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In this paper, stochastic optimisation of CVaR is applied to maintain risk-averse viability and improve resilience of a supply chain under propagated disruptions. In order to establish the risk-averse boundaries on supply chain viability space, two stochastic optimisation models are developed with the two conflicting objectives: minimisation of Conditional Cost-at-Risk and maximisation of Conditional Service-at-Risk. Then, the risk-averse viable production trajectory between the two boundaries is selected using a stochastic mixed integer quadratic programming model. The proposed approach is applied to maintain the supply chain viability in the smartphone manufacturing and the results of computational experiments are provided. The findings indicate that when the decision-making is more risk-aversive, the size of the viability space between the two boundaries is greater. As a result, more room is available for selecting viable production trajectories under severe disruptions. Moreover, the larger is viability space, the higher is both worst-case and average resilience of the supply chain. Risk-neutral, single-objective decision-making may reduce the supply chain viability. A single-objective supply chain optimisation which moves production to the corresponding boundary of the viability space, should not be applied under severe disruption risks to avoid greater losses. [ABSTRACT FROM AUTHOR]

Incorporating decision-makers' risk preferences into data-driven newsvendor models and developing machine learning methods to solve the models are the challenging problems addressed in this study. To consider different distributions and decision-makers' different risk preferences for the two losses of the total cost newsvendor model, the symmetrical, the partial symmetrical and the asymmetrical CVaR criteria are introduced. The regularisation, the primal-dual approach and the kernels in support vector machines are used to transform the data-driven risk-averse newsvendor problems under the CVaR criterion into the convex quadratic programming problems with good theoretical properties. Computational experiments are conducted on a real-world dataset. The models under the partial symmetrical and the asymmetrical CVaR criteria obtained good performances, but that under the symmetrical CVaR criterion suffered the underfitting problem. Two factors including the degrees of risk aversion for the two losses in the total cost newsvendor model and the empirical errors of data-driven models affect order decisions. The degrees of risk aversion for the two losses have anti-directional effects on order quantities. The introduction of asymmetrical CVaR criterion paves a new way to reveal the effects of different risk references for different losses on order decisions, and has the potential to improve newsvendor decisions. [ABSTRACT FROM AUTHOR]

For civil engineering structures, structural damage usually occurs at limited positions in the preliminary stage of the structural failure. Compared with the numerous elements of the entire structure, the damaged elements are sparsely distributed in space. Based on this important prior information, this paper proposed to utilize a sparse Bayesian learning method to identify the damage to structures while considering the measurement noise and modeling error. The particle Swarm Optimization (PSO) algorithm was first introduced to address the associated computational efficiency issue, and the optimization performances of PSO and Sequential Quadratic Programming (SQP) algorithm in the process of model updating were compared, positive outcomes revealed that the PSO algorithm has the stronger searching ability and better robustness. To investigate the effectiveness and practicality of the sparse Bayesian learning with a PSO algorithm in structural damage detection, an asymmetrical frame in different scenarios (e.g. with single and multiple damages) was constructed in the laboratory. The encouraging results of the experimental case studies compellingly demonstrate that the presented methodology not only can detect the location and extent of structural damage with high precision and efficiency, but also can proficiently assess the posterior uncertainties associated with the damage detection results. [ABSTRACT FROM AUTHOR]

Simultaneous regulation of multiple properties in next-generation tokamaks like ITER and fusion pilot plant may require the integration of different plasma control algorithms. Such integration requires the conversion of individual controller commands into physical actuator requests while accounting for the coupling between different plasma properties. This work proposes a tokamak and scenario-agnostic actuator-sharing algorithm (ASA) to perform the above-mentioned command-request conversion and, hence, integrate multiple plasma controllers. The proposed algorithm implicitly solves a quadratic programming (QP) problem formulated to account for the saturation limits and the relation between the controller commands and physical actuator requests. Since the constraints arising in the QP program are linear, the proposed ASA is highly computationally efficient and can be implemented in the tokamak plasma control system in real time. Furthermore, the proposed algorithm is designed to handle real-time changes in the control objectives and actuators' availability. Nonlinear simulations carried out using the Control Oriented Transport SIMulator illustrate the effectiveness of the proposed algorithm in achieving multiple control objectives simultaneously. [ABSTRACT FROM AUTHOR]

