Form Of Quadratic Programming Research Articles

Heavy-duty hexapod robot sideline tipping judgment and recovery

AbstractHeavy-duty hexapod robots are well-suited for physical transportation, disaster relief, and resource exploration. The immense locomotion capabilities conferred by the six appendages of these systems enable traversal over unstructured and challenging terrain. However, tipping can be a serious concern when moving with a tripod gait in these challenging environments, which may cause irreversible consequences such as compromised movement control and potential damage. In this paper, we focus on heavy-duty hexapod robot sideline tipping judgment and recovery during tripod gait motion, and a novel sideline tipping judgment and recovery method is proposed by adjusting an optimal swinging leg to the stance state. Considering the locomotion environments, motion mode, and tipping analysis, the robot’s stability margin is quantified, and the tipping event is evaluated by the Force Angle Stability Measure (FASM). The recovery method is initiated upon detecting that the robot is tipping, which involves the selection of an adjustment leg and the determination of an optimal foothold. Since the FASM is based on the foot force and robot center of gravity (CoG), the stability margin quantification expression is reformulated to the constraint form of quadratic programming (QP). Furthermore, a foot force distribution method, integrating stability margin considerations into the QP model, has been devised to ensure post-adjustment stability of the landing leg. Experiments on tipping judgment and recovery demonstrate the effectiveness of the proposed approaches on tipping judgment and recovery.

Adaptive eco-cruising control for connected electric vehicles considering a dynamic preceding vehicle

Energy consumption and driving safety of a vehicle are greatly influenced by the driving behaviors of the vehicle in front (also termed the preceding vehicle). Inappropriate responses to unanticipated changes in the preceding vehicle can lead to decreased energy efficiency and an increased risk of rear-end collisions. To address this issue, this study proposes an innovative Adaptive Eco-cruising Control Strategy (AECS) for connected electric vehicles (CEVs) considering the dynamic behavior prediction of the preceding vehicle. The AECS, which is designed with a two-stage receding horizon control framework, can adapt to scenarios where the preceding vehicle cuts in or moves out in a safer and energy-efficient manner compared to traditional eco-cruising strategies, which merely focus on a constant preceding vehicle. In the first stage, a prediction model for characterizing the dynamic behavior of preceding vehicles is developed using the Bayesian network. This model is trained using real-world vehicle driving data, allowing it to anticipate the driving trajectories of vehicles changing lanes in front. In the second stage, an energy-saving, safety, and driving comfort-oriented optimization problem is formulated as a quadratic programming form. The eco-cruising speed is then optimized to adapt to the dynamic traffic environment, especially when the preceding vehicle changes over time. Finally, several simulations are conducted to validate the AECS. The results demonstrate that the AECS can improve the energy efficiency of CEVs by up to 11.80% and 19.53% on average compared to the existing cruise control strategies and ensure vehicle driving safety and comfort, without compromising travel time. Additionally, the vehicle cut-in position, the cut-in vehicle speed, and the ego vehicle speed affect the energy efficiency improvement performance of the AECS.

The effect of responsive demand penetration on key parameters of the two-sided market by using structural decomposition of the electricity market

Today, with the development of price-responsive demand programs in the electricity industry and consumers’ desire for it, two-sided market is more prepared than before. In a two-sided market, factors such as responsive demand or congestion in transmission lines change market variables (unit generation, price per bus). Recognizing these changes helps the independent market operator to have proper market control. The primary purpose of this study is to investigate and quantify the effect of presence and increase of the penetration of responsive demand in the network on critical components of the market, including locational marginal prices (LMPs), power generation of units, power consumption of responsive demand, power flow of lines and congestion. To achieve this goal, after identifying and classifying the problem parameters in the form of quadratic programming (QP) problem, structural decomposition is implemented by using the Lagrange function and the Kuhn–Tucker (KKT) conditions to decompose all variables of the electricity market, such as responsive demand sensitivity, electricity price, and positive duality of generation units, into key parameters to calculate the share of individual key market parameters in the two-side electricity market. Finally, the sensitivity of market variables to price-responsive demand parameters has been investigated. The proposed approach is evaluated on the IEEE 24-bus system, and the results are discussed.

