Quadratic Programming Method Research Articles

Effect of constant eddy viscosity assumption on optimization using a discrete adjoint method

This paper presents a thorough study of the effect of the Constant Eddy Viscosity (CEV) assumption on the optimization of a discrete adjoint-based design optimization system. First, the algorithms of the adjoint methods with and without the CEV assumption are presented, followed by a discussion of the two methods’ solution stability. Second, the sensitivity accuracy, adjoint solution stability, and Root Mean Square (RMS) residual convergence rates at both design and off-design operating points are compared between the CEV and full viscosity adjoint methods in detail. Finally, a multi-point steady aerodynamic and a multi-objective unsteady aerodynamic and aeroelastic coupled design optimizations are performed to study the impact of the CEV assumption on optimization. Two gradient-based optimizers, the Sequential Least-Square Quadratic Programming (SLSQP) method and Steepest Descent Method (SDM) are respectively used to draw a firm conclusion. The results from the transonic NASA Rotor 67 show that the CEV assumption can deteriorate RMS residual convergence rates and even lead to solution instability, especially at a near stall point. Compared with the steady cases, the effect of the CEV assumption on unsteady sensitivity accuracy is much stronger. Nevertheless, the CEV adjoint solver is still capable of achieving optimization goals to some extent, particularly if the flow under consideration is benign.

A structured modified Newton approach for solving systems of nonlinear equations arising in interior-point methods for quadratic programming

AbstractThe focus in this work is on interior-point methods for inequality-constrained quadratic programs, and particularly on the system of nonlinear equations to be solved for each value of the barrier parameter. Newton iterations give high quality solutions, but we are interested in modified Newton systems that are computationally less expensive at the expense of lower quality solutions. We propose a structured modified Newton approach where each modified Jacobian is composed of a previous Jacobian, plus one low-rank update matrix per succeeding iteration. Each update matrix is, for a given rank, chosen such that the distance to the Jacobian at the current iterate is minimized, in both 2-norm and Frobenius norm. The approach is structured in the sense that it preserves the nonzero pattern of the Jacobian. The choice of update matrix is supported by results in an ideal theoretical setting. We also produce numerical results with a basic interior-point implementation to investigate the practical performance within and beyond the theoretical framework. In order to improve performance beyond the theoretical framework, we also motivate and construct two heuristics to be added to the method.

Hierarchical control of differential steering for four-in-wheel-motor electric vehicle.

The purpose of this paper is to study the control of differential steering for four-in-wheel-motor electric vehicles. The so-called differential steering means that the front wheel steering is realized through the differential driving torque between the left and right front wheels. With the consideration of tire friction circle, a hierarchical control method is proposed to realize the differential steering and the constant longitudinal speed simultaneously. Firstly, the dynamic models of the front wheel differential steering vehicle, the front wheel differential steering system and the reference vehicle are established. Secondly, the hierarchical controller is designed. The upper controller is to obtain the resultant forces and resultant torque required by the front wheel differential steering vehicle tracking the reference model through the sliding mode controller. In the middle controller, the minimum tire load ratio is selected as the objective function. Combined with the constraints, the resultant forces and resultant torque are decomposed into the longitudinal and lateral forces of four wheels by the quadratic programming method. The lower controller provides the required longitudinal forces and tire sideslip angles for the front wheel differential steering vehicle model through the tire inverse model and the longitudinal force superposition scheme. Simulation results show that the hierarchical controller can guarantee the vehicle to track the reference model well on both of the high and low adhesion coefficient road with all of the tire load ratios smaller than 1. It can be drawn that the control strategy proposed in this paper is effective.