This work studies the deployment of the ship‐from‐store omnichannel strategy and the pricing and inventory decisions for an online retailer. Robust optimization models are constructed for the online‐only and the ship‐from‐store modes under a budgeted uncertainty set. The ARIMA model is used to predict the parameter values of the budgeted uncertainty set using historical demand data. The closed‐form optimal solution for the online‐only mode is obtained. The robust counterpart model for the ship‐from‐store mode is converted to a mixed integer quadratic programming model. Numerical studies are conducted to validate the theoretical results and to verify the effectiveness and practicality of the developed robust optimization solution approach. The results show that adopting a ship‐from‐store strategy may hurt the retailer's profit if a significant proportion of consumers are time‐sensitive with high travel cost. The ship‐from‐store strategy is optimal if it significantly boosts market growth. [ABSTRACT FROM AUTHOR]

The task of collecting and transporting luggage trolleys in airports, characterized by its complexity within dynamic public environments, presents both an ongoing challenge and a promising opportunity for automated service robots. Previous research has primarily developed on universal platforms with robot arms or focused on handling a single trolley, creating a gap in providing cost‐effective and efficient solutions for practical scenarios. In this paper, we propose a low‐cost mobile manipulation robot incorporated with an autonomy framework for the collection and transportation of multiple trolleys that can significantly enhance operational efficiency. The method involves a novel design of the mechanical system and a vision‐based control strategy. We design a lightweight manipulator and the docking mechanism, optimized for the sequential stacking and transportation of trolleys. On the basis of the Control Lyapunov Function and Control Barrier Function, we propose a vision‐based controller with online Quadratic Programming, which improves the docking accuracy. The practical application of our system is demonstrated in real‐world scenarios, where it successfully executes the multiple‐trolley collection task. [ABSTRACT FROM AUTHOR]

The synthesis of large‐scale integrated water networks is typically formulated as nonconvex mixed‐integer quadratic constrained programming (MIQCP) or QCP problems. With the complexity arising from bilinear terms in modeling mass flows of contaminants and binary variables representing the presence of units or streams, numerous local optima exist, thus presenting a significant optimization challenge. This study introduces a deterministic global optimization algorithm based on mixed‐integer programming (MIP) to tackle such problems. The approach involves dynamically strengthening the relaxed problems to converge towards the original problems. A simultaneous partition strategy is proposed combining locally uniform division with dynamic partitioned variables choosing. Furthermore, several adaptive bound contraction schemes are introduced to efficiently manage the size of the relaxed problems, assisting in accelerating the solution process. The algorithm's effectiveness and robustness are demonstrated with a large test set, showing superior performance compared to commercial solvers specifically on MIQCP problems. [ABSTRACT FROM AUTHOR]

The needs of solid oxide fuel cells (SOFC) and batteries in large ships are analyzed by estimating the amount of fuel consumption and CO2 emissions. Three types of systems are proposed: 1) fuel cells-battery-generator engine system, 2) battery-generator engine system, and 3) generator engine system. This study is based on the time-varying electric power demand and adopted the sequential quadratic programming (SQP) method to find the optimal power distribution of mixed power sources. CO2 emissions in the SOFC hybrid system are 11.6% lower than in the conventional generator engine system, and those in the battery-generator engine system are 5.1% lower than in the conventional system. The reduction of CO2 emissions come from three factors: the operation of the generator engine at a relatively high load rate, the battery sharing the operation of the generator engine, and the high efficiency of the SOFC running. The SOFC hybrid system can be a sustainable technology in large vessels. [ABSTRACT FROM AUTHOR]

