Quadratic Programming Algorithm Research Articles

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.

Optimizing heat source distribution in sintering molds: Integrating response surface model with sequential quadratic programming

The sintering mold imposes strict requirements for temperature uniformity. The mold geometric parameters and the power configuration of heating elements exert substantial influence. In this paper, we introduce an optimization approach that combines response surface models with the sequential quadratic programming algorithm to optimize the geometric parameters and heating power configuration of a heating system for sintering mold. The response surface models of the maximum temperature difference, maximum temperature, and minimum temperature of the sintering area are constructed utilizing the central composite design method. The model's reliability is rigorously confirmed through variance analysis, residual analysis, and generalization capability validation. The models demonstrate remarkable predictive accuracy within the design space. A nonlinear constrained optimization model is established based on the response surface models, and the optimal parameters are obtained after 9 iterations using the sequential quadratic programming algorithm. Under the optimal parameters, the maximum temperature difference is maintained at less than 5 °C, confirming exceptional temperature uniformity. We conduct parameter analysis based on standardized effects to determine the main influencing factors of temperature uniformity, revealing that the distance between adjacent heating rods and the power density of the inner heating rods exert significant influence. Enhanced temperature uniformity can be achieved by adopting a larger distance between heating rods and configuring the power density of the heating rods to a relatively modest level. This work introduces a practical approach to optimize the heating systems for sintering molds, with potential applications in various industrial mold optimization.

On the parallel solution of hydro-mechanical problems with fracture networks and contact conditions

The paper presents a numerical method for simulating flow and mechanics in fractured rock. The governing equations that couple the effects in the rock mass and in the fractures are obtained using the discrete fracture-matrix approach. The fracture flow is driven by the cubic law, and the contact conditions prevent fractures from self-penetration. A stable finite element discretization is proposed for the displacement-pressure-flux formulation. The resulting nonlinear algebraic system of equations and inequalities is decoupled using a robust iterative splitting into the linearized flow subproblem, and the quadratic programming problem for the mechanical part. The non-penetration conditions are solved by means of dualization and an optimal quadratic programming algorithm. The capability of the numerical scheme is demonstrated on a benchmark problem for tunnel excavation with hundreds of fractures in 3D. The paper's novelty consists in a combination of three crucial ingredients: (i) application of discrete fracture-matrix approach to poroelasticity, (ii) robust iterative splitting of resulting nonlinear algebraic system working for real-world 3D problems, and (iii) efficient solution of its mechanical quadratic programming part with a large number of fractures in mutual contact by means of own solvers implemented into an in-house software library.

A Hierarchical Trajectory Planning Algorithm for Automated Guided Vehicles in Construction Sites

Herein, to address the challenges faced by Automatic Guided Vehicles (AGVs) in construction site environments, including heavy vehicle loads, extensive road search areas, and randomly distributed obstacles, this paper presents a hierarchical trajectory planning algorithm that combines coarse planning and precise planning. In the first-level coarse planning, lateral and longitudinal sampling is performed based on road environment constraints. A multi-criteria cost function is designed, taking into account factors such as deviation from the road centerline, shortest path cost, and obstacle collision safety cost. An efficient dynamic programming algorithm is used to obtain the optimal path. Considering nonholonomic constraints of vehicles, eliminating inflection points using improved B-Spline path fitting, and a quadratic programming algorithm is proposed to enhance path smoothness, completing the coarse planning algorithm. In the second-level precise planning, the coarse planning path is used as a reference line, and small-range sampling is conducted based on AGV motion constraints, including lateral displacement and longitudinal velocity. Lateral and longitudinal polynomials are constructed. To address the impact of randomly appearing obstacles on vehicle stability and safety, an evaluation function is designed, considering factors such as jerk and acceleration. The optimal trajectory is determined through collision detection, ensuring both safe obstacle avoidance and AGV smoothness. Experimental results demonstrate the effectiveness of this method in solving the path planning challenges faced by AGVs in construction site environments characterized by heavy vehicle loads, extensive road search areas, and randomly distributed obstacles.

Optimization of surface texture distribution on the thrust bearing using the mass-conserving cavitation boundary condition: Theory and experiments

This study developed a numerical optimization model for the texture distribution in thrust bearings, employing the flat-headed chevron and circular dimple, and utilizing a mass-conserving cavitation boundary. A hybrid of the genetic algorithm and sequential quadratic programming algorithm is utilized. The results indicate the highest load-carrying capacity can be obtained by optimizing the texture distribution based on the flat-headed chevron. The primary mechanism is that the optimal distribution can efficiently harness the collective effect of texture, thereby effectively building up pressure. The optimal distributions of the flat-headed chevron and circular dimples exhibit asymmetric chevron and herringbone shapes, respectively. Furthermore, verification experiments show that the optimal distribution can shift the transition point to a lower rotation speed and higher normal load.

