Quadratic Programming Algorithm Research Articles

A computational approach for phase-field model of quasi-brittle fracture under dynamic loading

AbstractA computational model is formulated for studying dynamic crack propagation in quasi-brittle materials exposed to time-dependent loading conditions. Under such conditions, inertial effects of structural components play an important role in modelling crack propagation problems. The computational model is proposed within the theory of regularised cracks which uses a damage-like internal variable. Here, fracture considers phase-field damage which gives rise to a material degradation in a narrow material strip defining the regularised crack. Based on the energy formulation using the Lagrangian of the system, the proposed computational approach introduces a staggered scheme adopted to solve the coupled system and providing it in a variational form within the time stepping procedure. The numerical data are obtained by quadratic programming algorithms implemented together with a finite element code.

Event-Triggered Neural Adaptive Distributed Cooperative Control for the Multi-Tug Towing of Unactuated Offshore Platform with Uncertainties and Unknown Disturbances

An event-triggered neural adaptive cooperative control is proposed for the towing system (TS) with model parameter uncertainties and unknown disturbances. Different from ordinary multi-vessel formation control, the tugs and unactuated offshore platform in the TS are connected together by towlines, and the resultant tension of the towlines serves as the actual drag force for the platform. Initially, based on the radial basis function neural network (RBFNN), an adaptive RBFNN is designed to compensate unknown disturbances and model parameter uncertainties of the TS, and we use minimal learning parameter (MLP) algorithm to reduce the online learning parameters of adaptive RBFNN. Combined with dynamic surface technology and event-triggered control (ETC) mechanism, an event-triggered neural adaptive virtual controller is designed to obtain the desired drag force of the platform. According to the quadratic programming algorithm, the desired drag force is allocated as the desired tensions of towlines. Subsequently, the desired towline length and the desired position information of the tugs are obtained sequentially through the towline model and the position relationship between the tugs and the platform. Then, according to the desired positions of tugs, an event-triggered neural adaptive distributed cooperative controller is designed for achieving the multi-tug towing of the offshore platform. The ETC mechanism is introduced to reduce the communication burden within the TS and the execution frequency of the tugs’ thrusters. Finally, the stability of the closed-loop system is proven using the Lyapunov theory, and the ETC mechanism proves that no Zeno behavior occurs. The effectiveness of the ETC mechanism and the MLP-based adaptive RBFNN on the controllers of TS is verified through simulations and comparison analysis.

An Obstacle Avoidance Trajectory Planning Methodology Based on Energy Minimization (OTPEM) for the Tilt-Wing eVTOL in the Takeoff Phase

Electric tilt-wing flying cars are an efficient, economical, and environmentally friendly solution to urban traffic congestion and travel efficiency issues. This article addresses the high energy consumption and obstacle interference during the takeoff phase of the tilt-wing eVTOL (electric Vertical Takeoff and Landing), proposing a trajectory planning method based on energy minimization and obstacle avoidance. Firstly, based on the dynamics analysis, the relationship between energy consumption, spatial trajectory, and obstacles is sorted out and the decision variables for the trajectory planning problem with obstacle avoidance are determined. Secondly, based on the power discretization during the takeoff phase, the energy minimization objective function is established and the constraints of performance limitations and spatial obstacles are derived. Thirdly, by integrating the optimization model with the SLSQP (Sequential Least Squares Quadratic Programming algorithm), the second-order sequential quadratic programming model and decision variable update equations are derived, establishing the solution process for the trajectory planning problem of the tilt-wing eVTOL takeoff with obstacle avoidance. Finally, the Airbus Vahana A3 is taken as an example to verify and validate the effectiveness, stability, and robustness of the model and optimization algorithm proposed. The validation results show that the OTPEM (obstacle avoidance trajectory planning methodology based on energy minimization) can effectively handle changes in the takeoff end state and exhibits good stability and robustness in different obstacle environments. It can provide a certain reference for the three-dimensional obstacle avoidance trajectory planning of Airbus Vahana A3 and other tilt-wing eVTOL trajectory planning problems.