Determination of Energy-Saving Drying Modes in Vibrofluidized Bed Apparatus

The traditional pectin production technology is highly energy-intensive and environmentally unsafe. One of the possible ways to improve the technological process of pectin production is to dry directly the petine hydrolyzate before it is precipitated with ethyl alcohol. The most effective method of drying pectin hydrolyzate is drying in a vibrofluidized layer of an inert material, which provides high productivity in terms of evaporated moisture per unit volume of the chamber and the quality of the resulting dry product. This paper proposes a method for optimizing the drying process of pectin hydrolyzatein the apparatus of a vibrofluidized layer of an inert material, which makes it possible to determine the values of regime parame- ters at which the drying process proceeds with minimal costs for thermal and electrical energy. The technique is based on the experimentally obtained relationship between the specific productivity of the drying unit and the following operating parameters of the drying process: the air velocity in the drying chamber, the initial air temperature, the specific load related to the area of the gas distribution grid, the initial concentration for dry substances. On the basis of this experimental dependence, the criteria for assessing the reduced costs for heat and electric energy are formalized. A complex criterion for optimizing the drying process in a vibrofluidized bed is formulated, the minimization of which makes it possible to increase the efficiency of the drying process. Restrictions on the ranges of variation of the operating parameters of the drying process are formulated as well. The posed problem of optimization of the drying process in a vibrofluidized bed is solved numerically using the method of sequential quadratic programming and recommendations are formulated on the values of operating parameters for conducting the process in the optimal mode.

Minimax design of two-channel critically sampled graph QMF banks

We address here the issue of designing high spectral selectivity graph filter banks, which require high-degree polynomial approximation. To achieve sharp transition band roll required for high-selectivity, the minimax criterion is used in the design formulation. A constraint optimization method is used for the design process, and a spectral transformation is employed to circumvent the numerical problems that arise with high-degree polynomials. Using the transformation, approximation problem can be recast as an approximation problem with trigonometric polynomials. The transformed constraint optimization problem can be solved using the readily available sequential quadratic programming (SQP) method. High order filters, with low maximum approximation error (MAE) and low maximum reconstruction error (MRE), can be designed with this method. An algorithm is also developed that allows the user to choose design parameters that will give the lowest possible MRE. The method can also be adapted to trade-off between reconstruction quality and spectral selectivity of the resulting filter bank. The suite of techniques presented allow the user to easily shape the spectral response of the filters, to suit the application at hand. Numerous examples, with comparisons, will be presented to demonstrate the versatility of the proposed techniques. Applications to nonlinear approximation and denoising of graph signal will also be considered.

A Hierarchical Motion Planning System for Driving in Changing Environments: Framework, Algorithms, and Verifications

In this article, a hierarchical real-time motion planning system is proposed to solve complex navigation problem in realistic dynamic traffic environments. First, a longitudinal safety spacing model is established to describe the possible collision risk in the lane-changing (LC) process, and a piecewise linearization method is proposed to convert the nonlinear constraints into linear constraints. Second, a decision-making strategy is proposed to decide whether the trajectory should be replanned according to the real-time prediction of the surrounding environments, and select the optimal lane. Third, the quintic B-spline curve method and the quadratic programming method are integrated to obtain the optimal LC trajectory, considering factors of safety, comfort, and efficiency. The terminal position objective function based on the artificial potential field is designed to soften the hard security constraints and guide the LC trajectory toward the center of safety zone. Finally, a model predictive control method based on the kinematics vehicle model is utilized to track the planned trajectory. The experimental results of the miniature intelligent vehicle group verify the real-time performance and effectiveness of the proposed motion planning system.

Receding Horizon D-Optimal Input Design for Identification of Wireless Power Transfer Systems

This paper develops a method of input design for the identification of wireless power transfer (WPT) systems based on receding horizon D-optimization. The dynamic behavior of the system is characterized by a discrete-time, Single-Input, Single-Output (SISO) model, and the associated model parameters are estimated by a recursive least-squares method. To improve the quality of the parameter estimates, the excitation signal of the system is designed based on receding horizon D-optimization. To improve the convergence and efficiency of the input design process, the Sequential Quadratic Programming (SQP) method is employed to solve the receding horizon D-optimization. Numerical and experimental results are presented to demonstrate the effectiveness of the proposed method.

