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This work proposes an improved pedestrian social force model for pedestrian trajectory prediction to prevent intelligent vehicles from colliding with pedestrians while driving on the road. In this model, the intelligent vehicle performs motion planning on the basis of predicted pedestrian trajectory results. A path is planned by using the fifth-order Bezier curve, the optimal coordinate is acquired by adjusting the weight coefficient of each optimisation goal, and the optimal driving trajectory curve is planned. In speed planning, the pedestrian collision boundary is proposed to ensure pedestrian safety. The initial speed planning is performed by a dynamic programming algorithm, and then the optimal speed curve is obtained by quadratic programming. Finally, the front pedestrian deceleration or uniform speed scene is set for simulation verification. Simulation results show that the vehicle speed reaches a maximum value of 6.39 m/s under the premise of ensuring safety and that the average speed of the intelligent vehicle is 4.6 m/s after a normal start process. The maximum and average speed values obtained with trajectory prediction indicate that the intelligent vehicle ensures pedestrian and vehicle safety as well as the intelligent vehicle's economy. [ABSTRACT FROM AUTHOR]

Urban railways in coastal areas are exposed to the risk of extreme weather conditions. A cost-effective and robust wind monitoring system, as a vital part of the railway infrastructure, is essential for ensuring safety and efficiency. However, insufficient sensors along urban rail lines may result in failure to detect local strong winds, thus impacting urban rail safety and operational efficiency. This paper proposes a hybrid method based on historical wind speed data analysis to optimize wind monitoring system deployment. The proposed methodology integrates warning similarity and trend similarity with a linear combination and develops a constrained quadratic programming model to determine the combined weights. The methodology is demonstrated and verified based on a real-world case of an urban rail line. The results show that the proposed method outperforms the single similarity-based method and spatial interpolation approach in terms of both evaluation accuracy and robustness. This study provides a practical data-driven tool for urban rail operators to optimize their wind sensor networks with limited data and resources. It can contribute significantly to enhancing railway system operational efficiency and reducing the hazards on rail infrastructures and facilities under strong wind conditions. Additionally, the novel methodology and evaluation framework can be efficiently applied to the monitoring of other extreme weather conditions, further enhancing urban rail safety. [ABSTRACT FROM AUTHOR]

Topology optimization has evidenced its capacity to provide new optimal designs in many different disciplines. However, most novel methods are difficult to apply in commercial software, limiting their use in the academic field and hindering their application in the industry. This article presents a new open methodology for solving geometrically complex non-self-adjoint topology optimization problems, including stress-constrained and stress minimization formulations, using validated FEM commercial software. The methodology was validated by comparing the sensitivity analysis with the results obtained through finite differences and solving two benchmark problems with the following optimizers: Optimality Criteria, Method of Moving Asymptotes, Sequential Least-Squares Quadratic Programming (SLSQP), and Trust-constr optimization algorithms. The SLSQP and Trust-constr optimization algorithms obtained better results in stress-minimization problem statements than the methodology available in ABAQUS®. A Python implementation of this methodology is proposed, working in conjunction with the commercial software ABAQUS® 2023 to allow a straightforward application to new problems while benefiting from a graphic user interface and validated finite element solver. [ABSTRACT FROM AUTHOR]

Ride-hailing is a creative idea created by transportation supported by science and technology. Ride-hailing services can help daily community activities. The issue with ride-hailing is that traffic conditions are unpredictable, implying that waiting times are uncertain. The time passengers spend waiting from when they book a ride service until the driver arrives at the pick-up location is called waiting time. This study suggests a quadratic programming technique for minimizing waiting time while accounting for the unpredictability of pick-up travel time. The interval-valued fuzzy quadratic programming method handles the uncertainty and imprecision of the anticipated journey time. When allocating drivers to pick up passengers, interval-valued fuzzy numbers can provide a more realistic representation of waiting time uncertainty. As a result, the interval-valued fuzzy quadratic programming model can handle the uncertainty in waiting time for ride-hailing assignment problems. The model's performance is evaluated using waiting time and the number of people served. The model's performance is demonstrated numerically using the simulation-based case study. This study shows how to utilize a mathematical method to solve real-world problems with uncertainty and improve user welfare. [ABSTRACT FROM AUTHOR]