An Obstacle Avoidance Trajectory Planning Methodology Based on Energy Minimization (OTPEM) for the Tilt-Wing eVTOL in the Takeoff Phase

Electric tilt-wing flying cars are an efficient, economical, and environmentally friendly solution to urban traffic congestion and travel efficiency issues. This article addresses the high energy consumption and obstacle interference during the takeoff phase of the tilt-wing eVTOL (electric Vertical Takeoff and Landing), proposing a trajectory planning method based on energy minimization and obstacle avoidance. Firstly, based on the dynamics analysis, the relationship between energy consumption, spatial trajectory, and obstacles is sorted out and the decision variables for the trajectory planning problem with obstacle avoidance are determined. Secondly, based on the power discretization during the takeoff phase, the energy minimization objective function is established and the constraints of performance limitations and spatial obstacles are derived. Thirdly, by integrating the optimization model with the SLSQP (Sequential Least Squares Quadratic Programming algorithm), the second-order sequential quadratic programming model and decision variable update equations are derived, establishing the solution process for the trajectory planning problem of the tilt-wing eVTOL takeoff with obstacle avoidance. Finally, the Airbus Vahana A3 is taken as an example to verify and validate the effectiveness, stability, and robustness of the model and optimization algorithm proposed. The validation results show that the OTPEM (obstacle avoidance trajectory planning methodology based on energy minimization) can effectively handle changes in the takeoff end state and exhibits good stability and robustness in different obstacle environments. It can provide a certain reference for the three-dimensional obstacle avoidance trajectory planning of Airbus Vahana A3 and other tilt-wing eVTOL trajectory planning problems.

Design and Research of a Strain Elastic Element with a Double-Layer Cross Floating Beam for Strain Gauge Wireless Rotating Dynamometers.

Cutting force is one of the most basic signals that can reflect the information of the cutting process, so it is very necessary to study the strain elastic element of strain gauge wireless rotating dynamometers. This paper proposes a strain elastic element with a double-layer cross floating beam that can be applied to the strain gauge wireless rotating dynamometer, which can simultaneously obtain the four-component cutting force/torque information of FX, FY, FZ, and MZ. Based on the proposed strain elastic element, a compact strain gauge wireless rotating dynamometer is designed, which is composed of a tool holder, upper connection flange, strain elastic element, lower connection flange, tool base, and data acquisition and wireless transmission system. The static model of the double-layer cross floating beam on the strain elastic element is established by the segmented rigid body method, and the relationships between the material, force, structural parameters, and the strain and deformation of the floating beam are obtained. The static model is consistent with the finite element solution, which proves the rationality of the static model. Based on the established static model, the sequential quadratic programming algorithm is used to optimize the structural parameters of the double-layer cross floating beam to maximize the sensitivity of the floating beam. The overall structure of the strain elastic element is analyzed by finite element software, and the strain of the structure under simulation conditions is obtained, which provides a reference for subsequent calibration tests and circuit design. The calibration matrix and dynamic performance of the strain elastic element are obtained by the static calibration test, dynamic calibration test, and cutting test. The results show that the proposed strain elastic element has high sensitivity and low cross-sensitivity error, and can be applied to the strain gauge wireless rotating dynamometer to measure medium- and low-speed cutting forces.

A PWR core power control using optimized PID controller with SQP based on control rod positioning and variable coolant flow rate

To ensure safety and stability, it is optimal for nuclear power plants to operate at their nominal power level. However, to meet the needs of power systems, NPPs must also be able to adjust their output for load-following purposes. This necessitates finding an effective control algorithmto maintain stable/safe operating conditions. The current study investigates the performance of PID controllersoptimized using Sequential Quadratic Programming algorithm and applied using two control techniques: control rod positioning and variable coolant flow rate. Simulation is done using model of four-loop Westinghouse PWR-1200 MW nuclear reactor. The proposed controller’s performance is evaluated in three scenarios:sudden control rod withdrawal, sudden change in coolant inlet temperature, and linear load tracking. The influences of model parametric uncertainty are also investigated. Simulation results revealed that the performance of the control algorithm applied using variable coolant flow rate was superior to the one usingcontrol rod positioning.