Real-time power optimization for application server clusters based on Mixed-Integer Programming

In the environment of peer competition and energy conservation, optimizing the deployment of application server clusters in real time according to actual workload conditions to reduce operating costs and energy consumption is an important issue that must be urgently addressed. In this paper, we propose a real-time power optimization strategy for application server clusters, and the optimization measures include CPU dynamic voltage/frequency scaling and server dynamic switching. First, the feasibility of defining variables for server types is proved, and appropriate variables are defined to describe the cluster power optimization as a mixed-integer programming (MIP) problem. Then, two solution methods are proposed: the exact method based on the Gurobi optimizer and the approximate method based on primary–secondary optimization and differential evolution with two mutations (PSODE). The former turns the MIP problem into a standard mixed-integer quadratic programming form by introducing intermediate variables and solves it using the Gurobi optimizer. The latter rewrites the MIP problem as a primary–secondary optimization problem and proposes a differential evolutionary-based solution algorithm for the primary optimization problem. The evolutionary process consists of two mutation operations, inter- and intraindividual mutations, which both use a heuristic policy to accelerate the evolution convergence. The test results reveal that the Gurobi-based method can quickly determine the global optimal deployment when the cluster size is small. The PSODE-based method can quickly determine the global optimal deployment or high-quality suboptimal deployment when applied to large-scale clusters.

Optimal Power Flow in AC/DC Microgrids With Enhanced Interlinking Converter Modeling

In this article, we propose an optimal power flow (OPF) paradigm for hybrid ac/dc microgrids. A meticulous model of the interlinking converter (IC) is developed and integrated into the OPF problem formulation. The resulting formulation is capable of solving the OPF of ac and dc subgrids in their standalone operations. A computationally efficient parabolic relaxation method transforms the nonconvex OPF model into a convex quadratic-constrained quadratic programming form. A sequential penalization method is applied to the relaxed OPF to achieve feasible solutions for the original formulation. The developed OPF formulation is tested on multiple modified 5-, 14-, 30-, 24-, 118-bus test systems, and a significant reduction in computational time is achieved in comparison with semidefinite programming relaxation. For a sequential penalized ac/dc OPF, the optimal values of both relaxations have a maximum difference of 0.025% for a 5-bus system. Finally, the modified IEEE 14-bus system is emulated in a real-time controller/hardware-in-the-loop setup to validate the proposed framework with continuously varying loads and IC switching status.

Design of a real-time three-axis controller for contour error reduction based on model predictive control

The machining accuracy is mainly indicated by the contour error especially in high-precision processing. Previously, scholars have proposed many controllers to reduce contour errors in real-time machining, such as the cross coupling controller and sliding mode controller. In this paper, we propose a controller based on model predictive control (MPC), and the contour error caused during path tracking can be effectively reduced by this controller. First of all, for two-dimensional (2D) and three-dimensional (3D) tool paths, their contour errors are deduced based on coordinate system transform. Second, the MPC-based controller is designed with the state-space discrete model of a machine tool. The contour error is regarded as a constraint during receding optimization. These are reasons why the presented control scheme is adapted with both bi-axis and three-axis machine tools. Furthermore, in order to improve the efficiency of receding optimization, the contour error of a 3D curve is simplified. Subsequently, the optimization problem is transformed into the standard form of quadratic programming. Finally, a 2D tool path and a 3D tool path are machined to test the proposed controller. Simulations and experiments show satisfactory results which indicate effectiveness of the proposed method.

Optimal Control Method of Path Tracking for Four-Wheel Steering Vehicles

Path tracking is a key technique for intelligent electric vehicles, while four-wheel steering (4WS) technology is of great significance to improve its accuracy and flexibility. However, the control methods commonly used in path tracking for a 4WS vehicle cannot take full advantage of the additional steering freedom of the 4WS vehicle, because of restricting the relationship between the front and rear wheels steering angle. To address this issue, we derive a kinematic model without the restriction based on the small-angle assumption. Then, the objective function and constraints of system control quantity optimization are designed based on the tracking error model. After the optimization problem is solved in the form of quadratic programming with constraints, the control sequence with the smallest performance index is obtained through rolling optimization. The proposed method is tested on a high-fidelity Carsim/Simulink co-simulation platform and an experimental vehicle. The results show that the standard deviation of the lateral error and the yaw angle error of the algorithm is less than 0.1 m and 3.0°, respectively. Compared with the other two algorithms, the control of the front and rear wheels angle of this method is more flexible and the tracking accuracy is higher.