Optimal Maneuvers Around Binary Asteroids Using Particle Swarm Optimization and Machine Learning

Designing optimal transfer trajectories and reference orbit tracking in binary asteroid systems is both challenging and computationally expensive. This paper proposes a method of bypassing the high computational overhead by leveraging a collection of known techniques. Indeed, the proposed framework is based on the combination of artificial intelligence techniques, such as the particle swarm optimization and neural networks, along with the inverse dynamics and the B-splines approximation of the trajectory. The real irregular shapes of the asteroids are considered in the free dynamics of the system, which are obtained via the mutual polyhedral model. The gravitational accelerations of the single asteroids acting on the spacecraft are approximated by using two single-layer neural networks trained via an extreme learning machine. By using a combination of these techniques, the computational time of the whole optimization is decreased from hours to minutes. The proposed approach is applied to the optimal trajectory design around the binary asteroid system, 1999 KW4, showing the feasibility of the proposed optimization approach, reducing the computational effort and time, and increasing the reliability of the obtained results. It is shown through a Monte Carlo analysis that our optimization strategy yields more accurate solutions than other optimization algorithms, such as the interior point and sequential quadratic programming methods, when a random initial guess is provided. Finally, the proposed optimization approach can be used in combination with other techniques to provide a feasible and reliable initial guess for a better solution refinement.t

Vehicle Control Strategy Evaluation Based on the Driving Stability Region

Vehicle stability control strategies can improve driving safety effectively; however, there is still a lack of unified evaluation criteria for different control strategies. This paper proposes a vehicle control strategy evaluation method based on the driving stability region and is analyzed by using direct yaw moment control (DYC) and four-wheel steering (4WS) as examples. Firstly, the five-degree-of-freedom (5DOF) vehicle system models including DYC and 4WS are established, and the effectiveness of the control strategies is verified by nonlinear analysis methods; the dynamic characteristics of the system are also analyzed. Following this, a hybrid algorithm combining the Genetic Algorithm (GA) and Sequential Quadratic Programming (SQP) methods is used to solve the system equilibrium points, and the driving stability regions under different control strategies are obtained. Finally, the driving stability regions are tested based on the CarSim and Simulink simulations, and the control performance is evaluated. The results indicate that DYC and 4WS can improve vehicle stability and expand the range of driving stability regions. When the initial longitudinal velocity is below 30 m/s, the driving stability regions under DYC and 4WS expand to different extents compared to the original driving stability region. The expanded driving stability regions show that the stability region of the vehicle with DYC is larger than that of 4WS; thus, the control effect of DYC is better than that of 4WS. The proposed method can be used to evaluate the effective range of different control strategies.

Dynamic Optimization of Variable Load Process for Combined Heat and Power Unit Based on Sequential Quadratic Programming and Interior Point Method Alternating Solution Method

Aiming at the problem that the modeling and solving method of combined heat and power (CHP) unit variable load control process is challenging to meet the demand for efficient analysis of complex systems, this paper proposes a method based on sequential quadratic programming and interior point method (SQP-IPM) alternating solution for dynamic optimization of the CHP unit variable load process. Firstly, by constructing the CHP unit mechanism model, multi-variable coordination control constraints, and output variable process constraints, the dynamic optimization proposition of the CHP unit variable load control process is formed. Then, the large-scale nonlinear programming (NLP) problem formed by using the orthogonal configuration method to discrete the state and control variables is optimally solved using the IPM-SQP alternating solution method. Further, from the perspective of balancing the accuracy of the solution and computational efficiency, the flexible convergence depth control (CDC) strategy is introduced into the alternative solution method to improve the real-time performance of the algorithm. Finally, the variable load control process of 300MW extraction CHP unit is simulated to verify that the proposed method reduces the calculation time for 12 consecutive variable load scenarios by about 70%, effectively improving the real-time performance of scenario applications.