Fatigue-resistant design of carbon/epoxy composites based on a failure tensor polynomial model by particle swarm optimization-sequential quadratic programming algorithm

This article introduces a design procedure to find the optimum fiber orientations of carbon/epoxy composite laminates for fatigue life advancement. The approach incorporates a fatigue failure tensor polynomial model and employs a hybrid algorithm, combining particle swarm optimization and sequential quadratic programming. Firstly, material properties of quasi-static and fatigue of the carbon/epoxy composites, fabricated by the vacuum-assisted resin transfer molding method, were determined to be used in the model. Various design problems involving two optimization scenarios were then solved using the hybrid algorithm. The algorithm’s performance was also evaluated by specific test problems, confirming its speed and robustness. The optimally fiber-oriented carbon/epoxy composite laminates having maximum fatigue lives were obtained for many critical in-plane cyclic loading cases. To validate the proposed design procedure, two optimum designs were experimentally verified under uniaxial loading conditions. The results indicated a good correlation between the estimated fatigue life of the optimally designed laminates and experimental data. This methodology offers a promising approach for the design of carbon/epoxy composite laminates with superior fatigue strength, particularly significant in specific industrial applications.

A Stochastic Inexact Sequential Quadratic Optimization Algorithm for Nonlinear Equality-Constrained Optimization

A stochastic algorithm is proposed, analyzed, and tested experimentally for solving continuous optimization problems with nonlinear equality constraints. It is assumed that constraint function and derivative values can be computed but that only stochastic approximations are available for the objective function and its derivatives. The algorithm is of the sequential quadratic optimization variety. Distinguishing features of the algorithm are that it only employs stochastic objective gradient estimates that satisfy a relatively weak set of assumptions (while using neither objective function values nor estimates of them) and that it allows inexact subproblem solutions to be employed, the latter of which is particularly useful in large-scale settings when the matrices defining the subproblems are too large to form and/or factorize. Conditions are imposed on the inexact subproblem solutions that account for the fact that only stochastic objective gradient estimates are employed. Convergence results are established for the method. Numerical experiments show that the proposed method vastly outperforms a stochastic subgradient method and can outperform an alternative sequential quadratic programming algorithm that employs highly accurate subproblem solutions in every iteration. Funding: This material is based upon work supported by the National Science Foundation [Awards CCF-1740796 and CCF-2139735] and the Office of Naval Research [Award N00014-21-1-2532].

High-Speed Motion Planning with Object Acceleration Constraint for Industrial Robots

In this paper, we propose a new approach to efficiently plan trajectories for industrial robots, where total trajectory time is reduced while limiting the robot end-effector acceleration to a safe threshold, which guarantees an object to be transported safely without damage or spills. We also propose to solve the optimization problem in two steps by utilizing both the quadratic programming algorithm and sparse sequential quadratic programming method. The proposed two-step procedure empirically proves that computing time of solving the optimization problem is significantly reduced. Effectiveness of the proposed approach was verified in Drake, where the obtained results are highly promising.

Fault-Tolerant Control of Autonomous Underwater Vehicle Actuators Based on Takagi and Sugeno Fuzzy and Pseudo-Inverse Quadratic Programming under Constraints.

Autonomous Underwater Vehicles (AUVs) play a significant role in ocean-related research fields as tools for human exploration and the development of marine resources. However, the uncertainty of the underwater environment and the complexity of underwater motion pose significant challenges to the fault-tolerant control of AUV actuators. This paper presents a fault-tolerant control strategy for AUV actuators based onTakagi and Sugeno (T-S) fuzzy logic and pseudo-inverse quadratic programming under control constraints, aimed at addressing potential actuator faults. Firstly, considering the steady-state performance and dynamic performance of the control system, a T-S fuzzy controller is designed. Next, based on the redundant configuration of the actuators, the propulsion system is normalized, and the fault-tolerant control of AUV actuators is achieved using the pseudo-inverse method under thrust allocation. When control is constrained, a quadratic programming approach is used to compensate for the input control quantity. Finally, the effectiveness of the fuzzy control and fault-tolerant control allocation methods studied in this paper is validated through mathematical simulation. The experimental results indicate that in various fault scenarios, the pseudo-inverse combined with a nonlinear quadratic programming algorithm can compensate for the missing control inputs due to control constraints, ensuring the normal thrust of AUV actuators and achieving the expected fault-tolerant effect.

