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This article focuses on the problem of robust adaptive safety control of a class of nonlinear systems with parametric uncertainties. Two novel definitions, that is, robust adaptive control Lyapunov function (RACLF) and robust adaptive control barrier function (RACBF) are introduced in this article. Also, an estimation of unknown parameters is obtained based on multiple identification models, state predictors and a logic switching mechanism. The switching mechanism plays a vital role in enhancing the transient properties of nonlinear systems. Meanwhile, a safe motion framework for differential robots is provided based on the existence of parametric uncertainties in RACLF and RACBF, and a safe and stable controller is obtained by solving quadratic programming. Finally, simulation results of differential robot capable of safe motion in space are presented to verify the validity of the design method. [ABSTRACT FROM AUTHOR]

This paper proposes a new algorithm based on sensitivity analysis and the Wolfe method to solve a sequence of parametric quadratic programming (QP) problems such as those that arise in quadratic model predictive control (QMPC). The Wolfe method, based on Karush–Kuhn–Tucker conditions, has been used to convert parametric QP problems to parametric linear programming (LP) problems, and then the sensitivity analysis is applied to solve the sequence of the parametric LP problems. This strategy obtains sensitivity analysis‐based QMPC (SA‐QMPC) algorithm. It is proved that the computational complexity of SA‐QMPC is O(Nn2)$O(Nn^2)$ for a region of the initial conditions and O(N2n2)$O(N^2n^2)$ for sufficiently small sampling time and all initial conditions, where N$N$ and n$n$ are the horizon time and dimension of the state vector, respectively. Numerical results indicate the potential and properties of the proposed algorithm. [ABSTRACT FROM AUTHOR]

In recent years, path-tracking controllers for autonomous passenger vehicles and Control Allocation (CA) methods for handling and stability control have both received extensive discussion in the literature. However, the integration of the path-tracking control with CA methods for autonomous racing vehicles has not attracted much attention. In this study, we design an integrated path-tracking and CA method for a prototype autonomous racing electric vehicle with a particular focus on the maximising the turning speed in tight cornering. The proposed control strategy has a hierarchical structure to improve the computational efficiency: the high-level path-tracking Model Predictive Control (MPC) based on a rigid body model is designed to determine the virtual control forces according to the desired path and desired maximum velocity profile, while the low-level CA method uses a Quadratically Constrained Quadratic Programming (QCQP) formulation to distribute the individual control actuator according to the desired virtual control values. The proposed controller is validated in a high-fidelity simulation vehicle model with the computational time of the optimisation controller presented to demonstrate the real-time control performance. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this paper, we propose and analyse a new full-Newton step feasible interior point method for convex quadratic programming. The basic idea of this method is to replace a complementarity condition by a non-negative variable weight vector. With a zero of weight vector, the limit of the weighted path exists and satisfies the complementarity condition, the limit yields an optimal solution of problem. In each main iteration of the new algorithm consisted of only full-Newton steps with a quadratic rate of convergence. The advantage of this method is the use of a full-Newton step, that is no calculation of the step size is required. Finally, some numerical results are reported to show the practical performance of the proposed algorithm with different parameters. [ABSTRACT FROM AUTHOR]

This paper explores the nonconvex second-order cone as a nonconvex conic extension of the known convex second-order cone in optimization, as well as a higher-dimensional conic extension of the known causality cone in relativity. The nonconvex second-order cone can be used to reformulate nonconvex quadratic programming and nonconvex quadratically constrained quadratic program in conic format. The cone can also arise in real-world applications, such as facility location problems in optimization when some existing facilities are more likely to be closer to new facilities than other existing facilities. We define notions of the algebraic structure of the nonconvex second-order cone and show that its ambient space is commutative and power-associative, wherein elements always have real eigenvalues; this is remarkable because it is not the case for arbitrary Jordan algebras. We will also find that the ambient space of this nonconvex cone is rank-independent of its dimension; this is also notable because it is not the case for algebras of arbitrary convex cones. What is more noteworthy is that we prove that the nonconvex second-order cone equals the cone of squares of its ambient space; this is not the case for all non-Euclidean Jordan algebras. Finally, numerous algebraic properties that already exist in the framework of the convex second-order cone are generalized to the framework of the nonconvex second-order cone. [ABSTRACT FROM AUTHOR]

This paper introduces an innovative approach for generating re-entry trajectories for a reusable winged spacecraft. This approach utilizes Fourier series parametrized control profiles. The Fourier coefficients are derived through a combination of the Improved Search Space Reduction (ISSR) technique and Sequential Quadratic Programming (SQP) optimization methods, which effectively limit the maximum heat rate experienced by the spacecraft. These re-entry trajectories and control profiles are then used to train artificial neural networks, enabling the controller to provide optimal control inputs based on the spacecraft's current altitude and velocity. To validate this methodology, Hardware-in-loop (HIL) simulations are conducted, integrating the designed neural network-based controller with a Texas Instruments TI Delfino TMSF28335 controller and a real-time simulator, the OPAL-RT OP4510. The results of the HIL simulation demonstrate that the generated re-entry trajectory accurately adheres to heat rate and terminal constraints. Additionally, the Fourier series parametrization of control profiles is applied to a high lift-to-drag ratio CAV-H vehicle, showcasing the method's versatility. Furthermore, resilience of proposed method to uncertainties in aerodynamic coefficients and atmospheric density is also demonstrated. The results show that the proposed method is generic and exhibits robustness to uncertainties. [ABSTRACT FROM AUTHOR]