Obstacle avoidance path planning is considered an essential requirement for unmanned aerial vehicle (UAV) to reach its designated mission area and perform its tasks. This study established a motion model and obstacle threat model for UAVs, and defined the cost coefficients for evading and crossing threat areas. To solve the problem of obstacle avoidance path planning with full coverage of threats, the cost coefficients were incorporated into the objective optimization function and solved by a combination of Sequential Quadratic Programming and Nonlinear Programming Solver. The problem of path planning under threat full coverage with no solution was resolved by improving the Bézier curve algorithm. By introducing the dynamic threat velocity obstacle model and calculating the relative and absolute collision cones, a path planning algorithm under multiple dynamic threats was proposed to solve the difficulties of dynamic obstacle prediction and avoidance. Simulation results revealed that the proposed Through-out method was more effective in handling full threat coverage and dynamic threats than traditional path planning methods namely, Detour or Cross Gaps. Our study offers valuable insights into autonomous path planning for UAVs that operate under complex threat conditions. This work is anticipated to contribute to the future development of more advanced and intelligent UAV systems. [ABSTRACT FROM AUTHOR]

Establishing an accurate and computationally efficient model for driving risk assessment, considering the influence of vehicle motion state and kinematic characteristics on path planning, is crucial for generating safe, comfortable, and easily trackable obstacle avoidance paths. To address this topic, this paper proposes a novel dual-layered dynamic path-planning method for obstacle avoidance based on the driving safety field (DSF). The contributions of the proposed approach lie in its ability to address the challenges of accurately modeling driving risk, efficient path smoothing and adaptability to vehicle kinematic characteristics, and providing collision-free, curvature-continuous, and adaptable obstacle avoidance paths. In the upper layer, a comprehensive driving safety field is constructed, composed of a potential field generated by static obstacles, a kinetic field generated by dynamic obstacles, a potential field generated by lane boundaries, and a driving field generated by the target position. By analyzing the virtual field forces exerted on the ego vehicle within the comprehensive driving safety field, the resultant force direction is utilized as guidance for the vehicle's forward motion. This generates an initial obstacle avoidance path that satisfies the vehicle's kinematic and dynamic constraints. In the lower layer, the problem of path smoothing is transformed into a standard quadratic programming (QP) form. By optimizing discrete waypoints and fitting polynomial curves, a curvature-continuous and smooth path is obtained. Simulation results demonstrate that our proposed path-planning algorithm outperforms the method based on the improved artificial potential field (APF). It not only generates collision-free and curvature-continuous paths but also significantly reduces parameters such as path curvature (reduced by 62.29% to 87.32%), curvature variation rate, and heading angle (reduced by 34.11% to 72.06%). Furthermore, our algorithm dynamically adjusts the starting position of the obstacle avoidance maneuver based on the vehicle's motion state. As the relative velocity between the ego vehicle and the obstacle vehicle increases, the starting position of the obstacle avoidance path is adjusted accordingly, enabling the proactive avoidance of stationary or moving single and multiple obstacles. The proposed method satisfies the requirements of obstacle avoidance safety, comfort, and stability for intelligent vehicles in complex environments. [ABSTRACT FROM AUTHOR]

Background: Inequalities in access to stroke care and the workload of physicians have been a challenge in recent times. This may be resolved by allocating physicians suitable for the expected demand. Therefore, this study analyzes whether reallocation using an optimization model reduces disparities in spatial access to healthcare and excessive workload. Methods: This study targeted neuroendovascular specialists and primary stroke centers in Japan and employed an optimization model for reallocating neuroendovascular specialists to reduce the disparity in spatial accessibility to stroke treatment and workload for neuroendovascular specialists in Japan. A two-step floating catchment area method and an inverted two-step floating catchment area method were used to estimate the spatial accessibility and workload of neuroendovascular specialists as a potential crowdedness index. Quadratic programming has been proposed for the reallocation of neuroendovascular specialists. Results: The reallocation of neuroendovascular specialists reduced the disparity in spatial accessibility and the potential crowdedness index. The standard deviation (SD) of the demand-weighted spatial accessibility index improved from 125.625 to 97.625. Simultaneously, the weighted median spatial accessibility index increased from 2.811 to 3.929. Additionally, the SD of the potential crowdedness index for estimating workload disparity decreased from 10,040.36 to 5934.275 after optimization. The sensitivity analysis also showed a similar trend of reducing disparities. Conclusions: The reallocation of neuroendovascular specialists reduced regional disparities in spatial accessibility to healthcare, potential crowdedness index, and disparities between facilities. Our findings contribute to planning health policies to realize equity throughout the healthcare system. [ABSTRACT FROM AUTHOR]