Training mode of university dance performers based on sequential quadratic programming algorithm

Dance performance is an art form, which needs to cultivate students’ dance skills, artistic accomplishment and stage performance ability. Sequential quadratic programming algorithm is an optimization algorithm that can be used to solve complex optimization problems. In this paper, Sequential Quadratic Programming (SQP) is applied to explore the training mode of dance performers in colleges to help dance performers develop the optimal training plan and program. Aiming at the problems existing in the training mode of dance performance talents in colleges, this paper put forward an optimization method based on SQP algorithm, and implemented its optimization scheme in actual colleges. In the planning of dance performance talent training mode, particle swarm optimization (PSO) is used to optimize SQP algorithm, so that it can have higher planning efficiency. This paper studied the goal and index system of the training of dance performance talents in colleges, generated a personalized training program, and further improved the scientific and practical effectiveness of the training mode. This paper investigated the current situation of dance performance talent training in several dance schools in a certain province of China. The survey data include practical curriculum planning, teachers’ teaching philosophy and teaching content. Combined with SQP algorithm, the teaching and training program is optimized. After evaluation, it can be concluded that the SQP algorithm optimized by PSO shows good stability and accuracy. It can calculate the optimal solution of the cultivation scheme, and when calculating the optimal solution, the running time of the Central Processing Unit (CPU) was only 5.6 s, which can further improve the efficiency of the planning. Finally, through the satisfaction and resource utilization test, it can be found that the number of people who are very satisfied with the teaching content of the dance performance talent training program optimized by SQP increased from 38.4% to 52.4%. After optimization, the average utilization rate of teaching resources reached 88.1%. It can be concluded that SQP algorithm can provide scientific basis for dance education institutions to improve the training mode of dance talents. This can help dance education institutions better improve the training mode, and improve the overall quality and dance skills of dance students.

Adaptive Nonsingular Fast Terminal Sliding Mode-Based Direct Yaw Moment Control for DDEV under Emergency Conditions

Adaptive Nonsingular Fast Terminal Sliding Mode-Based Direct Yaw Moment Control for DDEV under Emergency Conditions

A Reentry Trajectory Planning Algorithm via Pseudo-Spectral Convexification and Method of Multipliers

The reentry trajectory planning problem of hypersonic vehicles is generally a continuous and nonconvex optimization problem, and it constitutes a critical challenge within the field of aerospace engineering. In this paper, an improved sequential convexification algorithm is proposed to solve it and achieve online trajectory planning. In the proposed algorithm, the Chebyshev pseudo-spectral method with high-accuracy approximation performance is first employed to discretize the continuous dynamic equations. Subsequently, based on the multipliers and linearization methods, the original nonconvex trajectory planning problem is transformed into a series of relaxed convex subproblems in the form of an augmented Lagrange function. Then, the interior point method is utilized to iteratively solve the relaxed convex subproblem until the expected convergence precision is achieved. The convex-optimization-based and multipliers methods guarantee the promotion of fast convergence precision, making it suitable for online trajectory planning applications. Finally, numerical simulations are conducted to verify the performance of the proposed algorithm. The simulation results show that the algorithm possesses better convergence performance, and the solution time can reach the level of seconds, which is more than 97% less than nonlinear programming algorithms, such as the sequential quadratic programming algorithm.

Energy management for scalable battery swapping stations: A deep reinforcement learning and mathematical optimization cascade approach

The rapid growth of electric vehicles is driving the expansion of scalable Battery Swapping Stations (BSSs) to meet the demand for fast charging. However, existing BSS energy management struggles to adapt to the changes in battery counts online, the uncertainty of electricity prices and battery demand, as well as the complexity of demand response (DR). To address these issues, we propose a cascading approach that combines Deep Reinforcement Learning (DRL) with Mathematical Optimization (MO). Firstly, our method employs a two-layer optimization framework and establishes a BSS model. The upper controller uses DRL to make sequential decisions on total power for each time slot, addressing sequential decision-making under uncertainty. The lower controller uses MO to allocate total power to each charging bay for a single time slot, addressing space complexity. Secondly, we tailor proximal policy optimization algorithms and mixed-integer quadratic programming algorithms for BSS DR. The DRL is universally adaptable to scalable BSS, while the MO automatically generates and solves optimization models based on the working charging bay count. The proposed method is at least 33 times faster than existing methods and performs well in scalable BSSs under uncertain conditions. It can converge within a typical BSS DR scheduling slot of 15 min based on an i7-8950H CPU, even for a BSS with 3200 charging bays.