Aggregate blending is a complex process especially when more sizes of aggregates need to be blended. For rough usage or to offer an initial answer, the conventional approaches are adequate. However, to obtain a cost-effective blend that meets specification requirements, more aggregate sizes must be accommodated. Several methods were investigated by various authors to deal with this complex process. Most of the methods are confined to a blending of three or four sizes of aggregates only. In this study, an attempt has been made to assess various computational techniques for aggregate blending to optimize the aggregate gradation area. Aggregates grading requirements specified for Dense Bituminous Macadam Grade-2 in MORT&H 500-10 was chosen as a reference. For this grading specifications, various methods like trial-and-error, mid-point gradation, least-square optimization, Generalised Reduced Gradient (GRG) non-linear, GRG multi start, simplex linear programming, regression analysis, IRC SP:89-2010, quadratic programming, support vector machines-SMoreg, path variate analysis, interval method, R programming were employed, and optimal proportions for aggregate blending were obtained. Curve fitting along with integration was applied to determine the aggregate gradation area under the combined gradation curve and maximum density line. The existence of a gradation curve between upper and lower limits and close to the mid-point line is considered as the first check and the minimum aggregate gradation area is considered as a second check while evaluating different optimal proportions arrived. Least aggregate gradation area which implies the minimum percentage of air voids was obtained for simplex LP (UL and LL) and evolutionary algorithm (Genetic algorithm) methods, i.e., 6.885. But these two methods yielded a filler of zero percentage which is practically not possible, hence simplex LP (MID) satisfies all the criterion and is adopted as the best method for aggregate blending. [ABSTRACT FROM AUTHOR]

We consider estimation of the semiparametric additive hazards model with an unspecified baseline hazard function where the effect of a continuous covariate has a specific shape but otherwise unspecified. Such estimation is particularly useful for a unimodal hazard function, where the hazard is monotone increasing and monotone decreasing with an unknown mode. A popular approach of the proportional hazards model is limited in such setting due to the complicated structure of the partial likelihood. Our model defines a quadratic loss function, and its simple structure allows a global Hessian matrix that does not involve parameters. Thus, once the global Hessian matrix is computed, a standard quadratic programming method can be applicable by profiling all possible locations of the mode. However, the quadratic programming method may be inefficient to handle a large global Hessian matrix in the profiling algorithm due to a large dimensionality, where the dimension of the global Hessian matrix and number of hypothetical modes are the same order as the sample size. We propose the quadratic pool adjacent violators algorithm to reduce computational costs. The proposed algorithm is extended to the model with a time‐dependent covariate with monotone or U‐shape hazard function. In simulation studies, our proposed method improves computational speed compared to the quadratic programming method, with bias and mean square error reductions. We analyze data from a recent cardiovascular study. [ABSTRACT FROM AUTHOR]

The Bouc–Wen nonlinear hysteretic model is widely used in nonlinear systems, and it is difficult to identify the parameters of Bouc–Wen model because of its high nonlinearity. In the paper, a hybrid genetic algorithm combined with sequential quadratic programming is proposed to solve the problem about the parameter identification of Bouc–Wen model. Sequential quadratic programming method has good local convergence and superlinear convergence rate. Therefore, compared with the genetic algorithm, the proposed identification method can accelerate the convergence speed in parameter recognition of Bouc–Wen model and achieve excellent recognition accuracy. Through the function test and the numerical simulation of the shear structure, it is proved that the proposed method has high convergence speed and accurate identification. In addition, the theory and method proposed in this paper are combined with Bouc–Wen model to identify parameters of overall restoring force model of the energy-dissipation structures, the identification results are in good agreement with the experimental results, verifying reliability and accuracy of the model and robustness of the proposed identification method. [ABSTRACT FROM AUTHOR]

A primal quadratic simplex algorithm tailored to the optimization over the vertices of a polytope is presented. Starting from a feasible vertex, it performs either strictly improving or admissible non-deteriorating steps in order to determine a locally optimum basic feasible solution in terms of the quadratic objective function. The algorithm so generalizes over local improvement methods for according applications, including in particular quadratic optimization problems whose feasible solutions correspond to vertices of a 0-1 polytope. Computational experiments for unconstrained binary quadratic programs, maximum cut, and the quadratic assignment problem serve as a proof of concept and underline the importance of a pivoting rule that is able to accept at least a restricted class of degenerate steps. [ABSTRACT FROM AUTHOR]

Joint transceiver beamforming is a fundamental and crucial research task in the field of signal processing. Despite extensive efforts made in recent years, the joint transceiver beamforming of frequency diverse array (FDA)-based multiple-input and multiple-output (MIMO) radar has received relatively less attention and is confronted with some tricky challenges, such as range–angle decoupling and the interaction between multiple performance metrics. In this paper, we initially derive the generalized ambiguity function of the FDA-MIMO radar to explore the intrinsic correlation between its waveform design and resolution. Following that, the joint beamforming optimization is formulated as a nonconvex bivariate quadratic programming problem (NBQP) with the aim of maximizing the Signal-to-Interference-Noise Ratio (SINR) of the FDA-MIMO radar system. Building upon this, we introduce an innovative alternating manifold optimization with nested iteration (AMO-NI) algorithm to address the NBQP. By incorporating manifold optimization into iterative updates of transmit waveform and receiving filter, the AMO-NI algorithm considers the interdependencies among the optimization variables. The algorithm efficiently and expeditiously finds global optimum solutions within a finite number of iterations. Compared with other methods, our approach yields a superior beampattern and higher SINR. [ABSTRACT FROM AUTHOR]

We establish some properties of the Proximal Difference-of-Convex functions decomposition algorithm in indefinite quadratic programming under linear constraints. The first property states that any iterative sequence generated by the algorithm is root linearly convergent to a Karush–Kuhn–Tucker point, provided that the problem has a solution. The second property says that iterative sequences generated by the algorithm converge to a locally unique solution of the problem if the initial points are taken from a suitably chosen neighbourhood of it. Through a series of numerical tests, we analyse the influence of the decomposition parameter on the rate of convergence of the iterative sequences and compare the performance of the Proximal Difference-of-Convex functions decomposition algorithm with that of the Projection Difference-of-Convex functions decomposition algorithm. In addition, the performances of the above algorithms and the Gurobi software in solving some randomly generated nonconvex quadratic programs are compared. [ABSTRACT FROM AUTHOR]