Purpose: To assess the impact of different B0 shimming algorithms on MRS. Methods: B0 field maps and single‐voxel MR spectroscopy were acquired in the prefrontal cortex of five volunteers at 3 T using five different B0 shimming approaches. B0 shimming was achieved using Siemens' proprietary shim algorithm, in addition to the Pseudo‐Inverse (PI), Quadratic Programming (QuadProg), Least Squares (LSq), and Gradient optimization (Grad) algorithms. The standard deviation of the shimmed B0 field, as well as the SNR and FWHM of the measured metabolites, was used to evaluate the performance of each B0 shimming algorithm. Results: Compared to Siemens's shim, significant reductions (p < 0.01) in the standard deviation of the B0 field distribution within the MRS voxel were observed for the PI, QuadProg, and Grad algorithms (3.8 Hz, 7.3 Hz, and 3.9 Hz respectively, compared to 11.5 Hz for Siemens), but not for the LSq (12.9 Hz) algorithm. Moreover, significantly increased SNR and reduced FWHM for the N‐acetylaspartate metabolite were consistent with the improvement in B0 homogeneity for the aforementioned shimming algorithms. Conclusion: Here, we demonstrate that the choice of B0 shimming algorithm can have a significant impact on the quality of MR spectra and that significant improvements in spectrum quality could be achieved by using alternatives to the default vendor approach. [ABSTRACT FROM AUTHOR]

In epidemiological studies, evaluating the health impacts stemming from multiple exposures is one of the important goals. To analyze the effects of multiple exposures on discrete or time‐to‐event health outcomes, researchers often employ generalized linear models, Cox proportional hazards models, and machine learning methods. However, observational studies are prone to unmeasured confounding factors, which can introduce the potential for substantial bias in the multiple exposure effects. To address this issue, we propose a novel outcome model‐based sensitivity analysis method for non‐Gaussian and time‐to‐event outcomes with multiple exposures. All the proposed sensitivity analysis problems are formulated as linear programming problems with quadratic and linear constraints, which can be solved efficiently. Analytic solutions are provided for some optimization problems, and a numerical study is performed to examine how the proposed sensitivity analysis behaves in finite samples. We illustrate the proposed method using two real data examples. [ABSTRACT FROM AUTHOR]

The second-order method for the solution of quadratic programming (QP) with affine constraints is introduced in this paper. It belongs to an active-set method family. However, it uses a projection and a proportionality test to speed up active set identification. Matrix factor updates accompany active set changes to decrease the computational load. The development of the algorithm is motivated by problems arising in embedded applications of model predictive control in automotive, particularly in autonomous driving, hybridization, electrification, and system optimization. These applications typically lead to an ill-conditioned problem with heavy changes in an active set of solutions at each sample time. Further, underlying quadratic programming needs to be solved in a short time with limited computational and memory resources. Resistance against ill-conditioning, fast convergence, and low memory footprint are vital attributes of the proposed method. Practical aspects, namely preprocessing or Hessian factor updates, are described together with the proposed numerical method. Benchmark results accentuate the efficiency of the algorithm. [ABSTRACT FROM AUTHOR]

In this work, the containment control problem for a quadrotor team is addressed in the presence of multiple dynamic leaders with unknown bounded time-varying inputs. Both safety-critical constraints and input constraints are considered. Specifically, a linear extended state observer (ESO) is employed to handle the uncertainty and disturbance. A distributed fixed-time observer is designed to estimate the reference signal requiring no global information. The proposed nominal controller can guarantee the formation geometric constraint in steady states. Moreover, safety certificates for collision-free in transient states is enforced by using exponential control barrier functions (ECBFs). A real-time quadratic programming (QP) problem is constructed to modify the nominal controller such that both safety constraint and input constraint can be satisfied. Finally, simulations and experiments illustrate the effectiveness of the algorithm. [ABSTRACT FROM AUTHOR]