The classification problem is a key area of research in machine learning. The Least Squares Support Vector Machine (LSSVM) is an important classifier that is commonly used to solve classification problems. Its widespread use stems from its replacement of the inequality constraint in the Support Vector Machine (SVM) with the equality constraint, which transforms the convex quadratic programming (QP) problem of SVM into the solution of linear equations. However, when dealing with multi-class classification problems, LSSVM faces the challenges of lack of sparsity and sample noises, which can negatively impact its performance. Based on the modeling characteristics and data distribution of the multi-class LSSVM model, this paper proposes two improvements and establishes an improved fuzzy sparse multi-class least squares support vector machine (IF-S-M-LSSVM). The first improvement adopts a non-iterative sparse algorithm, which can delete training sample points to different degrees by adjusting the sparse ratio. The second improvement addresses the impact of sample noise on determining the optimal hyperplane by adding a fuzzy membership degree based on sample density. The advantages of the new model, in terms of training speed and classification accuracy, are verified through UCI machine learning standard data set experiments. Finally, the statistical significance of the IF-S-M-LSSVM model is tested using the Friedman and Bonferroni-Dunn tests. [ABSTRACT FROM AUTHOR]

Aiming at the problem of asynchronous multi-target tracking, this paper studies the AA fusion optimization problem of multi-sensor networks. Firstly, each sensor node runs a PHD filter, and the measurement information obtained from different sensor nodes in the fusion interval is flood communicated into composite measurement information. The Gaussian component representing the same target is associated with a subset by distance correlation. Then, the Bayesian Cramér–Rao Lower Bound of the asynchronous multi-target-tracking error, including radar node selection, is derived by combining the composite measurement information representing the same target. On this basis, a multi-sensor-network-optimization model for asynchronous multi-target tracking is established. That is, to minimize the asynchronous multi-target-tracking error as the optimization objective, the adaptive optimization design of the selection method of the sensor nodes in the sensor network is carried out, and the sequential quadratic programming (SQP) algorithm is used to select the most suitable sensor nodes for the AA fusion of the Gaussian components representing the same target. The simulation results show that compared with the existing algorithms, the proposed algorithm can effectively improve the asynchronous multi-target-tracking accuracy of multi-sensor networks. [ABSTRACT FROM AUTHOR]

In general, optimal motion planning can be performed both locally and globally. In such a planning, the choice in favor of either local or global planning technique mainly depends on whether the environmental conditions are dynamic or static. Hence, the most adequate choice is to use local planning or local planning alongside global planning. When designing optimal motion planning, both local and global, the key metrics to bear in mind are execution time, asymptotic optimality, and quick reaction to dynamic obstacles. Such planning approaches can address the aforementioned target metrics more efficiently compared to other approaches, such as path planning followed by smoothing. Thus, the foremost objective of this study is to analyze related literature in order to understand how the motion planning problem, especially the trajectory planning problem, is formulated when being applied for generating optimal trajectories in real-time for multirotor aerial vehicles, as well as how it impacts the listed metrics. As a result of this research, the trajectory planning problem was broken down into a set of subproblems, and the lists of methods for addressing each of the problems were identified and described in detail. Subsequently, the most prominent results from 2010 to 2022 were summarized and presented in the form of a timeline. [ABSTRACT FROM AUTHOR]

We apply an approach based on parametric mean-payoff games to develop bisection and Newton schemes for solving problems of tropical pseudolinear and pseudoquadratic optimization with general two-sided constraints. [ABSTRACT FROM AUTHOR]

We study nonlinear optimization problems with a stochastic objective and deterministic equality and inequality constraints, which emerge in numerous applications including finance, manufacturing, power systems and, recently, deep neural networks. We propose an active-set stochastic sequential quadratic programming (StoSQP) algorithm that utilizes a differentiable exact augmented Lagrangian as the merit function. The algorithm adaptively selects the penalty parameters of the augmented Lagrangian, and performs a stochastic line search to decide the stepsize. The global convergence is established: for any initialization, the KKT residuals converge to zero almost surely. Our algorithm and analysis further develop the prior work of Na et al. (Math Program, 2022. https://doi.org/10.1007/s10107-022-01846-z). Specifically, we allow nonlinear inequality constraints without requiring the strict complementary condition; refine some of designs in Na et al. (2022) such as the feasibility error condition and the monotonically increasing sample size; strengthen the global convergence guarantee; and improve the sample complexity on the objective Hessian. We demonstrate the performance of the designed algorithm on a subset of nonlinear problems collected in CUTEst test set and on constrained logistic regression problems. [ABSTRACT FROM AUTHOR]