In order to solve the problems of excessive weight and unreasonable structure of anchor machine parts caused by traditional design methods, a lightweight optimization method was proposed based on pre-stressed modal analysis. The design variables were determined, and the parameterized model was established by using ANSYS Workbench. Under ultimate load conditions, the strength of wall frame board and lower box bodies was simulated and calculated. Through modal analysis, the discretized natural frequencies under different design variables could be obtained. The multi-objective genetic algorithm and sequence quadratic programming were respectively used to calculate the lightweight analysis model. The results showed that the weight of the supporting components in ship anchor can be reduced by more than 5 % without reducing strength and equivalent stiffness. [ABSTRACT FROM AUTHOR]

In this paper, a new full-Newton step feasible interior-point method for convex quadratic programming is presented and analyzed. The idea behind this method is to replace the complementarity condition with a non-negative weight vector and use the algebraic equivalent transformation for the obtained equation. Under the selection of appropriate parameters, the quadratic rate of convergence of the new algorithm is established. In addition, the iteration complexity of the algorithm is obtained. Finally, some numerical results are presented to demonstrate the practical performance of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Querying the geodesic distance field on a given smooth surface is a fundamental research pursuit in computer graphics. Both accuracy and smoothness serve as common indicators for evaluating geodesic algorithms. In this study, we argue that ensuring that the norm of the triangle-wise estimated gradients is not larger than 1 is preferable compared to the widely used eikonal condition. Inspired by this, we formulate the geodesic distance field problem as a Quadratically Constrained Linear Programming (QCLP) problem. This formulation can be further adapted into a Quadratically Constrained Quadratic Programming (QCQP) problem by incorporating considerations for smoothness requirements. Specifically, when enforcing a Hessian-energy-based smoothing term, our formulation, named QCQP-Hessian, effectively mitigates the cusps in the geodesic isolines within the near-ridge area while maintaining accuracy in the off-ridge area. We conducted extensive experiments to demonstrate the accuracy and smoothness advantages of QCQP-Hessian. [ABSTRACT FROM AUTHOR]

Non-linear Programming (NLP) is an optimization technique for determining the optimum solution to a broad range of research issues. Many times, the objective function is nonlinear, owing to various economic behaviors such as demand, cost, and many others. Since the appearance of Kuhn and Tucker's fundamental theoretical work, a general NLP problem can be resolved using many methods to find the optimum results. This article tackles the challenge of nonlinear programming (NLP) problems with uncertainty in inequality constraints. Traditional, "crisp" NLP methods might not be ideal when dealing with imprecise or subjective data. Here, we propose a fuzzy mathematical model that incorporates Beale's condition to handle such NLPPs. Furthermore, the model demonstrates how quadratic programming problems can be solved using membership functions(MF's). This leads to more realistic and robust solutions. The model unfolds in three stages: Mathematical Formulation: Establishing the fuzzy NLP framework with Beale's condition and membership functions. Computational Procedures: Outlining algorithms for solving fuzzy NLP problems based on MF's and a robust ranking index. Numerical Illustration: Applying the model to a specific case study and comparing results from both approaches. Through comprehensive analysis, we demonstrate the model's ability to find optimal solutions while considering vagueness and uncertainty in NLPPs. This opens door for more adaptable and realistic optimization in various problem domains. [ABSTRACT FROM AUTHOR]

We describe a class of combinatorial design problems which typically occur in professional sailing league competitions. We discuss connections to resolvable block designs and equitable coverings and to scheduling problems in operations research. We in particular give suitable boolean quadratic and integer linear optimization problem formulations, as well as further heuristics and restrictions, that can be used to solve sailing league problems in practice. We apply those techniques to three case studies obtained from real sailing leagues and compare the results with previously used tournament plans. [ABSTRACT FROM AUTHOR]

We propose a coderivative-based generalized regularized Newton method with positive definite regularization term (GRNM-PD) to solve C 1 , 1 optimization problems. In GRNM-PD, a general positive definite symmetric matrix is used to regularize the generalized Hessian, in contrast to the recently proposed GRNM, which uses the identity matrix. Our approach features global convergence and fast local convergence rate even for problems with nonisolated solutions. To this end, we introduce the p-order semismooth ∗ property which plays the same role in our analysis as Lipschitz continuity of the Hessian does in the C 2 case. Imposing only the metric q-subregularity of the gradient at a solution, we establish global convergence of the proposed algorithm as well as its local convergence rate, which can be superlinear, quadratic, or even higher than quadratic, depending on an algorithmic parameter ρ and the regularity parameters p and q. Specifically, choosing ρ to be one, we achieve quadratic local convergence rate under metric subregularity and the strong semismooth ∗ property. The algorithm is applied to a class of nonsmooth convex composite minimization problems through the machinery of forward–backward envelope. The greater flexibility in the choice of regularization matrices leads to notable improvement in practical performance. Numerical experiments on box-constrained quadratic programming problems demonstrate the efficiency of our algorithm. [ABSTRACT FROM AUTHOR]

In order to improve autonomous vehicles path-tracking accuracy and stability, a lateral–longitudinal coordination path-tracking control method is proposed. The proposed coordination control consists of path-tracking control and speed tracking control. First, the desired safety speed is planned according to the known road curvature and adhesion coefficient in order to prevent the tire force saturation. Based on the three-degree-of-freedom (3DOF) vehicle dynamic model and the preview tracking error model, model predictive control (MPC) theory is adopted to design the speed-varying vehicle path-tracking controller. Then, the quadratic programming (QP) method is used to solve the objective function with constraints, which calculates the steering angle to control the vehicle track the reference path. In addition, a PID speed controller is designed to calculate the torque of each wheel to track the desired speed. Finally, according to the yaw rate error and the vehicle slip angle error, a yaw moment stability controller based on the fuzzy logic control theory is designed to balance the vehicle stability and motility. The simulation results based on a Matlab/Carsim platform show that the coordination path-tracking control method proposed in this paper can effectively improve the vehicle tracking accuracy and the stability on different roads. [ABSTRACT FROM AUTHOR]