The unpreconditioned H‐TFETI‐DP (hybrid total finite element tearing and interconnecting dual‐primal) domain decomposition method introduced by Klawonn and Rheinbach turned out to be an effective solver for variational inequalities discretized by huge structured grids. The basic idea is to decompose the domain into non‐overlapping subdomains, interconnect some adjacent subdomains into clusters on a primal level, and enforce the continuity of the solution across both the subdomain and cluster interfaces by Lagrange multipliers. After eliminating the primal variables, we get a reasonably conditioned quadratic programming (QP) problem with bound and equality constraints. Here, we first reduce the continuous problem to the subdomains' boundaries, then discretize it using the boundary element method, and finally interconnect the subdomains by the averages of adjacent edges. The resulting QP problem in multipliers with a small coarse grid is solved by specialized QP algorithms with optimal complexity. The method can be considered as a three‐level multigrid with the coarse grids split between primal and dual variables. Numerical experiments illustrate the efficiency of the presented H‐TBETI‐DP (hybrid total boundary element tearing and interconnecting dual‐primal) method and nice spectral properties of the discretized Steklov–Poincaré operators as compared with their finite element counterparts. [ABSTRACT FROM AUTHOR]

Nowadays, power system protection is increasingly important because of the growing number of customers and the pressing need for timely fault resolution and relay operations. This paper addresses the non‐linear nature of the objective function in the optimal coordination of directional overcurrent relays (DOCRs) by employing a quadratic Taylor series expansion around an operating point, converting the problem into a quadratically constrained quadratic programming problem, ensuring a global optimal solution with increased computational efficiency. Additionally, the quadratic constraints are converted into second‐order cone constraints for compatibility with the CPLEX solver. Using the least square method, the operating point values are determined and further fine‐tuned using iterations with the DOCR operation times. The IEEE 3‐bus, IEEE 8‐bus, and IEEE 14‐bus test systems are used to test the method, which shows higher improvement rates in reducing DOCR operation times and enhancing cooperation than conventional and metaheuristic methods. The simulation results verify the numerical superiority of the method in optimizing the protection system's efficiency while obtaining rapid and accurate solutions. The proposed method was tested on IEEE 3‐bus, 8‐bus, and 14‐bus systems, optimizing relay operating times to 0.87, 2.96, and 7.05 s, respectively, demonstrating the method's efficiency over conventional approaches. [ABSTRACT FROM AUTHOR]

Fast and dramatic voltage disturbances caused by the electric propulsion and dynamic positioning process are severe issues in the DC shipboard integrated power system (DC‐SIPS). The secondary voltage control (SVC) equipped in the diesel genset (DG) and hybrid energy storage system (HESS) becomes an effective solution. However, the conventional SVC cannot distinguish the different voltage regulation characteristics between DG and HESS in a cost‐effective way when allocating the voltage regulation responsibility (VRR). The cost optimization achieved by the conventional tertiary control cannot be used for the DC‐SIPS due to frequent and unpredictable load fluctuations. In this paper, a cost‐effective secondary voltage control is proposed to realize voltage restoration and cost minimization simultaneously. First, the voltage regulation cost model is developed considering the different voltage regulation characteristics of DG and HESS. Then, the optimization problem of VRR distribution is addressed by minimizing the total voltage regulation cost function using a quadratic programming algorithm. Moreover, the voltage regulation ability of each energy storage system is fully used with the state of charge balance. Thus, the conflict among voltage restoration, cost minimization, and SoC balance is effectively addressed. Finally, promising hardware‐in‐loop test results illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