Potential field‐based path planning for emergency collision avoidance with a clothoid curve in waypoint tracking

AbstractA novel potential field‐based model curve fitting method (PF‐MCF) is presented in this paper to handle emergency collision avoidance in waypoint tracking (following waypoints from a leading vehicle). It is reported that the PF has high performance on real‐time obstacle avoidance in robotic path planning. However, some inherent limitations exist in the PF, such as no passage between closely spaced obstacles and oscillations in the presence of obstacles, which is rarely discussed in the research field of PF‐based autonomous vehicles (AVs), especially in waypoint tracking. To solve these problems, we propose the PF‐MCF method to transform the clothoid curve into a quadratic programming form and solve the optimization under reasonable constraints to consider the different waypoints from the PF and the leading vehicle. The proposed PF‐MCF method is validated via MATLAB/Simulink and CarSim to avoid multiple obstacle vehicles in waypoint tracking compared with the two latest methods (PF‐based model predictive controller and PF‐based curve fitting method). The simulation results confirm the efficiency of finding a passage in closely spaced obstacle vehicles and eliminating oscillations (under 0.5 [deg] in tire steering angle) in the presence of obstacles compared to other latest methods.

Joint Resource Optimization for IRS-Assisted Mmwave MIMO Under QoS Constraints

This paper focuses on the non-convex joint optimization with a dynamic resource of multi-user for an intelligent reflecting surface-enhanced mmWave system, where all users have individual rates or quality of service requirements. Firstly, the objective function of the above non-linear problem is converted into a quadratic programming form under the quality of service constraints. Further, a multi-blocks alternating optimization framework with dynamic power allocation is proposed to obtain the maximum sum-rate, where the relaxed ADMM algorithm is adopted to tackle the optimal full-digital precoder and the corresponding passive reflecting matrix is obtained by the gradient-projection. The numerical results verify that beam optimization should be emphasized in high SNR, but joint dynamic resource allocation can further improve system performance even if the hardware dimensions reaches the limit.

Displacement Control of Nonlinear Pin-Jointed Assemblies Based on Force Method and Optimization

The geometry of the structure and internal bar forces under varying service load situations or prestressing actually impact on the structure’s serviceability. Or else, prestressed cable structures are defined by the joint locations and delicate to external stimuli due to their high flexibility and light weight, and the shape distortion is supposed unacceptable. Consequently, based on the force method, the displacement control through updating coordinates of the structure and optimization on the form of quadratic programming is suggested to attain the nonlinear displacement control (NDC) of the geometrically nonlinear systems (including prestressed cable structures). The technique preserves the prestress level in the structural bar elements to any level required. The proposed method has been compared with other prior NDC techniques corresponding to the requirements. It shows that the computational results of the current approach are in good response with the previous NDC techniques. The method can exactly achieve the target values without any significant errors for the corresponding outcomes. Simultaneously, the technique keeps the prestress level of the structural members to the targeted level. The proposed approach technique also proved to control both small and large displacement without any remarkable error.

Eddy current de-tumbling large geostationary debris based on feedback linearization model predictive control

In this paper, we investigate the application of Feedback Linearization Model Predictive Control (FLMPC) for the eddy current de-tumbling of space tumbling targets. Based on the Clohessy-Wiltshire (C-W) equation and the Euler rotational equations of motion, the dynamic model of the eddy current de-tumbling process is established, and the error dynamic model is further derived. After that, the safety constraint of the eddy current de-tumbling process is deduced and linearized. On this basis, real-time optimal trajectory is obtained with the optimal equilibrium solver, and FLMPC is proposed to control the system. In order to ensure the simplicity and rapidity of the controller, the feedback linearization input constraint is directly used as the global prediction constraint and the MPC constraint problem is converted into the form of Quadratic Programming (QP) which can be effectively solved. Simulation results show that the proposed algorithm can realize quick and safe de-tumbling of the target with the various constraints ensured and a very small range of steady-state errors.

Model predictive control in optimizing stock portfolio based on stock prediction data using Holt-Winter’s exponential smoothing

This study aims to solve an optimization problem on stock portfolio. There are two main subtopics of this research, namely stock price prediction using Holt Winter’s Exponential Smoothing method and stock portfolio optimization using Model Predictive Control (MPC) method. The steps that have been taken are: collecting and analysing stock price data, determination of smoothing parameters and stock price prediction, calculation of stock price prediction returns, determining the stock portfolio model and system constraints, converting the objective function into a quadratic programming form, and initialization of optimization parameters and program simulation. Based on the simulation results, all control variables are within the predetermined constraints. The application of MPC in optimizing all capital in a portfolio based on stock price predictions can provide satisfactory results. This is represented by the decisions given by the MPC which resulted in the investor’s total capital increasing closer to the expected target.