Numerous classification and regression problems have extensively used Support Vector Machines (SVMs). However, the SVM approach is less practical for large datasets because of its processing cost. This is primarily due to the requirement of optimizing a quadratic programming problem to determine the decision boundary during training. As a result, methods for selecting data instances that have a better likelihood of being chosen as support vectors by the SVM algorithm have been developed to help minimize the bulk of training data. This paper presents a density-based method, called Density-based Border Identification (DBI), in addition to four different variations of the method, for the lessening of the SVM training data through the extraction of a layer of border instances. For higher-dimensional datasets, the extraction is performed on lower-dimensional embeddings obtained by Uniform Manifold Approximation and Projection (UMAP), and the resulting subset can be repetitively used for SVM training in higher dimensions. Experimental findings on different datasets, such as Banana, USPS, and Adult9a, have shown that the best-performing variations of the proposed method effectively reduced the size of the training data and achieved acceptable training and prediction speedups while maintaining an adequate classification accuracy compared to training on the original dataset. These results, as well as comparisons to a selection of related state-of-the-art methods from the literature, such as Border Point extraction based on Locality-Sensitive Hashing (BPLSH), Clustering-Based Convex Hull (CBCH), and Shell Extraction (SE), suggest that our proposed methods are effective and potentially useful. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Carbon capture, utilization, and storage (CCUS) is a crucial part of the energy industry nowadays, aiming to reduce the overall carbon emission into the environment. One solution to CCUS is via the means of CO 2 enhanced recovery processes in a depleted oil reservoir. In such a case, life-cycle production optimization plays a crucial component, referring to optimizing a production-driven objective function via varying well controls during a reservoir's lifetime. One challenge is to obtain the optimal cash flow while trying to maintain the maximum CO 2 storage. Another challenge is the nonlinear constraints (such as field liquid production rate) which need to be honored due to the capacity of the processing facilities. This study presents an application of a stochastic gradient-based framework to solve the CO 2 storage multi-objective optimization problem. Our study focuses on carbon capture and storage via the means of nonlinearly constrained production optimization workflow for a CO 2 enhanced recovery process, in which we aim to bi-objectively maximize both the net-present-value (NPV) and the net present carbon tax credits (NPCTC). The main framework used in this work is line-search sequential quadratic programming (LS-SQP) with stochastic simplex approximated gradients (StoSAG). We demonstrate the performance and results of the algorithmic framework in a field-scale realistic problem. The case study being investigated is a multiphase flow Brugge model under CO 2 injection, simulated using a commercial compositional reservoir simulator. Results show that the LS-SQP algorithm with StoSAG gradients performs computationally efficiently and effectively in handling nonlinear state constraints imposed onto the problem. The workflow successfully solves both the single-objective and the multi-objective optimization problems with minimal and acceptable constraint violations. Various numerical settings have been experimented with to estimate the Pareto front for the bi-objective optimization problem, showing the trade-off between the two objectives NPV and NPCTC. We have demonstrated an approach to the carbon capture, utilization, and storage (CCUS) in the context of multi-objective production optimization of a CO 2 enhanced recovery process for a field-scale realistic reservoir model. The algorithmic framework used in this study has proven to be computationally effective on the problem and especially useful when utilized in conjunction with commercial flow simulators that lack the capability of computing adjoint-based gradients. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

While gravitational lens inversion holds great promise to reveal the structure of the light-deflecting mass distribution, both light and dark, the existence of various kinds of degeneracies implies that care must be taken when interpreting the resulting lens models. This article illustrates how thinking in terms of the projected potential helps to gain insight into these matters. Additionally it is shown explicitly how, when starting from a discretized version of the projected potential of one particular lens model, the technique of quadratic programming can be used to create a multitude of equivalent lens models that preserve all or a subset of lens properties. This method is applied to a number of scenarios, showing the lack of grasp on the mass outside the strong lensing region, revisiting mass redistribution in between images, and applying this to a recent model of the SDSS J1004+4112 cluster, as well as illustrating the generalized mass sheet degeneracy and source-position transformation. In the case of J1004, we show that this mass redistribution did not succeed at completely eliminating a dark mass clump recovered by grale near one of the quasar images. [ABSTRACT FROM AUTHOR]

We consider interval systems of linear equations and inequalities with a restriction to some a priori given set. We focus on a characterization of strong solvability, that is, solvability for each realization of interval values, and we compare this with an existence of a strong solution defined analogously. The motivation comes from the area of interval-valued optimization problems, where strong solvability means guaranteed feasibility of any realization of the problem. Strong solvability with strict inequalities implies the robust Slater condition, which ensures that standard optimality conditions can be used. We apply the issues particularly in two optimization classes, convex quadratic programming with quadratic constraints and posynomial geometric programming. For the former, we also utilize the presented result to improve a characterization of the worst case optimal value. Eventually, we state several open problems that emerged while deriving the results. [ABSTRACT FROM AUTHOR]

Support vector machine (SVM) is a supervised machine-learning method which can be used for both classification and regression models. In this paper, we introduce a new model of SVM which any of training samples containing inputs and outputs are considered the random variables with known probability functions. The SVM is first converted into equivalent quadratic programming (QP) formulations in linear and nonlinear cases. An artificial neural network for SVM learning is then proposed. The presented neural network framework guarantees to obtain the optimal solution of the SVM problem. The existence and convergence of the trajectories of the network are studied. The Lyapunov stability for the considered neural network is also shown. The efficiency of the proposed method is shown by four illustrative examples. [ABSTRACT FROM AUTHOR]