Joint beamforming and power splitting design for MISO downlink communication with SWIPT: a comparison between cell-free massive MIMO and small-cell deployments

Simultaneous wireless information and power transfer (SWIPT) has been advocated as a highly promising technology for enhancing the capabilities of 5G and 6G devices. However, the challenge of dealing with large propagation path loss poses a significant hurdle. To address this issue, massive multiple-input multiple-output (MIMO) is employed to enhance the efficiency of SWIPT in cellular-based networks with multiple small cells, and especially increase the energy for cell-edge users. In addition, by leveraging a large set of spatially distributed base stations to collaboratively serve SWIPT-enabled user equipment, the cell-free massive MIMO has the potential to provide even better performance than the conventional small-cell systems. In this work, we extend the investigation to include the application of SWIPT technology with alternating current (AC) logic in the cell-free networks and the small-cell networks and propose joint beamforming and power splitting optimization frameworks to maximize the system sum-rate, subject to the constraints on harvested energy, AC logic energy supply, and total transmit power. The optimization problem is shown to be non-convex, posing a significant challenge. To address this challenge, we resort to a two-stage decomposition approach. Specifically, we first introduce quadratic transform-based fractional programming (FP) algorithms to iteratively solve the non-convex optimization problems in the first stage, achieving near-optimal solutions with low time complexities. To further reduce the complexities, we also incorporate conventional schemes such as zero forcing, maximum ratio transmission, and signal-to-leakage-and-noise ratio for the design of beamforming vectors. Second, to determine the optimal power splitting ratio within the framework, we develop a one-dimensional (1-D) search algorithm to tackle the single variable optimization problem reduced in the second stage. These algorithms are then evaluated in the context of cell-free MIMO and small-cell networks with numerical experiments. The results show that the FP-based algorithms can consistently outperform those utilizing the conventional beamforming schemes, and the solutions of this work can achieve up to fivefold improvement in the system sum-rate than the small-cell counterpart while providing different but comparable performance trends in energy harvesting (EH).

Real‐time multi‐objective speed planning ATO considering assist driving for subway

AbstractSpeed curve planning is one of the most important functions of automatic train operation (ATO). To improve the real‐time optimization capability and driver‐friendliness of the existing ATO, an extended ATO framework considering both automatic driving and assisted driving is designed. A multi‐objective optimization model based on quadratic programming is established considering energy‐saving, punctuality, and comfort. However, due to the influence of the weight of multi‐objectives, this method cannot directly obtain the speed curve satisfying the trip time constraint. Further, based on the analysis about the weight of multi‐objects, a time‐constrained quadratic programming algorithm is proposed. With the proposed method, the speed curve can be calculated in real‐time both before operations and during operations. For the former, time‐varying train mass and trip time are considered to guarantee an optimal solution. For the latter, deviations, delays, and maloperations on the way are corrected. Simulation experiments verify the solvability and real‐time performance of the proposed method. In particular, compared with the dynamic programming and (mixed‐integer linear programming) MILP method, the proposed method is more energy‐efficient and easier to be followed by the driver. In addition, a prototype is developed for commercial tests on a Beijing subway line. The relevant performance is verified in commercial tests.