In this paper, we study the convex quadratic optimization problem with indicator variables. For the 2 × 2 case, we describe the convex hull of the epigraph in the original space of variables, and also give a conic quadratic extended formulation. Then, using the convex hull description for the 2 × 2 case as a building block, we derive an extended SDP relaxation for the general case. This new formulation is stronger than other SDP relaxations proposed in the literature for the problem, including the optimal perspective relaxation and the optimal rank-one relaxation. Computational experiments indicate that the proposed formulations are quite effective in reducing the integrality gap of the optimization problems. [ABSTRACT FROM AUTHOR]

To alleviate the congestion caused by the tidal traffic and to improve the operational performance of both directions in arterials, this paper proposes a coordinated control model for arterials with asymmetric traffic demands in both oversaturated and unsaturated directions. The model utilizes a three-step architecture: (1) A mixed-integer linear programming model is built to maximize the throughput according to the relationship between traffic supply and demand as well as the balance between inflow and outflow. (2) A quadratic programming model is constructed to minimize the vehicle delay in the oversaturated direction based on Lighthill-Whitham-Richards theory. (3) A mixed-integer linear programming model is built to maximize the variable bandwidth in the unsaturated direction by introducing the relaxation variable. Furthermore, a three-step algorithm is used to solve the model and obtain the optimal arterial signal timing. Finally, a simulation model is put forward to verify the coordinated model. The results indicate that the model meet the asymmetric traffic demand through optimizing the arterial throughput, reducing delay in the oversaturated direction and maximizing the green wave bandwidth in the unsaturated direction. [ABSTRACT FROM AUTHOR]

Connected and Autonomous Vehicles (CAVs) in a platoon can exchange real-time information using Vehicle-to-Vehicle (V2V) communication technology to enhance platoon control performance. However, the V2V communication technology also provides opportunities for cyber-attacks, where falsified information can be injected into vehicle controllers to disrupt the platoon operation and even induce vehicle collisions. To address this problem, this study proposes a robust platoon control strategy for CAVs to mitigate the impacts of the falsified information to maneuver the CAV platoon to achieve consensus safely. The proposed control strategy consists of three components: (i) a H ∞ robust control law, which consistently negates the disturbance induced by falsified information; (ii) a state observer which estimates the vehicle states and disturbance induced by falsified information and inputs the estimated results into the H ∞ robust control law to compute a synthesized control decision; and (iii) a control decision regulator which applies a Control Barrier Function-based Quadratic Programming (CBF-QP) to regulate the control decision computed by the H ∞ robust control law to avoid actuator saturation issue and ensure safe spacing for each vehicle in the platoon. Numerical experiments demonstrate that the proposed control strategy can effectively drive the CAV platoon to the desired consensus safely and efficiently under the impacts of falsified information injection. [ABSTRACT FROM AUTHOR]

In this paper, a general expression formula for the Boubaker scaling (BS) operational matrix of the derivative is constructed. Then it is used to study a new parameterization direct technique for treating calculus of the variation problems approximately. The calculus of variation problems describe several important phenomena in mathematical science. The first step in our suggested method is to express the unknown variables in terms of Boubaker scaling basis functions with unknown coefficients. Secondly, the operational matrix of the derivative together with some important properties of the BS are utilized to achieve a non-linear programming problem in terms of the unknown coefficients. Finally, the unknown parameters are obtained using the quadratic programming technique. Some numerical examples are included to confirm the accuracy and applicability of the suggested direct parameterization method. [ABSTRACT FROM AUTHOR]

We propose IPRQP, an enhanced primal-dual interior-point relaxation method (IPRM), for solving convex quadratic programming. This method is based on a smoothing barrier augmented Lagrangian function for convex quadratic programming. IPRQP inherits the advantages of IPRM, including not requiring iterative points to be interior points, which makes IPRQP suitable for the warm-starting of combinatorial optimization problems. Compared to IPRM, the customized starting points allow the line search of IPRQP to contain only vector operations. In addition, IPRQP improves the updating scheme of the barrier parameter and provides a certificate of infeasibility. Some results on global convergence are presented. We implement the algorithm on convex quadratic programming problems from Maros-Mészaros and the benchmark problem sets NETLIB and Kennington, which contain feasible and infeasible linear programming problems. The numerical results show that our algorithm is reliable for feasible problems and efficient for detecting the infeasibility of infeasible problems. [ABSTRACT FROM AUTHOR]