We propose logarithmic-barrier decomposition-based interior-point algorithms for solving two-stage stochastic quadratically constrained convex quadratic programming problems in a Hilbert space. We prove the polynomial complexity of the proposed algorithms, and show that this complexity is independent on the choice of the Hilbert space, and hence it coincides with the best-known complexity estimates in the finite-dimensional case. We also apply our results on a concrete example from the stochastic control theory. [ABSTRACT FROM AUTHOR]

(1) Background: Generally, in nuclear medicine and nuclear power plants, energy spectrum measurements and radioactive nuclide identification are required for evaluation of strong radiation fields to ensure nuclear safety and security; thereby, damage is prevented to nuclear facilities caused by natural disasters or the criminal smuggling of nuclear materials. High count rates can lead to signal accumulation, negatively affecting the performance of gamma spectrometers, and in severe cases, even damaging the detectors. Higher pulse throughput with better energy resolution is the ultimate goal of a gamma-ray spectrometer. Traditionally, pileup pulses, which cause dead time and affect throughput, are rejected to maintain good energy resolution. (2) Method: In this paper, an ultra-throughput boost (UTB) off-line processing method was used to improve the throughput and reduce the pileup effect of the spectrometer. Firstly, by fitting the impulse signal of the detector, the response matrix was built by the functional model of a dual exponential tail convolved with the Gaussian kernel; then, a quadratic programming method based on a non-negative least squares (NNLS) algorithm was adopted to solve the constrained optimization problem for the inversion. (3) Results: Both the simulated and experimental results of the UTB method show that most of the impulses in the pulse sequence from the scintillator detector were restored to δ-like pulses, and the throughput of the UTB method for the NaI(Tl) spectrometer reached 207 kcps with a resolution of 7.71% @661.7 keV. A reduction was also seen in the high energy pileup phenomenon. (4) Conclusions: We conclude that the UTB method can restore individual and piled-up pulses to δ-like sequences, effectively boosting pulse throughput and suppressing high-energy tailing and sum peaks caused by the pileup effect at the cost of a slight loss in energy resolution. [ABSTRACT FROM AUTHOR]

Safety and stability considerations play a crucial role in the development of learning based strategies for control design of systems that require high levels of safety. Safe reinforcement learning (RL) based approaches traditionally seek learning of the control laws that are optimal with respect to system performance whilst ensuring system stability and safety. In this article, an off‐policy safe RL based approach is proposed for nonlinear systems affine in control in continuous time. In this novel work, safety and stability are guaranteed during initialization and exploration phases by adjusting the control input with the solution of a quadratic programming problem combining both input to state stable‐control Lyapunov function and robust control barrier function (R‐CBF) conditions. Moreover, the safety of the learned policy is assured by augmenting the cost function with a CBF to maintain safety and optimize performance simultaneously. Novel mathematically rigorous proofs are provided to establish the stability and safety guarantees, offering a sound theoretical foundation for the approach. To demonstrate the effectiveness of the algorithm, two examples are presented: engine surge and stall dynamics, and an unstable nonlinear system. [ABSTRACT FROM AUTHOR]

This paper studies several solution paths of sparse quadratic minimization problems as a function of the weighing parameter of the bi-objective of estimation loss versus solution sparsity. Three such paths are considered: the " ℓ 0 -path" where the discontinuous ℓ 0 -function provides the exact sparsity count; the " ℓ 1 -path" where the ℓ 1 -function provides a convex surrogate of sparsity count; and the "capped ℓ 1 -path" where the nonconvex nondifferentiable capped ℓ 1 -function aims to enhance the ℓ 1 -approximation. Serving different purposes, each of these three formulations is different from each other, both analytically and computationally. Our results deepen the understanding of (old and new) properties of the associated paths, highlight the pros, cons, and tradeoffs of these sparse optimization models, and provide numerical evidence to support the practical superiority of the capped ℓ 1 -path. Our study of the capped ℓ 1 -path is interesting in its own right as the path pertains to computable directionally stationary (= strongly locally minimizing in this context, as opposed to globally optimal) solutions of a parametric nonconvex nondifferentiable optimization problem. Motivated by classical parametric quadratic programming theory and reinforced by modern statistical learning studies, both casting an exponential perspective in fully describing such solution paths, we also aim to address the question of whether some of them can be fully traced in strongly polynomial time in the problem dimensions. A major conclusion of this paper is that a path of directional stationary solutions of the capped ℓ 1 -regularized problem offers interesting theoretical properties and practical compromise between the ℓ 0 -path and the ℓ 1 -path. Indeed, while the ℓ 0 -path is computationally prohibitive and greatly handicapped by the repeated solution of mixed-integer nonlinear programs, the quality of ℓ 1 -path, in terms of the two criteria—loss and sparsity—in the estimation objective, is inferior to the capped ℓ 1 -path; the latter can be obtained efficiently by a combination of a parametric pivoting-like scheme supplemented by an algorithm that takes advantage of the Z-matrix structure of the loss function. [ABSTRACT FROM AUTHOR]