Surge-Elimination Strategy for Aero-Engine Transient Control

Abstract The fundamental principle of the transient state control method for turbofan engines, which is based on the acceleration ratio of high-pressure rotational speed (N-dot), involves sacrificing a portion of the safety margin to obtain satisfactory acceleration performance. However, it could induce surge in the engine's compressor. To prevent the destructive damage caused by surge to both the engine and its components, a surge-elimination control strategy for the engine based on an N-dot controller is proposed. First, the engine mathematical model, which incorporates the effects of engine volumetric dynamics, stall zone characteristics, and combustion chamber flameout characteristics, is established to simulate surge mechanism. Subsequently, the acceleration schedule of the N-dot is calculated by employing sequential quadratic programming (SQP) algorithm to solve the multiconstraint optimization problem, while designing the transition state controller of N-dot based on a high-order filter. Finally, the surge detection logic and surge-elimination strategy based on the μ-correction method are proposed and designed to realize active control of surge elimination. The simulation results demonstrate that the N-dot control method offers significant advantages in mitigating the steady-state errors resulting from inevitable engine degradations. The surge state is effectively suppressed by the proposed surge-elimination control method, and the surge duration is significantly shorten during the acceleration phases. Furthermore, compared to the one without any surge-elimination control, the proposed method decreases the acceleration time by 5.53%.

Full-period operation optimization of the semi-regenerative reactor based on dehydrogenation reaction and deactivation kinetics

Semi-regenerative reactors are adopted in many catalytic processes. Based on industrial data, a one-dimensional pseudo-homogeneous reactor model was established for the semi-regenerative reactor of the dehydrogenation of heavy paraffins. The validation results show high accuracy of the model prediction. The Sequential Quadratic Programming (SQP) algorithm was employed for the full-period operation optimization of the reactor, resulting in a 3.04% increase in the yield of mono-olefins, but the optimized operation conditions are not consistent with common combination according to the practical production experience described in the literature. Further investigations for semi-regenerative reactors with different dehydrogenation systems show that the optimized combination of operation conditions in a full period is dependent on the depth of dehydrogenation, the rate of catalyst deactivation, and the duration of the period.

Model-Scale Evaluation of Autonomous Ship Landing Guidance and Control Modes

This paper presents the results of an extensive model-scale experimental evaluation of autonomous ship landing guidance and control modes, with flight tests performed in the Maneuvering and Seakeeping (MASK) Basin at the U.S. Naval Surface Warfare Center Carderock Division. The experiments were performed using a commodities-based multirotor unmanned aerial vehicle (UAV) operating from a 20-ft-long model scale ship subject to scaled wave conditions. During testing, two separate guidance algorithms were evaluated: a quadratic programming (QP) based landing algorithm that plans the trajectory to a forecasted deck state and a simpler “baseline??? method that tracks deck motions while closing the distance between the aircraft and deck at a constant rate. Both algorithms commanded a Froude-scaled explicit model following control law, and the control law parameters were modified to progressively degrade aircraft tracking bandwidths. The results showed that the predictive capabilities of the QP algorithm allowed more direct landing paths to be planned when compared to the baseline algorithm and also allowed the QP algorithm to land with lower tracking bandwidths. But while the QP algorithm performed well in the majority of cases, there were several landings where a combination of poor deck state predictions and how the QP algorithm utilizes predictions to choose a land time resulted in significant terminal velocity and attitude errors. The baseline guidance algorithm, on the other hand, proved to be both simple and reliable when the UAV was in high bandwidth configurations but required a high reference tracking bandwidth.

A Robot Positional Error Compensation Method Based on Improved Kriging Interpolation and Kronecker Products

This paper proposes a stable and high-accuracy model-free calibration method for unopened robotic systems, which can significantly improve the robot positional accuracy. Two improvements are made to the existing kriging-based error compensation method to achieve robustness/practicality enhancement goals: (1) The semi-variogram model is solved using the sequential quadratic programming (SQP) algorithm, and the distance weight coefficients are added to the objective function. The accuracy of semi-variogram modeling is guaranteed, thereby improving the performance and stability of error compensation. (2) The hand-eye (the pose matrix between the robot base and the laser tracker) and the tool center point (TCP) position are calibrated based on Kronecker products without relying on the spatial analyzer (SA) software to construct the robot base coordinate system separately. Thus, the calibration accuracy and efficiency are significantly improved. Experiments have been conducted, and the results reveal that the proposed method can significantly reduce the robot positional error. Furthermore, the proposed approach performs better than the existing kriging-based error compensation method without Kronecker products. The maximum, mean, and root mean square (RMS) values of the absolute positional errors are reduced by 34.48%, 8.09%, and 10.05%, respectively.