This paper proposes a novel matrix rank-one decomposition for quaternion Hermitian matrices, which admits a stronger property than the previous results in Ai W et al (Math Progr 128(1):253–283, 2011), Huang Y, Zhang S (Math Oper Res 32(3):758–768, 2007), Sturm JF, Zhang S (Math Oper Res 28(2):246–267 2003). The enhanced property can be used to drive some improved results in joint numerical range, S -Procedure and quadratically constrained quadratic programming (QCQP) in the quaternion domain, demonstrating the capability of our new decomposition technique. [ABSTRACT FROM AUTHOR]

We propose an entropy regularized splitting model using low-rank factorization for solving binary quadratic programming with linear inequality constraints. Different from the semidefinite programming relaxation model, our model preserves the rank-one constraint and aims to find high quality rank-one solutions directly. The factorization transforms the variables into low-rank matrices, while the entropy term enforces the low-rank property of the splitting variable. A customized alternating direction method of multipliers is utilized to solve the proposed model. Specifically, our method uses the augmented Lagrangian function to deal with inequality constraints, and solves one subproblem on the oblique manifold by a regularized Newton method. Numerical results on the multiple-input multiple-output detection problem, the maxcut problem and the quadratic 0 - 1 problem indicate that our proposed algorithm has advantage over the SDP methods. [ABSTRACT FROM AUTHOR]

This paper proposes a wheeled mobile robot (WMR) robust control scheme. The feasible strategy is developed to achieve an efficient and robust autonomous mobile robot motion. To realize kinematic autonomous planning and control of the WMR, a novel controller is designed based on control Lyapunov function. This part can be divided into the following two aspects: 1) considering the nonholonomic constraints in the autonomous mobile robot trajectory tracking, a dynamic feedback‐linearization is adopted by utilizing differential flatness‐based integrated control framework to achieve full‐state controllability; 2) to compensate the structured uncertainties and slippage disturbances related to the robot kinematic model, a robust controller is designed based on control Lyapunov function with quadratic programming. Such a strategy can achieve autonomous motion even with unknown slippage disturbances subject to various constraints. Moreover, the sufficient condition is also analyzed to ensure the WMR system exponential stability. The effectiveness and performance of the proposed method are verified by numerical simulation. [ABSTRACT FROM AUTHOR]

A class of fault-tolerant safety-critical controller design methods based on high-order control barrier function (HOCBF) is proposed to address the problem of safety and stability of system affected by actuator faults in safety-constrained nonlinear affine system. Firstly, the fault information is incorporated into the conventional HOCBF to obtain a new type of HOCBF with faults. Secondly, in the case of a strictly required range of control inputs, a sufficient condition is proposed to satisfy the existing constraints, where the control inputs are always within the restricted range and the sufficient condition is expressed as feasibility constraints. Next, based on the quadratic programming (QP) method, the control Lyapunov function, fault HOCBF, and feasibility constraints are incorporated together to ensure that the overall feasibility, stabilization, and safety are guaranteed of the considered closed-loop system. Finally, the adaptive cruise control system is taken as an example to verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Robust adaptive beamforming (RAB) can be used to suppress interference signals while retaining the desired signals received by a sensor array. However, desired signal self-cancellation and model mismatch can affect RAB performance. In this paper, a novel interference-plus-noise covariance matrix (INCM) reconstruction method is proposed for RAB to solve these problems. The proposed method divides the desired signal into two ranges according to the input signal-to-noise ratio (SNR), namely low SNR and high SNR. In the low SNR range, INCM reconstruction directly uses the same sample covariance matrix as the sample matrix inversion (SMI) beamformer to retain the advantages of the traditional SMI algorithm. In the high SNR range, the eigenvalues of the sample covariance matrix are used to estimate the interference power and noise power. The optimized interference steering vector (SV) is obtained by solving a quadratic convex optimization problem in an interference subspace. The INCM is reconstructed from the interference SVs, interference power, and noise power. The reconstructed INCM is then used to correct the desired signal SV via maximizing the beamformer output power. This is achieved by solving a quadratically constrained quadratic programming (QCQP) problem. Analysis and simulation results are presented which demonstrate that the proposed method performs well under a variety of mismatch conditions. [ABSTRACT FROM AUTHOR]

In this paper, we deal with second-order conic programming (SOCP) duals for a robust convex quadratic optimization problem with uncertain data in the constraints. We first introduce a SOCP dual problem for this robust convex quadratic optimization problem with polytopic uncertain sets. Then, we obtain a zero duality gap result between this robust convex quadratic optimization problem and its dual problem in terms of a new robust type characteristic cone constraint qualification. We also construct a SOCP dual problem for this robust convex quadratic optimization problem with norm-constrained uncertain sets and obtain the corresponding zero duality gap result between them. Moreover, some numerical examples are given to explain the obtained results. [ABSTRACT FROM AUTHOR]