Voltage and Reactive Power Optimization Using a Simplified Linear Equations at Distribution Networks with DG

In this paper, the VVO (Volt/Var optimization) is proposed using simplified linear equations. For fast computation, the characteristics of voltage control devices in a distribution system are expressed as a simplified linear equation. The voltage control devices are classified according to the characteristics of voltage control and represented as the simplified linear equation. The estimated voltage of distribution networks is represented by the sum of the simplified linear equations for the voltage control devices using the superposition principle. The voltage variation by the reactive power of distributed generations (DGs) can be expressed as the matrix of reactance. The voltage variation of tap changing devices can be linearized into the control area factor. The voltage variation by capacitor banks can also be expressed as the matrix of reactance. The voltage equations expressed as simplified linear equations are formulated by quadratic programming (QP). The variables of voltage control devices are defined, and the objective function is formulated as the QP form. The constraints are set using operating voltage range of distribution networks and the control ranges of each voltage control device. In order to derive the optimal solution, mixed-integer quadratic programming (MIQP), which is a type of mixed-integer nonlinear programming (MINLP), is used. The optimal results and proposed method results are compared by using MATLAB simulation and are confirmed to be close to the optimal solution.

Benders Decomposition-based video bandwidth allocation in mobile media cloud network

Due to the fast growth of wireless multimedia applications, mobile media cloud network is getting more and more popular. In the architecture of mobile media cloud network, the wireless access points are placed on edge of the cloud to provide media services for the mobile users. The video bandwidth allocation managed by a centralized media cloud directly affect the user’s experiences. In this paper, the problem of the video bandwidth allocation in the mobile media cloud access network is explored. Firstly, this paper formulates the problems in bandwidth allocation in the form of quadratic programming in order to maximize the system revenue on the basis of video bitrates capacity between the user and the Mobile Access Edge Point (MAEP). The optimization model could more vividly explicate the trade-off between the expected bitrates capacity and the allocation fairness of User Equipment (UE). Then this paper subdivides the problem into major and minor ones and proposes an algorithm based on Benders’ Decomposition to deal with it. The optimality of the solution is proved by both theoretical and experimental investigations. The error tolerance is analyzed as the algorithm disavows the trade-off between the convergence time and the system performance. The experiments show that the average computing time and confidence interval of the proposed algorithm are lower than Simplex algorithm by 68% and 94% and Barrier algorithm by 46% and 75% respectively at most. Finally, some conclusions are derived from evaluations on the system performance against various network topologies and different values for parameters of the proposed algorithms.

CROSS ENTROPY UNTUK OPTIMASI LAGRANGE MULTIPLIERS PADA SUPPORT VECTOR MACHINES SEBAGAI MODEL PREDIKSI FINANCIAL DISTRESS

The competence in predicting financial distress becomes an important research due tothe advantage in preventing companies financial failure. Besides, financial distressprediction model will give benefit to the investors and creditors. This research developa financial distress prediction model for listed manufacturing companies in Indonesiausing Support Vector Machines (SVM). Mathematically, SVM is formulated in the formof quadratic programming, which requires high computational time in finding theoptimal solution. In this research, Cross Entropy (CE) is used to optimize one of theSVM’s parameter that is Lagrange multipliers to find the optimal solution or nearoptimal solution of dual Lagrange SVM. The accuracy of the prediction model andcomputation time will be compared between standard SVM and CE-SVM. Finally, notethat the CE-SVM can solve classification problems in computing time 9.7 times shorterthan the standard SVM with good accuracy results. Keywords: cross entropy, lagrange multipliers, support vector machines, financialdistress

A Method of Constraint Handling for Speed-Controlled Induction Machines

This paper focuses on the constraint handling for induction machines (IMs) using model predictive control (MPC) to enhance the optimality. Commonly, the constraints of IMs are represented by stator current and voltage limits, which are described as quadratic inequality in dq -frame. Due to the spherical feature, the constraints have to be replaced by approximation by polygon in order to get a standard form of quadratic programming (QP). In this paper, a novel approach is proposed to convert the quadratic inequalities into linear ones without approximation, whereat the inequality is parameter-varying. To tackle this parameter-varying inequality, the multiparametric quadratic program (mp-QP) algorithm for reference tracking is utilized and extended. To ensure the optimization problem solved in real time, an explicit MPC (EMPC) via mp-QP is applied instead of any online numerical solver.