We introduce DiffOpt.jl, a Julia library to differentiate through the solution of optimization problems with respect to arbitrary parameters present in the objective and/or constraints. The library builds upon MathOptInterface, thus leveraging the rich ecosystem of solvers and composing well with modeling languages like JuMP. DiffOpt offers both forward and reverse differentiation modes, enabling multiple use cases from hyperparameter optimization to backpropagation and sensitivity analysis, bridging constrained optimization with end-to-end differentiable programming. DiffOpt is built on two known rules for differentiating quadratic programming and conic programming standard forms. However, thanks to its ability to differentiate through model transformations, the user is not limited to these forms and can differentiate with respect to the parameters of any model that can be reformulated into these standard forms. This notably includes programs mixing affine conic constraints and convex quadratic constraints or objective function. History: Accepted by Ted Ralphs, Area Editor for Software Tools. Funding: The work of A. Sharma on DiffOpt.jl was funded by the Google Summer of Code program through NumFocus. M. Besançon was partially supported through the Research Campus Modal funded by the German Federal Ministry of Education and Research [Grant 05M14ZAM, 05M20ZBM]. J. Dias Garcia was supported in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior – Brasil (CAPES) – Finance Code 001. B. Legat was supported by a BAEF Postdoctoral Fellowship, the NSF [Grant OAC-1835443], and the ERC Adv. [Grant 885682]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information (https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.0283), as well as from the IJOC GitHub software repository (https://github.com/INFORMSJoC/2022.0283). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/. [ABSTRACT FROM AUTHOR]

This article studies the projection test for high-dimensional mean vectors via optimal projection. The idea of projection test is to project high-dimensional data onto a space of low dimension such that traditional methods can be applied. We first propose a new estimation for the optimal projection direction by solving a constrained and regularized quadratic programming. Then two tests are constructed using the estimated optimal projection direction. The first one is based on a data-splitting procedure, which achieves an exact t-test under normality assumption. To mitigate the power loss due to data-splitting, we further propose an online framework, which iteratively updates the estimation of projection direction when new observations arrive. We show that this online-style projection test asymptotically converges to the standard normal distribution. Various simulation studies as well as a real data example show that the proposed online-style projection test retains the Type I error rate well and is more powerful than other existing tests. for this article are available online. [ABSTRACT FROM AUTHOR]

The proposed research work analyzes the bio-inspired problem through artificial neural networks with a feed-forward approach utilized to approximate the numerical results for singular nonlinear bio-heat equation (BHE) with boundary conditions based on four different scenarios created on the variation of environmental temperature to illustrate the effects of temperature on the human dermal region. The log-sigmoid function is used to construct the fitness function, while the optimization solvers: pattern search and genetic algorithm, are then hybridized with the active set technique, interior point technique, sequential quadratic programming for accurate and reliable results of the proposed BHE with various scenarios where the convergence of the numerical results is also analyzed. Moreover, a comparison of the proposed technique is expressed through residual error that reveals the nature of the numerical results and their efficiency. Additionally, a comprehensive statistical analysis is presented for the designed technique to better illustrate the accuracy, reliability, and efficiency of the obtained results. [ABSTRACT FROM AUTHOR]

In this article, a quadratic programming problem is considered to identify all link flows in an arterial network when there are unmeasured link flows. A graphical method is provided to determine the minimum number of measurements and sensor locations required to obtain a fully observable model. It is shown that this method is also valid for the augmented graph with turn ratio measurements. If the minimum measurements required are met, a fully determined network can be obtained. If there is not enough measurement, a bound on the magnitude of the resulting inaccuracy in terms of vehicle kilometers traveled (VKT) can be calculated by the proposed linear programming method. The model is that of a queueing network; the parameters describe network geometry, saturation flow rates, turning ratios, timing plan and link flows. Three case studies are conducted to validate this approach. The first two cases are to calculate all missing flows by using a few numbers of measurements and minimum number of measurements required, respectively. Upper and lower bounds in terms of VKT are also calculated for these cases. Third case is to obtain a fully determined network with the minimum number of flow measurements when turn ratio sensors are included. Real measurements are collected from a network in Mugla including 55 links and 16 intersections. Vissim simulator is used to analyze the accuracy of the link flow calculations obtained from the proposed method. The results show that the proposed programming method can calculate the missing flows with a high accuracy and short computation time. [ABSTRACT FROM AUTHOR]

The catenation effect of the rope of the long-span hoisting robot is studied. Firstly, the kinematic and dynamic models of the robot were established by using the cable as linear model. Secondly, there is gravity in the cable, and the long span cable was catenary model, in order to solve the cable tension in the catenary model, the quadratic programming method was used to solve the optimal solution of cable tension. Based on the statics equation, wrench feasible workspace and wrench closure workspace of the hoisting robot were obtained. Finally, the simulation was verified by MATLAB, the simulation results show that wrench feasible workspace is smaller than wrench closure workspace. Comparing the cable length of the two models, the length of the first cable changes the most, the cable tension is small, and the cable self-weight cannot be ignored. [ABSTRACT FROM AUTHOR]

To enable autonomous vehicles to generate smooth and collision-free trajectories and improve their driving performance on structured roads, this paper proposes a hierarchical trajectory planning algorithm based on an improved artificial potential field method. To improve the applicability of the algorithm to complex scenarios, the Frenet coordinate system was established to address these limitations. First, the safety distance model is applied to the risk assessment of the improved artificial potential field method. Then, the hierarchical solution is carried out, and the road solvable convex space and the rough path solution are solved by combining the artificial potential field method. On this basis, the potential field term and the smoothing term cost function are established, and the sequential quadratic programming (SQP) algorithm is used to solve the exact path that meets the requirements of safety and smoothness. Hierarchical planning shortens the solution time by quickly determining the bounds of the convex space. Finally, in the speed planning, in order to take into account the comfort and safety of the occupants, the speed curve is solved by considering the dynamic constraints of the vehicle. The obstacle avoidance effects of the algorithm on static and dynamic obstacles are tested in different simulation scenarios. The results of the simulation experiment show that the proposed algorithm can successfully achieve obstacle avoidance on complex structured roads. [ABSTRACT FROM AUTHOR]