Superconducting (SC) magnets for accelerator concepts are often synthesized by numerically optimizing magnetic field waveforms, a process that requires a subsequent solution of a constrained inverse problem to identify suitable SC magnet windings. When the desired field distribution is intuitive, the inverse process is facilitated by seeding preconceived coil distributions into design optimization methods for refinement. With more complex magnetic field distributions, an initial design may be unknown, and topology optimization tools are required to synthesize current distributions without a priori guidance from a subject matter expert. In this work, we develop a constrained inverse Biot-Savart topology optimization methodology that synthesizes optimal distributions of current density in racetrack-like SC coils. The problem structure is exploited through a computationally efficient quadratic programming formulation, and the method is applied to recently published magnetic field waveforms for a recirculating proton phase shifter, a proton therapy gantry, and dipole magnets with sharp field transitions. The method and results herein identify novel winding configurations that can help magnet designers bring accelerator concepts to fruition.

The article presents an efficient method of optimal thrust allocation over the actuators in a dynamically positioned ship, according to the DNV-ST-0111 standard, Level 1. The optimisation task is approximated to a convex problem with linear constraints and mathematically formulated as quadratic programming. The case study is being used to illustrate the use of the proposed approach in assessing the DP capability of a rescue ship. The quadratic programming-based approach applied for dynamic positioning capability assessment allows for fast calculations to qualitatively compare different ship designs. In comparison with the DNV tool, it gives 100% successful validation for a ship with azimuth thrusters and a pessimistic solution for a ship equipped with propellers with rudders. Therefore, it can be safely applied at an early design stage.

To address the compounded uncertainty in the observed output data, we introduce a new method of fuzzy regression modeling which is based on quadratic programming and fuzzy weights, so that the objective function represents the quadratic error for all of the central tendencies and the spreads. Also, the fuzzy weights are optimized for the fuzzy regression model estimation with crisp input and fuzzy output based on the adaptive fuzzy networks, considering symmetrical triangular fuzzy output. This paper aims to use the proposed method for the prediction of the output value in empirical applications where the observed value is a range or mean of several values, rather than a real fixed number. Two numerical examples were employed to demonstrate the efficiency of the method and compare the results of the proposed method with the previous ones such as linear programming (LP), quadratic programming (QP), as well as combination of linear programming and fuzzy weights (FWLP). The results show that the proposed method provides better prediction accuracy than other methods in surface roughness prediction of the grinding process.

Abstract This paper proposes moving horizon estimation (MHE) to estimate the state variables of autonomous vehicle linear systems under measurement noises. To solve the MHE optimization problem, quadratic programming is employed. The steering angle, yaw angle, and global position constraints of an autonomous vehicle are considered in the estimation design. According to the simulation results, it can be observed that although the longer MHE step can give better results compared to the shorter MHE step, the difference in the MHE step only slightly affects the estimated results. However, the longer MHE step can increase the computational time. Additionally, the proposed MHE scheme is compared to the Kalman filter (KF) estimator. Based on the obtained results, the KF gives a better estimation than the MHE, but this notion must be verified for other case studies. Keywords: autonomous vehicle; Kalman filter; linear system; MHE; quadratic programming. Abstrak Paper ini mengusulkan moving horizon estimation (MHE) untuk mengestimasi variabel keadaan sistem linier kendaraan otonom karena pengaruh noise pengukuran. Untuk menyelesaikan masalah optimasi MHE, digunakan pemrograman kuadratik. Kendala sudut kemudi, sudut yaw dan posisi global dari kendaraan otonom dipertimbangkan dalam desain estimasi. Dari hasil simulasi dapat diketahui bahwa meskipun langkah MHE yang lebih panjang dapat memberikan hasil yang lebih baik dibandingkan dengan langkah MHE yang lebih pendek, perbedaan langkah MHE hanya sedikit mempengaruhi hasil estimasi. Namun, langkah MHE yang semakin panjang dapat meningkatkan waktu komputasi. Selain itu, skema MHE yang diusulkan dibandingkan dengan estimator Kalman filter (KF). Berdasarkan hasil yang diperoleh, KF memberikan estimasi yang lebih baik daripada MHE, tetapi gagasan ini harus diverifikasi untuk studi kasus lainnya. Kata Kunci: kendaraan otonom; Kalman filter; sistem linier; MHE; pemrograman kuadratik. 2020MSC: 62P35, 65D19

