The block Cimmino method is successfully used for the parallel solution of large linear systems of equations due to its amenability to parallel processing. Since the convergence rate of block Cimmino depends on the or...
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The block Cimmino method is successfully used for the parallel solution of large linear systems of equations due to its amenability to parallel processing. Since the convergence rate of block Cimmino depends on the orthogonality between the row blocks, advanced partitioning methods are used for faster convergence. In this work, we propose a new partitioning method that is superior to the state-of-the-art partitioning method, GRIP, in several ways. Firstly, our proposed method exploits the Mongoose partitioning library which can outperform the state-of-the-art methods by combining the advantages of classical combinatoric methods and continuous quadratic programming formulations. Secondly, the proposed method works on the numerical values in a floating-point format directly without converting them to integer format as in GRIP. This brings an additional advantage of obtaining higher quality partitionings via better representation of numerical values. Furthermore, the preprocessing time is also improved since there is no overhead in converting numerical values to integer format. Finally, we extend the Mongoose library, which originally partitions graphs into only two parts, by using the recursive bisection paradigm to partition graphs into more than two parts. Extensive experiments conducted on both shared and distributed memory architectures demonstrate the effectiveness of the proposed method for solving different types of real-world problems.
The primary challenge is to design feedback controls that enable robots to autonomously reach predetermined destinations while avoiding collisions with obstacles and other robots. Various control algorithms, such as t...
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The primary challenge is to design feedback controls that enable robots to autonomously reach predetermined destinations while avoiding collisions with obstacles and other robots. Various control algorithms, such as the control barrier function-based quadratic programming (CBF-QP) controller, address collision avoidance problems. Control barrier functions (CBFs) ensure forward invariance, which is critical for guaranteeing safety in robotic collision avoidance within agricultural fields. The goal of this study is to enhance the safety and mitigation of potential collisions in smart agriculture systems. The entire system was simulated in the MATLAB/Simulink environment, and the results demonstrated a 93% improvement in steady-state error over rapidly exploring random tree (RRT). These findings indicate that the proposed controller is highly effective for collision avoidance in smart agricultural systems.
An optimal strategy for simultaneous charging of electric vehicle battery packs is proposed as a multiobjective optimization problem in this article. The charger consists of n constant voltage current sources for char...
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An optimal strategy for simultaneous charging of electric vehicle battery packs is proposed as a multiobjective optimization problem in this article. The charger consists of n constant voltage current sources for charging n batteries, respectively. Considering the energy loss and the charging criteria, a battery charging issue for the charging mode is formulated as a multiobjective optimization problem and the optimal solution is obtained with the application of quadratic programming. In addition, an adaptive momentum-based steepest descent algorithm is propounded to minimize the simultaneous charging time in the charging mode. Simulation and experimental results show that the actual state of charge converges to the same value within the theoretical shortest time for under the charging mode.
Human multirobot interaction enables humans to work in a shared workspace with multiple robots that conduct cooperative tasks such as cotransporting a rigid object. To guarantee human safety, each robot has to execute...
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Human multirobot interaction enables humans to work in a shared workspace with multiple robots that conduct cooperative tasks such as cotransporting a rigid object. To guarantee human safety, each robot has to execute unplanned motions via human-in-the-loop control. However, the robot's compliant motions with humans may violate the constraints imposed by the cooperative task with other robots. A distributed controller that guarantees human safety and task constraints is still a challenge. This article proposes a control framework based on distributed quadratic programming (QP). First, safety control sets based on local and global inequality constraints are formulated using control barrier functions to guarantee human safety. Furthermore, task control sets based on local and global equality constraints are formulated to achieve the constraints of the cooperative task. Then, distributed QPs are constructed by separating the global equality and inequality constraints into local constraints with discrepancy variables. Finally, a recurrent neural network converging to the local optimality of a distributed QP is designed, and adaptation laws of discrepancy variables using only exchanged information between adjacent robots are designed to make the distributed QPs reach global optimality. The effectiveness of the proposed control framework is verified in simulation and experiment.
The conventional zeroing neural network (ZNN) model faces significant challenges in handling time-varying noise, with its convergence speed being highly sensitive to initial conditions. In this paper, we propose a new...
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The conventional zeroing neural network (ZNN) model faces significant challenges in handling time-varying noise, with its convergence speed being highly sensitive to initial conditions. In this paper, we propose a new parameter-changing integral ZNN model with nonlinear activation (NAPCIZNN) to effectively tackle time-varying quadratic programming problems with inequality constraints (IC-TVQP). By integrating a nonlinear activation function and dynamic parameter adjustment, the proposed NAPCIZNN model exhibits superior convergence speed and robust noise tolerance. We rigorously derive the theoretical upper bound for convergence time under noisy environments, providing a strong foundation for the model's reliability. Comprehensive numerical simulations demonstrate that NAPCIZNN significantly outperforms traditional ZNN variants-including the original ZNN, nonlinear activated ZNN, integral ZNN, and piecewise variable parameter ZNN-in solving time-varying quadratic programming problems. Moreover, the practical application of the NAPCIZNN model in controlling the PUMA560 robotic manipulator showcases its robustness and precision in real-world scenarios. Empirical evidence from these applications validates the model's exceptional capability in executing complex butterfly trajectory tracking controls with high accuracy and reliability.
Data-driven methods for constructing HIs are now well-established for incipient fault detection and prognostic analysis. In order for physics-explainable diagnositic and prognostic information to be easily embeded int...