This study proposes an innovative approach that integrates the subdomain method with sequential quadratic programming (SQP) to optimize the volume of a high-speed surface-mounted permanent magnet synchronous motor in an air compressor operating at 110 000 rpm. Unlike conventional optimization tools that often rely on finite element analysis (FEA) software, by leveraging the subdomain method for electromagnetic modeling, we obtain an analytical solution that rapidly represents the behaviors of the motor. Subsequently, the SQP technique is applied to optimize the volume of the model while satisfying design constraints. The proposed model is verified by FEA simulation. [ABSTRACT FROM AUTHOR]

To avoid the expensive quadratic programming in the L2-loss support vector regression (SVR) model, smooth approximation and iteratively reweighted least square (IRLS) techniques were introduced in literature, resulting in smoothed SVR (SSVR) and IRLS-SVR. However, for nonlinear models, SSVR and IRLS-SVR both involve operations with matrices and vectors of the same size as the training set. Thus, as the training set becomes large, nonlinear SSVR and IRLS-SVR both need long training time and large memory. To further alleviate the training cost, this paper projects the original data into a low dimensional space via random Fourier feature. The inner product of the random Fourier features of two data points is approximately the same as the kernel function evaluated at these two data points. Hence, it is possible to use a linear model in the new low dimensional space to approximate the original nonlinear model, and consequently the time/memory efficient linear training algorithms could be applied. This paper applies the idea of random Fourier features to nonlinear SSVR and IRLS-SVR, and our testing results on real-world datasets show that, the introduction of random Fourier features makes SSVR and IRLS-SVR achieve similar prediction accuracy as the original nonlinear version with substantially higher time efficiency. [ABSTRACT FROM AUTHOR]

In order to improve the security of power remote telemetry system, this paper studies the parameter identification method of power remote telemetry system based on real-time cross-section data and error-proof topology analysis. The method is based on a synchronization vector measurement unit. It uses the multi-source measurement method to fuse the real-time cross-section data of the power remote telemetry system, we reconstruct the fault-proof topology map of the power grid based on the fused real-time cross-section data. And according to the grid error prevention topology diagram, we set the grid line impedance parameters, calculate the sum and variance of voltage squares and so on. After the set parameters are established, the constraint conditions are divided, and the constraint conditions are transformed by linear function through quadratic programming. By judging whether the parameter identification function complies with its constraints, the parameter identification of the power remote telemetry system is realized. The experimental results show that this method can accurately obtain the real-time cross-section data of the power remote telemetry system. Moreover, it can accurately reconstruct the fault-proof topology of the power grid, and the maximum deviation of parameter identification is only 0.5223. [ABSTRACT FROM AUTHOR]

In order to fully consider the random variation of sieving process parameters,this paper constructs the reliability-based optimization model for reconstituted tobacco process parameters,which taking the percentage of fibers below 12 mesh as the optimization objective,water flow rate and pulp concentration as the design parameters, and the percentage of fibers over 50 mesh as the probabilistic constraint. Firstly, the current process parameters are used as inheritance points for Latin hypercube sampling and screening experiments. Based on this, an initial Kriging model is constructed to fit the implicit relationship between water flow velocity, smoke slurry solid content, and the proportion of fiber mass below 12 mesh and above 50 mesh. And local adaptive sampling (LAS) was carried out to update the Kriging model to ensure the approximate accuracy of key positions at optimization iteration. Finally,Monte Carlo simulation (MCS)-Sequential quadratic programming (SQP) was used to solve the optimization model of screening process parameters. The results indicated that the optimized water flow rate and pulp concentration were 6.31 L/ min and 0.53%, respectively. Under this process parameter, the proportion of fiber below 12 mesh was 13.72%, which was 7.19% higher than before optimization. The proportion of fibers over 50 mesh was 17.65%, which was a decrease of 4.13% compared to before optimization. This method could meet the optimization requirements of screening process parameters for paper making reconstituted tobacco leaves. [ABSTRACT FROM AUTHOR]

In this paper, the safety control problem for spacecraft inspection mission is investigated, which means that there is no position and attitude obstacle collisions between the inspection spacecraft and the defined forbidden zones. We propose a control strategy that ensures safety, utilizing the control barrier function to address multiple safety constraints with logical relationships among them. Firstly, the position and attitude constraints are defined, and the hybrid logical relationship among different attitude constraints is analyzed. To handle complex position and attitude constraints, the Kreisselmeier-Steinhauser function is introduced to approximate the max/min function, thereby expressing them as continuous and differentiable functions. Subsequently, the control barrier function-based quadratic programming (CBF-QP) problems are solved to generate safe velocity and angular velocity. These problems have explicit solutions and do not require extensive computational resources. The safe position and attitude are then obtained by integrating the safe velocity and angular velocity. Notably, the forbidden regions are expanded by a constant in the construction of CBF-QP problems, which acts as a margin for the tracking controller's performance. Finally, attitude and position tracking controllers based on the control Lyapunov barrier function (CLBF) are designed respectively, taking into account the lumped disturbance in the system, which means that the attitude and position control are computed independently. Numerical simulation results demonstrate that the proposed control strategy effectively handles complex constraints in inspection missions, ensuring system stability and safety, even under severe conditions. [ABSTRACT FROM AUTHOR]

The paper proposes a motion control framework for the unmanned wheel-legged hybrid vehicle to track the motion trajectory considering uncertain disturbances. The whole-body dynamic model is built with the contact force of each rolling wheel, which serves as the foundation to obtain trajectory tracking. The angular momentum and linear momentum are optimized by the robust model predictive control algorithm considering the soft constraint of the relaxation variable. The contact force between wheel and ground is solved by the quadratic programming algorithm to efficiently obtain the flexion/extension joint and wheel motion planning. Then, the explicit algorithm to calculate the torque commands of the flexion/extension joint considering the feed-forward torque and feedback torque to improve the control accuracy. Simulation results validate that the control framework based on the robust model predictive control algorithm can solve the uncertain disturbances in process of the vehicle running on the rough road. [ABSTRACT FROM AUTHOR]