Abstract The paper addresses the problem of accelerating predictive control of non‐linear system models augmented with Gaussian processes (GP‐MPC). Due to the non‐linear and stochastic prediction model, predictive control of GP‐based models requires to solve a stochastic optimization problem. Different model simplification methods have to be applied to reformulate this problem to a deterministic, non‐linear optimization task that can be handled by a numerical solver. As these problems are still complex, especially with exact moment calculations, real‐time implementation of GP‐MPC is extremely challenging. The existing solutions accelerate the computations at the solver level by linearizing the non‐linear optimization problem and applying sequential convexification. In contrast, this paper proposes a novel GP‐MPC solution approach that without linearization formulates a series of surrogate quadratic programs (QP‐s) to iteratively obtain the solution of the original non‐linear optimization problem. The first step is embedding the non‐linear mean‐variance dynamics of the GP‐MPC prediction model in a linear parameter‐varying (LPV) structure and rewriting the constraints in parameter‐varying form. By fixing the scheduling trajectory at a known variation (based on previously computed or initial state‐input trajectories), optimization of the input sequence for the remaining varying linear model reduces to a linearly constrained quadratic program. After solving the QP, the non‐linear prediction model is simulated for the new control input sequence and new scheduling trajectories are updated. The procedure is iterated until the convergence of the scheduling, that is, the solution of the QP converges to the solution of the original non‐linear optimization problem. By designing a reference tracking controller for a 4DOF robot arm, we illustrate that the convergence is remarkably fast and the approach is computationally advantageous compared to current solutions. The proposed method enables the application of GP‐MPC algorithms even with exact moment matching on fast dynamical systems and requires only a QP solver.

The rapid advancement of unmanned aerial vehicle (UAV) technologies has led to an increasing demand for UAV operations in low-altitude, high-density, and complex airspace such as mountains or urban areas. In order to handle complex scenarios and ensure flight safety for UAVs with different flight missions beyond visual line of sight in such environments, a fusion framework of onboard autonomous flight trajectory management and decision-making system using global strategical path planning and local tactical trajectory optimization combination is proposed in this paper. The global strategical path planning is implemented by an enhanced A* algorithm under the multi-constraint of UAV positioning uncertainty and obstacle density to improve the safety and cost-effectiveness. The local tactical trajectory optimization is realized using quadratic programming to ensure smoothness, kinematic feasibility, and obstacle avoidance of the planned trajectory in dynamic environments. Receding-horizon control is used to ensure the flight path and trajectory planning efficiently and seamlessly. To assess the performance of the system, a terrain database and a navigation system are employed for environment and navigation performance simulation. The experimental results confirm that the fusion approach can realize better safety and cost-effectiveness through path planning with kino-dynamic feasible trajectory optimization.

This paper presents an innovative three-level direct yaw moment control strategy for distributed drive electric vehicles (DDEV) under emergency conditions. The phase plane analysis is used at the supervisory level to design the stability boundary function taking into account the impact of the road adhesion coefficient. To guarantee the performance of finite-time convergence and singularity-free methods, the adaptive nonsingular fast terminal sliding mode control (ANFTSMC) is developed at the decision level to determine the extra yaw moment for tracking the intended side slip angle and yaw rate. Among this, the unstable domain in the phase plane is further separated into moderately and severely unstable according to the degree of vehicle instability, which is defined by the distance between the state phase point and the stability boundary. Meanwhile, the adaptive weight between the handling and stability is obtained. At the executive level, the quadratic programming algorithm is adopted to allocate four-wheel torque with the objective of optimal tire utilization rate. Finally, the co-simulation test is executed in both closed-loop and open-loop circumstances; according to the simulation results, the presented ANFTSMC method outperforms the SMC, and it can decrease the tracking error and improve the handling and stability.

Due to some limitations in the data collection process caused either by human-related errors or by collection electronics, sensors, and network connectivity-related errors, the important values at some points could be lost. However, a complete dataset is required for the desired performance of the subsequent applications in various fields like engineering, data science, statistics, etc. An efficient data imputation technique is desired to fill in the missing data values to achieve completeness within the dataset. The fuzzy integral is considered one of the most powerful techniques for multi-source information fusion. It has a wide range of applications in many real-world decision-making problems that often require decisions to be made with partially observable/available information. To address this problem, algorithms impute missing data with a representative sample or by predicting the most likely value given the observed data. In this article, we take a completely different approach to the information fusion task in the ordered weighted averaging (OWA) context. In particular, we empirically explore for different distributions how the weights/importance of the missing sources are distributed across the observed inputs/sources. The experimental results on the synthetic and real-world datasets demonstrate the applicability of the proposed methods.