Variable weight coefficient MPC control strategy for qZSI‐VSG wind power grid‐connected system

AbstractQuasi‐Z source inverters (qZSI) can overcome the disadvantages of conventional wind power systems, because of achieving the balanced DC‐link voltage by using its boost ability. The majority of currently used control methods for conventional inverters are susceptible to parameter changes, and the qZSI are controlled by finite switching sequence model predictive control (FSS‐MPC). In this paper, a Variable weight coefficient Model Predictive Control (V‐MPC) strategy is proposed. First, based on the optimal scheduling algorithm, according to the priority of the controlled object. The proportioning weights of the global feasible solution and the local optimal solution in the algorithm are coordinated. Then, using the equality‐constraints quadratic programming method, according to the relationship between the system frequency and the reference value, increase the weight of the qZSI algorithm or increase the proportion of VSG control to improve the ability to suppress frequency fluctuations. It can give full play to the short‐term power support role of the virtual synchronous wind turbine. The modeling and testing findings validate the suggested control strategy. When compared to the conventional finite control set model predictive control (FCS‐MPC), the V‐MPC can minimize the big store inductance current ripple and have lower THD in the load currents waveform.

Identification of fractional order non– homogeneous Hammerstein-Wiener MISO continuous systems

Aiming at the problem of difficult identification of parameters in fractional non-homogeneous Hammerstein-Wiener nonlinear MISO time-delay continuous systems, an algorithm that can simultaneously identify coupled coefficients, orders, and time-delays in nonlinear fractional-order systems is designed. In this algorithm, a fractional order fitting model is constructed by using the Legendre wavelet operation matrix, and a full-parameter partial derivative model of the time-delay nonlinear system is derived. Second, the sequential quadratic programming (SQP) method is used to simultaneously estimate the non-homogeneous order, delay parameters, and coefficient parameters of the fractional order system. Finally, the effectiveness of the proposed algorithm is demonstrated through an academic example and a two-wall heat conduction system with a nonlinear fractional order system of MISO.

A global-local hybrid strategy with adaptive space reduction search method for structural health monitoring

The difficulty in computational convergence poses challenges of application for traditional heuristic optimization algorithms to solve the optimization-based structural identification problem, especially for the large-scale and complex structural systems where considerable number of unknown parameters and degrees of freedom involved. Unlike the classic identification methods, in this paper, a novel hybrid strategy, coarsely exploring the relatively large search limits with the improved Jaya algorithm and adaptive search space reduction method in the global stage, and then fine-tuning the identified best solution with local optimization methods to the optimum in the local stage, is proposed and evaluated. The improved Jaya algorithm includes three improvements compared to its original version, fuzzy clustering competitive learning, experience learning and Cauchy mutation mechanisms. Gradient based Levenberg-Marquardt method, sequential quadratic programming method and non-gradient based Nelder-Mead simplex method are inserted as local mathematical optimizers to further enhance identification accuracy and efficiency. The superiority of proposed improved Jaya algorithm is validated in optimizing classical and CEC05 benchmark functions by comparing with several state-of-the-art algorithms. Furthermore, the effectiveness of proposed global-local hybrid method is verified by a numerical example of truss structure and an experimental test of the steel grid benchmark structure with incomplete set of noise-polluted measurements. The statistical results show that the improved Jaya algorithm and adaptive search space reduction method combined with sequential quadratic programming can achieve better performance in structural damage identification than other methods.

Fresh Pork as Protein Source in the USDA Thrifty Food Plan 2021: A Modeling Analysis of Lowest-Cost Healthy Diets.