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Data-driven methods for constructing HIs are now well-established for incipient fault detection and prognostic analysis. In order for physics-explainable diagnositic and prognostic information to be easily embeded into the HI construction process, existing optimization-based weight learning approaches are limited by considering only linear fusion functions. Integrating the physical information related to bearing degradation into the optimization based HI construction process in a nonlinear form, has yet to be fully explored. To solve this problem, this study first proposes a novel nonlinear optimization-based weight learning model for constructing a HI. By introducing kernel methods, the model maximizes the correlation between the latest measured time series and previously measured time series while simultaneously minimizing the fitting error, effectively capturing the nonlinear relations between spectral components. We also explore how the bearing degradation-related physics information can be fully revealed from the built HIs and how this information can be used to explain the superior performance of the HIs in terms of diagnosis and prognosis. Moreover, the constructed HIs are utilized for remaining useful life (RUL) prediction based on a stochastic degradation modelling approach. The ability of the proposed nonlinear weight learning model to detect incipient faults and model degradation is verified through two bearing run-to-failure case studies.
This paper proposes a novel one-layer neural network to solve quadratic programming problems in real time by using a control parameter and transforming the optimality conditions into a system of projection equations. ...
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This paper proposes a novel one-layer neural network to solve quadratic programming problems in real time by using a control parameter and transforming the optimality conditions into a system of projection equations. The proposed network includes two existing dual networks as its special cases, and an existing model can be derived from it. In particular, another new model for linear and quadratic programming problems can be obtained from the proposed network. Meanwhile, a new Lyapunov function is constructed to ensure that the proposed network is Lyapunov stable and can converge to an optimal solution of the concerned problem under mild conditions. In contrast with the existing models for quadratic programming, the proposed network requires the least neurons while maintaining weaker stability conditions. The effectiveness and characteristics of the proposed model are demonstrated by the limited simulation results.
The paper introduces a quadratic programming algorithm for real-time local path planning of autonomous vehicles. The algorithm relies on discretized sampling points and an enhanced cost function. Initially, we formula...
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The paper introduces a quadratic programming algorithm for real-time local path planning of autonomous vehicles. The algorithm relies on discretized sampling points and an enhanced cost function. Initially, we formulate the cost function to optimize the reference trajectory and establish the Frenet coordinate system. The drivable region undergoes discretization to generate sampling points in the Frenet coordinate system. We apply the principles of convex spatial obstacle avoidance to define the vehicle's drivable area, taking into account the vehicle's kinematics and establishing barrier boundary conditions. Subsequently, quadratic programming is employed to determine an optimal path within the vehicle's drivable area. Concurrently, two cost functions are devised, the first evaluates the distance between the vehicle and obstacles, while the second assesses ride comfort, these cost functions are employed to evaluate sampling points and speed profiles, facilitating the planning of an optimal speed profile on the selected path. Finally, the algorithm undergoes validation through co-simulation using Matlab/Simulink, PreScan, and CarSim software. Various road scenarios, including straight and S-curve roads with both dynamic and static obstacles, are created to assess the method's feasibility. The test results demonstrate the algorithm's efficacy in avoiding moving and stationary obstacles and generating an ideal path compliant with driving conditions.
This paper deals with a class of quadratic programming problems having intuitionistic fuzzy parameters and bounded constraints. Such problems are designed to handle uncertain parameters in quadratic programming and pr...
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This paper deals with a class of quadratic programming problems having intuitionistic fuzzy parameters and bounded constraints. Such problems are designed to handle uncertain parameters in quadratic programming and provide a better representation of many real-life situations. This study presents the utilization of (alpha,u)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\alpha ,u)$$\end{document} and (beta,v)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\beta ,v)$$\end{document} cuts and a new solution methodology is suggested to obtain the lower and upper bounds of the objective function in the problem. Using the bounds obtained, we construct the membership and non-membership functions of the optimal values graphically. By expressing the optimal value through membership and non-membership functions instead of a crisp value, this method offers a more detailed and nuanced view of the data, which can lead to better-informed decision-making. Moreover, it has been found that the proposed method yields more efficient solutions, requiring less computational work. We illustrate the solution procedure of the proposed technique by applying it to a real-life problem in textile industry.
We introduce a new sequential algorithm for the Standard quadratic programming Problem (StQP), which exploits a formulation of StQP as a Linear Program with Linear Complementarity Constraints (LPLCC). The algorithm is...
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We introduce a new sequential algorithm for the Standard quadratic programming Problem (StQP), which exploits a formulation of StQP as a Linear Program with Linear Complementarity Constraints (LPLCC). The algorithm is finite and guarantees at least in theory a delta\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\delta $$\end{document}-approximate global minimum for an arbitrary small delta\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\delta $$\end{document}, which is a global minimum in practice. The sequential algorithm has two phases. In Phase 1, Stationary Points (SP) with strictly decreasing objective function values are computed. Phase 2 is designed for giving a certificate of global optimality for the last SP computed in Phase 1. Two different Nonlinear programming Formulations for LPLCC are proposed for each one of these phases, which are solved by efficient enumerative algorithms. New procedures for computing a lower bound for StQP are also proposed, which are easy to implement and give tight bounds in general. Computational experiments with a number of test problems from known sources indicate that the two-phase sequential algorithm is, in general, efficient in practice. Furthermore, the algorithm seems to be an efficient way to study the copositivity of a matrix by exploiting an StQP with this matrix.
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