In solving specific problems, physical laws and mathematical theorems directly express the connections between variables with equations/inequations. At times, it could be extremely hard or not viable to solve these equations/inequations directly. The PE (principle of equivalence) is a commonly applied pragmatic method across multiple fields. PE transforms the initial equations/inequations into simplified equivalent equations/inequations that are more manageable to solve, allowing researchers to achieve their objectives. The problem-solving process in many fields benefits from the use of PE. Recently, the ZE (Zhang equivalency) framework has surfaced as a promising approach for addressing time-dependent optimization problems. This ZEF (ZE framework) consolidates constraints at different tiers, demonstrating its capacity for the solving of time-dependent optimization problems. To broaden the application of ZEF in time-dependent optimization problems, specifically in the domain of motion planning for redundant manipulators, the authors systematically investigate the ZEF-I2I (ZEF of the inequation-to-inequation) type. The study concentrates on transforming constraints (i.e., joint constraints and obstacles avoidance depicted in different tiers) into consolidated constraints backed by rigorous mathematical derivations. The effectiveness and applicability of the ZEF-I2I are verified through two optimization motion planning schemes, which consolidate constraints in the velocity-tier and acceleration-tier. Schemes are required to accomplish the goal of repetitive motion planning within constraints. The firstly presented optimization motion planning schemes are then reformulated as two time-dependent quadratic programming problems. Simulative experiments conducted on the basis of a six-joint redundant manipulator confirm the outstanding effectiveness of the firstly presented ZEF-I2I in achieving the goal of motion planning within constraints.

Introduction: Compared to Genome-Wide Association Studies (GWAS) for common variants, single-marker association analysis for rare variants is underpowered. Set-based association analyses for rare variants are powerful tools that capture some of the missing heritability in trait association studies. Methods: We extend the convex-optimized SKAT (cSKAT) test set procedure which learns from data the optimal convex combination of kernels, to the full Generalised Linear Model (GLM) setting with arbitrary non-genetic covariates. We call this extended cSKAT (ecSKAT) and show that the resulting optimization problem is a quadratic programming problem that can be solved with no additional cost compared to cSKAT. Results: We show that a modified objective is related to an upper bound for the pvalue through a decreasing exponential term in the objective function, indicating that optimizing this objective function is a principled way of learning the combination of kernels. We evaluate the performance of the proposed method on continuous and binary traits using simulation studies and illustrate its application using UK Biobank Whole Exome Sequencing data on hand grip strength and systemic lupus erythematosus rare variant association analysis. Discussion: Our proposed ecSKAT method enables correcting for important confounders in association studies such as age, sex or population structure for both quantitative and binary traits. Simulation studies showed that ecSKAT can recover sensible weights and achieve higher power across different sample sizes and misspecification settings. Compared to the burden test and SKAT method, ecSKAT gives a lower p-value for the genes tested in both quantitative and binary traits in the UKBiobank cohort. [ABSTRACT FROM AUTHOR]

Recently, many robust adaptive beamforming (RAB) algorithms have been proposed to improve beamforming performance when model mismatches occur. For a uniform linear array, a larger aperture array can obtain higher array gain for beamforming when the inter-sensor spacing is fixed. However, only the small aperture array can be used in the equipment limited by platform installation space, significantly weakening beamforming output performance. This paper proposes two beamforming methods for improving beamforming output in small aperture sensor arrays. The first method employs an integration algorithm that combines angular sector and gradient vector search to reconstruct the interference covariance matrix (ICM). Then, the interference-plus-noise covariance matrix (INCM) is reconstructed combined with the estimated noise power. The INCM and ICM are used to optimize the desired signal steering vector (SV) by solving a quadratically constrained quadratic programming (QCQP) problem. The second method proposes a beamforming algorithm based on a virtual extended array to increase the degree of freedom of the beamformer. First, the virtual conjugated array element is designed based on the structural characteristics of a uniform linear array, and received data at the virtual array element are obtained using a linear prediction method. Then, the extended INCM is reconstructed, and the desired signal SV is optimized using an algorithm similar to the actual array. The simulation results demonstrate the effectiveness of the proposed methods under different conditions. [ABSTRACT FROM AUTHOR]