Location choice and risk attitude of a decision maker

In this paper we study the effect of a decision maker׳s risk attitude on the median and center problems, two well-known location problems, with uncertain demand in the mean–variance framework. We provide a mathematical programming formulation for both problems in the form of quadratic programming and develop solution procedures. In particular, we consider the vertex and absolute median problems separately, and identify a dominant set for the center problem. Glover׳s linearization method is applied to solve the vertex median problem. We also develop a branch and bound algorithm and a heuristic as the linearization technique takes too long for the vertex median problem on large networks. A computational experiment is conducted to compare the performance of the algorithms. We demonstrate the importance of taking into account the volatility and correlation structure when a location decision is made. The closest assignment property is also discussed for these location problems under the mean–variance objective.

Multi-label core vector machine with a zero label

Multi-label core vector machine (Rank-CVM) is an efficient and effective algorithm for multi-label classification. But there still exist two aspects to be improved: reducing training and testing computational costs further, and detecting relevant labels effectively. In this paper, we extend Rank-CVM via adding a zero label to construct its variant with a zero label, i.e., Rank-CVMz, which is formulated as the same quadratic programming form with a unit simplex constraint and non-negative ones as Rank-CVM, and then is solved by Frank–Wolfe method efficiently. Attractively, our Rank-CVMz has fewer variables to be solved than Rank-CVM, which speeds up training procedure dramatically. Further, the relevant labels are effectively detected by the zero label. Experimental results on 12 benchmark data sets demonstrate that our method achieves a competitive performance, compared with six existing multi-label algorithms according to six indicative instance-based measures. Moreover, on the average, our Rank-CVMz runs 83 times faster and has slightly fewer support vectors than its origin Rank-CVM.

Applications of L1 regularisation

The lasso algorithm for variable selection in linear models, introduced by Tibshirani, works by imposing an $l_1$~norm bound constraint on the variables in a least squares model and then tuning the model estimation calculation using this bound. This introduction of the bound is interpreted as a form of regularisation step. It leads to a form of quadratic program which is solved by a straight-forward modification of a standard active set algorithm for each value of this bound. Considerable interest was generated by the discovery that the complete solution trajectory parametrised by this bound is piecewise linear and can be calculated very efficiently. Essentially it takes no more work than the solution of either the unconstrained least squares problem or the quadratic program at a single bound value. This has resulted in the study both of the selection problem for different objective and constraint choices and of applications to such areas as data compression and the generation of sparse solutions of very under-determined systems. One important class of generalisation is to quantile regression estimation problems. The original continuation idea extends to these polyhedral objectives in an interesting two phase procedure which involves both the constrained and Lagrangian forms of the problem at each step. However, it is significantly less computationally effective than is the original algorithm for least squares objectives. In contrast, the piecewise linear estimation problem can be solved for each value of the $l_1$~bound by a relatively efficient simplicial descent algorithm, and that this can be used to explore trajectory information in a manner which is at least competitive with the homotopy algorithm in this context. The form of line search used in the descent steps has an important bearing on the effectiveness of the algorithm. A comparison is given between the relative performance of the simplicial descent algorithm used and an interior point method on the piecewise linear estimation problem. References I. Barrodale and F. D. K. Roberts. An improved algorithm for $l_1$ linear approximation. SIAM J. Numer. Anal., 10:839--848, 1973. P. Bloomfield and W. L. Steiger. Least Absolute Deviations. Birkhauser, Boston, 1983. H. D. Bondell and B. J. Reich. Simultaneous regression shrinkage, variable selection, and supervising clustering of predictors with {OSCAR}. Biometrics, 64:115--123, 2008. doi:10.1111/j.1541-0420.2007.00843.x E. Candes and T. Tao. The Dantzig selector: statistical estimation when $p$ is much larger than $n$. Ann. Statist., 35(6):2313--2351, 2007. doi:10.1214/009053606000001523 D. L. Donoho and Y. Tsaig. Fast solution of $l_1$-norm minimization problems when the solution may be sparse. 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Improving the stability level for on-line planning of mobile manipulators

SUMMARYThis paper presents a quadratic programming (QP) form algorithm to realize on-line planning of mobile manipulators with consideration for improving the stability level. With Lie group and screw tools, the general tree topology structure mobile robot dynamics and dynamic stability attributes were analysed. The stable support condition for a mobile robot is constructed not only in a polygonal support region, but also in a polyhedral support region. For a planar supporting region, the tip-over avoiding requirement is formulated as the tip-over prevent constraints with the reciprocal products of the resultant support wrench and the imaginary tip-over twists, which are constructed with the boundaries of the convex support polygon. At velocity level, the optimized resolution algorithm with standard QP form is designed to resolve the inverse redundant kinematics of the Omni-directional Mobile ManipulatorS (OMMS) with stability considerations. Numerical simulation results show that the presented methods successfully improve the stability level of the robot within an on-line planning process.