This paper details the development and validation of a temperature sensing methodology using an un-trimmed oscillator-based integrated sensor implemented in the 0.18- μ m SOI XFAB process, with a focus on thermal monitoring in system-on-chip (SoC) based DC-DC converters. Our study identifies a quadratic relationship between the oscillator output frequency and temperature, which forms the basis of our proposed calibration mechanism. This mechanism aims at mitigating process variation effects, enabling accurate temperature-to-frequency mapping. Our research proposes and characterizes several trimming-free calibration techniques, covering a spectrum from zero to thirty-one frequency-temperature measurement points. Notably, the Corrected One-Point calibration method, requiring only a single ambient temperature measurement, emerges as a practical solution that removes the need for a temperature chamber. This method, after adjustment, successfully reduces the maximum error to within ± 2.95 °C. Additionally, the Two-Point calibration method demonstrates improved precision with a maximum positive error of +1.56 °C at −15 °C and a maximum negative error of −3.13 °C at +10 °C ( R 2 value of 0.9958). The Three-Point calibration method performed similarly, yielding an R 2 value of 0.9956. The findings of this study indicate that competitive results in temperature sensor calibration can be achieved without circuit trimming, offering a viable alternative or a complementary approach to traditional trimming techniques. [ABSTRACT FROM AUTHOR]

The power system, as a core component of a launch vehicle, has a crucial impact on the reliability and safety of a rocket launch. Due to the limited measurement information inside the engine, it is often challenging to realize fast and accurate anomaly detection. For this reason, this paper introduces the rocket flight state data to expand the information source for anomaly detection. However, engine measurement and rocket flight state information have different data distribution characteristics. To find the optimal data fusion scheme for anomaly detection, a data set information fusion algorithm based on convex optimization is proposed, which solves the optimal fusion parameter using the convex quadratic programming problem and then adopts the adaptive CUSUM algorithm to realize the fast and accurate anomaly detection of engine faults. Numerical simulation tests show that the algorithm proposed in this paper has a higher detection accuracy and lower detection time than the traditional algorithm. [ABSTRACT FROM AUTHOR]

• The model of a cable driven parallel robot with multi-type actuators is derived and then verified by ADAMS software. • New trajectory planning algorithms for cable driven robot are developed by direct method schemes. • Direct shooting and collocation are adapted to the cable parallel robot dynamic in path planning. • The focus in trajectory planning is on cable constraints to satisfy control and smoothness. • An experimental platform is constructed to support direct shooting results. Cable tensions in cable robots make trajectory planning more complicated than in rigid-link robots. Since cables can only pull but not push, the cable tensions must be kept positive for a cable-driven system to maintain control. In this paper direct methods of trajectory planning including direct collocation and direct shooting are proposed to solve the two-point boundary value problem trajectory planning. Minimizing a robot's actuator force under cable constraints including positive forces and preventing severe changes in tensions are considered in this problem. The cable-driven robot consists of a 3-cable and a pneumatic cylinder, which betters robot tensionability. The direct methods are solved by the sequential quadratic programming algorithm and then compared with the GPOPS-II software package. The results designate that the direct methods of trajectory planning propose substantial benefits in satisfying essential continuity and smoothness of resulted profiles for a cable-driven robot with a multi-type actuation system. Experimental results confirm the numerical data, additional supporting the findings. [ABSTRACT FROM AUTHOR]

The current study presents a novel application of integrated intelligent computing solver for numerical treatment of second‐order prediction differential models by exploiting the continuous mapping of artificial neural network (ANN) models of differential operators, global/local search optimization competencies of combined genetic algorithms (GAs) and sequential quadratic programming (SQPs), that is, ANNGASQP. Neural network based differential models are arbitrary integrated to formulate merit function in mean squared error sense and merit function globally optimized with GAs aided with local refinements of SQP. The integrated neuro‐evolutionary ANNGASQP scheme is implemented on four different numerical examples of the prediction differential models for numerical solution to examine the precision, proficiency, and consistency. The comparison of proposed solutions through ANNGASQP for prediction differential models with available reference results indicate the good agreement with absolute errors around 10−6 to 10−8. The worth of ANNGASQP is further established through near optimal values of performance measures on statistical date for multiple trials. [ABSTRACT FROM AUTHOR]

We propose a parameter optimization method of multi-layer nested slit resonator (MNSR) for the converter transformer noise in a high voltage direct current (HVDC) converter station. With the optimization objective of achieving quasi-perfect sound absorption at the target frequencies and the structural parameters of MNSR as the optimization variables, the optimization model of the structural parameters of MNSR is established and then solved by the sequential quadratic programming algorithm (SQP). The theoretical and simulation results of the four validation cases show that the optimized MNSR can achieve quasi-perfect sound absorption at all target frequencies, which is consistent with the optimization objective. The parameter optimization design method provides an efficient method to design a dual-frequency quasi-perfect sound absorber for the converter transformer noise. [ABSTRACT FROM AUTHOR]

In this paper, fixed-time convergent RNNs with logarithmic settling time are proposed for solving time-variant quadratic programming (QP), where the domain of attraction of the RNN models can be reasonably estimated a priori. Two novel activation functions are designed, and the exact expressions of the settling time functions for each given initial condition are given; and upper bounds of the settling times for any given initial condition can be obtained. In addition, the generic activation functions are constructed and analyzed to achieve logarithmic fixed-time settling. The RNNs based on the generic activation function are designed, which have a faster convergence rate and a fixed-time convergence property. By estimating the bound of the settling time function under given initial conditions in the bounded region, the semi-global fixed-time convergence of the RNN model is in turn established. It is shown that the predefined-time convergence of modified RNN models can be assured by adopting the inverse of the bound. Simulation results verify effectiveness of the proposed computing schemes for the time-variant QP problem solving and the repetitive motion planning of a redundant manipulator. [ABSTRACT FROM AUTHOR]