum Fourier transform) and RQC (random quantum circuits) of 21 to 30 qubits and selected the state-of-the-art simulator QuEST (quantum exact simulation toolkit) as the benchmark. After experiments, we have concluded that PAS compared with QuEST can achieve a mean speedup of (QFT), (RQC) (up to , ) on the Intel Xeon E5-2670 v3 CPU.     

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.     

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.     

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.     

Robust control of the Hill's problem with drag

There are significant advantages associated with the analysis of satellite trajectory control problems in the Hill's analysis framework. As with the circular restricted three‐body problem (CRTBP) equations, the Hill's equations support three‐dimensional “halo” orbits that require station‐keeping control. These orbits are typically in regions of space close to a libration point. In most cases these orbits are unstable, with drag effects introducing uncertain exogenous forces. A two‐degree‐of‐freedom control strategy is used to maintain a pre‐selected orbit and introduce a quantifiable robust stability margin. The control study presented is based on a time‐periodic state feedback law, and a time‐periodic feed‐forward control that is based on a linearized drag model. The efficacy of these ideas is demonstrated by simulation.     

Quasi‐time‐dependent asynchronous filtering for discrete time switched systems via the event triggering mechanism

This article is concerned with the quasi‐time‐dependent asynchronous filter design problem for a class of discrete‐time switched systems via the event‐triggering mechanism. Applying the quasi‐time‐dependent Lyapunov functions and the mode‐dependent average dwell time technique, an asynchronous filter is designed with a weighted performance index; the filter parameter matrices are quasi‐time‐dependent in each event‐triggering‐dependent sampling interval; both cases (Case 1: no more than one switching, Case 2: multiple switchings) are taken into account in this sampling interval, by which the assumption, that the maximal asynchronous period is not larger than the minimal dwell time, is relaxed in this article. Simulation examples are given to show the less conservatism and effectiveness of the proposed results.