The USDA Thrifty Food Plan (TFP) is an estimate of a lowest-cost healthy diet that meets dietary guidelines while respecting existing eating habits. In the US, the TFP provides the basis for federal food assistance. Included in the TFP are protein foods from both animal and plant sources. The present goal was to explore the place of fresh pork among protein foods in the revised TFP 2021. Our analyses used the same databases and the same quadratic programming (QP) methods as had been used by the USDA to develop the TFP 2021. Dietary intakes came from the National Health and Nutrition Examination Survey (NHANES 2015-16); nutrient composition data came from the Food and Nutrient Database for Dietary Studies (FNDDS 2015-16), and national food prices came from the 2021 TFP report. Amounts and prices were for foods as consumed. Our QP Model 1 used USDA modeling categories to replicate the TFP 2021. The non-poultry meat category was then separated into pork and beef. Model 2 examined whether the TFP 2021 algorithm would select pork or beef. Model 3 sought the lowest cost healthy diet, the same as the TFP 2021. Model 4 replaced beef and poultry with pork; whereas Model 5 replaced pork and poultry with beef. Weekly costs were calculated for a family of four and eight age-gender groups. All models met the nutrient requirements. The market basket cost for a family of four in Model 1 was USD 189.88, compared to the purchase price of USD 192.84 in the TFP 2021. In Model 2, fresh pork was selected preferentially over beef. The lowest-cost healthy food plan in Model 3 increased fresh pork to 3.4 lbs/week. Replacing beef and poultry with pork in Model 4 led to a modest decrease in the weekly cost. Replacing pork and poultry with beef in Model 5 led to a major increase in the weekly cost. We conclude, based on TFP-analogous modeling, that fresh pork is the preferred meat source, providing high-quality protein at a low cost. QP methods, as used in the TFP 2021, are a valuable tool for designing food plans that are affordable, acceptable, and nutrient-rich.

ALESQP: An Augmented Lagrangian Equality-Constrained SQP Method for Optimization with General Constraints

We present a new algorithm for infinite-dimensional optimization with general constraints, called ALESQP. In short, ALESQP is an augmented Lagrangian method that penalizes inequality constraints and solves equality-constrained nonlinear optimization subproblems at every iteration. The subproblems are solved using a matrix-free trust-region sequential quadratic programming (SQP) method that takes advantage of iterative, i.e., inexact linear solvers, and is suitable for large-scale applications. A key feature of ALESQP is a constraint decomposition strategy that allows it to exploit problem-specific variable scalings and inner products. We analyze convergence of ALESQP under different assumptions. We show that strong accumulation points are stationary. Consequently, in finite dimensions ALESQP converges to a stationary point. In infinite dimensions we establish that weak accumulation points are feasible in many practical situations. Under additional assumptions we show that weak accumulation points are stationary. We present several infinite-dimensional examples where ALESQP shows remarkable discretization-independent performance in all of its iterative components, requiring a modest number of iterations to meet constraint tolerances at the level of machine precision. Also, we demonstrate a fully matrix-free solution of an infinite-dimensional problem with nonlinear inequality constraints.

Оптимизация сжатых деревянных стоек переменного сечения по критерию максимума критической нагрузки

The article presents a numerical and analytical solution to the problem of optimizing compressed rods according to the criterion of the maximum critical load with a possible loss of stability in two planes. We consider a wooden bar of rectangular cross section, the height of which varies according to a linear law, and the width is constant. The calculation is performed in an elastic formulation. A constraint on the constancy of the rod mass is introduced. Variable parameters are the ratio of the minimum section height to the maximum, as well as the ratio of the section width to the maximum height. Numerical search for the optimal solution is performed in the MATLAB environment using the method of sequential quadratic programming. It has been established that the use of rods with a cross-sectional height that varies linearly along the length is effective only if the rod is fixed in at least one of the planes according to the “pinched-free end” scheme. It has been established that the increase in the critical load when using rods with a linearly varying cross-sectional height can be up to 22%.

A Concurrent Framework for Constrained Inverse Kinematics of Minimally Invasive Surgical Robots.