MIMO radar partially correlated waveform design based on chirp rate diversity

Waveform design is a significant topic in multiple-input-multiple-output (MIMO) radar. In this paper, we address the problem of waveform design for colocated narrowband MIMO radar transmit beampattern synthesis. The existing methods have not comprehensively considered the transmit beampattern synthesis under multiple practical constraints, such as constant modulus constraint, Doppler tolerance, high range resolution and low auto-correlation sidelobe. We consider these practical constraints and propose a novel chirp rate diversity-based linear frequency modulated (CRD-LFM) waveform design for approximating the desired MIMO radar transmit beampattern. To tackle the problem, we improve the classical two-step approach. Firstly we design the covariance matrix using the existing closed-form solution. Then we model the problem of obtaining the waveforms from the covariance matrix as a nonlinear optimization problem, and we utilize the Sequential Quadratic Programming (SQP) algorithm to solve it. The simulations demonstrate that the waveforms obtained by this method can well approximate the desired transmit beampattern and have higher range resolution. Furthermore, we verify that the suppression of auto-correlation sidelobe can be achieved using amplitude weighting, which is easily realizable in practical engineering.

A robust nonlinear tracking MPC using qLPV embedding and zonotopic uncertainty propagation

In this paper, we propose a novel Nonlinear Model Predictive Control (NMPC) framework for tracking for piece-wise constant reference signals. The main novelty is the use of quasi-Linear Parameter Varying (qLPV) embeddings in order to describe the nonlinear dynamics. Furthermore, these embeddings are exploited by an extrapolation mechanism, which provides the future behaviour of the scheduling parameters with bounded estimation error. Therefore, the resulting NMPC becomes computationally efficient (comparable to a Quadratic Programming algorithm), since, at each sampling period, the predictions are linear. Benefiting from artificial target variables, the method is also able to avoid feasibility losses due to large set-point variations. Robust constraint satisfaction, closed-loop stability, and recursive feasibility certificates are provided, thanks to uncertainty propagation zonotopes and parameter-dependent terminal ingredients. A benchmark example is used to illustrate the effectiveness of the method, which is compared to state-of-the-art techniques.

Research on optimization method for flyby observation mission adapted to satellite on-board computation

In this paper, the optimization problem of orbital transfer strategy for orbital flyby observation missions is studied. A hybrid optimization method is proposed, which is improved to make it more suitable for satellite on-board computing. This new algorithm is designed to solve the initial value sensitivity problem of the sequential quadratic programming algorithm (SQP). It is consisted of the depth-first search algorithm (DFS) and the SQP algorithm and thus has the characteristics of fast convergence, high reliability, and good robustness. With this method, the DFS with a large step size is calculated first, and then the optimal value in the calculation result is used as the initial value of the SQP algorithm for further optimization. This method can obtain the approximate optimal solution available in engineering. The numerical simulation of an orbital transfer optimization problem is set to verify the effectiveness of the new hybrid algorithm. The simulation results compared with the genetic algorithm (GA) show that the proposed hybrid algorithm can effectively reduce the on-board resource occupation when getting similar results and thus can meet the needs of satellite on-board computing.

Design, optimization and verification of a conical guiding origami mechanism for underwater docking station

Underwater docking station requires a conical guiding device with a large tolerance capacity and smaller volume to recover unmanned underwater vehicles (UUVs). Here, this paper innovatively introduces a conical guiding origami mechanism designed by an array and rotation approach based on a rigid origami mechanism. The Jacobian matrix method systematically calculates the degree of freedom (DOF) of the device. The variation function of dihedral angle in the folding process of the origami mechanism is derived, and the kinematics model is established within the Cartesian coordinate system. Based on this model, we established a mathematical model for optimizing the origami mechanism by considering number of units and unit volume as the design variables, subject to minimizing the underwater flow area and length. The sequential quadratic programming algorithm is employed to identify the optimum design variables. Subsequently, based on optimized results, collision simulation is carried out, and a conical guiding device tailored for an underwater docking station is successfully designed. The proposed device can be used as an underwater docking station to recover UUVs for ocean exploration. The proposed device has a large tolerance capacity, minimal shrinkage state cross-sectional area and length, excellent hydrodynamic performance, and a high spatial utilization rate.

Dynamic price optimization of a solar integrated cogeneration system considering uncertainties of building demands

Introducing renewable and high-efficiency devices into conventional cogeneration systems has the potentials to reduce fossil fuel consumption and mitigate environmental issues. This study aims to incorporate solar power and thermal energy into the power and waste heat generated by the gas turbine, respectively, while utilizing a double-effect absorption heat pump to meet the total heat demands. Following the creation of thermodynamic models, a trading mechanism is introduced involving an operating participant known as the product seller, which is analogous to electricity companies in power trading models. To maximize the interests of the participants with different confidence levels, the master-slave game is employed, using Genetic and Quadratic programming algorithms. The hourly outputs of devices and responded demands are evaluated based on the dynamic purchasing and selling price of products. The results indicate that the optimal interest of the cogeneration system is the lowest among all the participants. The power proportions from gas turbine and power grid exceed 60 %, while the contribution of gas turbine decreases by 11.0 % due to the lower heat demands caused by reduced confidence level. Overall, this study offers valuable insights into the market-oriented development of solar assisted cogeneration systems.