Minimally invasive surgery has undergone significant advancements in recent years, transforming various surgical procedures by minimizing patient trauma, postoperative pain, and recovery time. However, the use of robotic systems in minimally invasive surgery introduces significant challenges related to the control of the robot's motion and the accuracy of its movements. In particular, the inverse kinematics (IK) problem is critical for robot-assisted minimally invasive surgery (RMIS), where satisfying the remote center of motion (RCM) constraint is essential to prevent tissue damage at the incision point. Several IK strategies have been proposed for RMIS, including classical inverse Jacobian IK and optimization-based approaches. However, these methods have limitations and perform differently depending on the kinematic configuration. To address these challenges, we propose a novel concurrent IK framework that combines the strengths of both approaches and explicitly incorporates RCM constraints and joint limits into the optimization process. In this paper, we present the design and implementation of concurrent inverse kinematics solvers, as well as experimental validation in both simulation and real-world scenarios. Concurrent IK solvers outperform single-method solvers, achieving a 100% solve rate and reducing the IK solving time by up to 85% for an endoscope positioning task and 37% for a tool pose control task. In particular, the combination of an iterative inverse Jacobian method with a hierarchical quadratic programming method showed the highest average solve rate and lowest computation time in real-world experiments. Our results demonstrate that concurrent IK solving provides a novel and effective solution to the constrained IK problem in RMIS applications.

An effective nonlinear interval sequential quadratic programming method for uncertain inverse problems

An effective nonlinear interval sequential quadratic programming method is proposed to provide an efficient tool for uncertain inverse problems. Assisted by the ideology of sequential quadratic programming and dimension-reduction analysis theory, the interval inverse problem is transformed into several interval arithmetic and deterministic optimizations, which could enhance computational efficiency without losing much accuracy. The novelty of the proposed method lies in two main aspects. First, an alternate updating strategy is proposed to identify the radii and midpoints of the interval inputs in each cycle, which could reduce the number of iterative steps. Second, the standard quadratic models are constructed based on the dimension-reduction analysis results, rather than the second-order Taylor expansion. Therefore, the interval arithmetic can be applied to efficiently calculate the interval response, which avoids the inner optimization. Moreover, a novel iterative mechanism is developed to accelerate the convergence rate of the proposed method. Finally, two numerical examples and an engineering application are adopted to verify its feasibility, accuracy and efficiency.

A Stabilized Sequential Quadratic Programming Method for Optimization Problems in Function Spaces

In this paper, we propose a stabilized sequential quadratic programming (SQP) method for optimization problems in function spaces. A form of the problem considered in this paper can widely formulate many types of applications, such as obstacle problems, optimal control problems, and so on. Moreover, the proposed method is based on the existing stabilized SQP method and can find a point satisfying the Karush-Kuhn-Tucker (KKT) or asymptotic KKT conditions. One of the remarkable points is that we prove its global convergence to such a point under some assumptions without any constraint qualifications. In addition, we guarantee that an arbitrary accumulation point generated by the proposed method satisfies the KKT conditions under several additional assumptions. Finally, we report some numerical experiments to examine the effectiveness of the proposed method.

Stability Control of Quadruped Robot Based on Active State Adjustment.

The quadruped robot has a strong motion performance and broad application prospects in practical applications. However, during the movement of the quadruped robot, it is easy to be affected by external disturbance and environmental changes, which makes it unable to achieve the ideal effect movement. Therefore, it is very important for the quadruped robot to adjust actively according to its own state detection. This paper proposes an active state adjustment control method based on its own state, which can realize disturbance recovery and active environment adaptation. Firstly, the controller is designed according to the physical model of the quadruped robot, and the foot forces are optimized using the quadratic program (QP) method. Then, the disturbance compensation method based on dynamic analysis is studied and combined with the controller itself. At the same time, according to the law of biological movement, the movement process of the quadruped robot is actively adjusted according to the different movement environment, so that it can adapt to various complex environments. Finally, it is verified in a simulation environment and quadruped robot prototype. The results show that the quadruped robot has a strong active disturbance recovery ability and active environment adaptability.