AbstractThe convex formulations of non-smooth dynamics (NSD) approach have been implemented successfully into many-body problems, such as granular material flow simulations. NSD for multibody-dynamics formulation results in a nonlinear programming problem because of additional constraint on quaternions. This study modifies the convex formulation into a framework for multibody systems applications dealing with joints with friction and clearances as well as ideal joints. This is achieved by: (1) Converting the existing formalism into canonical forms, which gives the advantage of utilizing advanced general-purpose convex optimization solvers. (2) Modifying the non-smooth integration scheme to preserve rotations, thus mitigating the drift. A detailed convexity analysis on the nonlinear formulation showed that variable step-size scheme makes the problem non-convex. Further, it was found that certain windows appear where step-size variation can be achieved without sacrificing the convexity. Based on the analysis, the NSD problem is reformulated as a canonical form quadratic programming (QP) problem. Then, a canonical second-order con-programming (SOCP) problem is presented for including friction in the joints with clearances. Furthermore, an analysis on state-of-the-art non-smooth integrator is presented which shows that the perceived drift is because of violation of normalization constraint on quaternions. Two strategies are derived for preserving the normalization constraint: Projection and Lie-integration on quaternions. The proposed methods are evaluated against state-of-the-art scheme using numerical experiments on a rigid pendulum with clearance. Further, the framework has been tested on a pendulum with ideal revolute joint, to establish the applicability of the framework on smooth, as well as, on non-smooth problems. [ABSTRACT FROM AUTHOR]

In this paper the author studies the problem of finding the farthest points in an intersection of balls to a given point 0. A polynomial algorithm is presented which solves the problem under the conditions that the given point is outside of the convex hull of the balls centers. It is shown that in this particular case the problem of finding the smallest ball centered in 0 which includes the intersection of balls is actually convex. [ABSTRACT FROM AUTHOR]

The integration of renewable energy into Intelligent Distribution Networks (IDNs) is challenged by the inherent variability and fluctuations in energy supply, particularly with photovoltaic (PV) generation as the primary form of distributed generation (DG). However, managing the fluctuations and variability in renewable energy supply presents significant challenges. To address these complexities, it is vital to optimally coordinate flexible resources from source–network–storage–load (SNSL) in a manner that aligns with cross-sectoral emission reduction strategies while enhancing grid stability and efficiency. This paper addresses these challenges by proposing a strategy that optimizes the coordination of PV-based DG, storage, and load resources through Robotic Process Automation (RPA) to enhance grid stability and support emissions reduction. We use a two-layer dispatching framework: the lower-layer model, formulated as a quadratic programming problem, maximizes PV utilization for individual users, while the upper-layer model, based on a second-order cone relaxation approach, manages the overall IDN to minimize operational costs. The iterative solution leverages tie-line power flow as boundary information to ensure convergence across the network. Validated on an enhanced IEEE 33-bus system, the approach demonstrates a 62% increase in PV-based DG consumption and a 25% reduction in active power losses, highlighting its potential to improve grid efficiency and contribute to emission reduction goals. [ABSTRACT FROM AUTHOR]

This paper analyses the solution of a specific quadratic sub-problem, along with its possible applications, within both constrained and unconstrained Nonlinear Programming frameworks. We give evidence that this sub–problem may appear in a number of Linesearch Based Methods (LBM) schemes, and to some extent it reveals a close analogy with the solution of trust–region sub–problems. Namely, we refer to a two-dimensional structured quadratic problem, where five linear inequality constraints are included. Finally, we detail how to compute an exact global solution of our two-dimensional quadratic sub-problem, exploiting first order Karush-Khun-Tucker (KKT) conditions. [ABSTRACT FROM AUTHOR]

In order to further enhance the stability of the orbital transportation, the modal characteristics of the orbital support structure were simulated and analyzed. The multi-objective optimization method was applied to design the structure for lightweighting while increasing the first-order natural frequency and reducing the stress peak. Using ANSYS Workbench, the parametric finite element model was established, the length of the intermediate support rod, and the lateral length of the rib were regarded as the parameterized dimensions. Through dynamic characteristic analysis, the natural frequencies, modal shapes, and harmonic response characteristics were obtained. Parametric samples were obtained by using Latin square method, and the approximate model was fitted by polynomial function. Multi-Objective Genetic Algorithm and Sequential Quadratic Programming were applied for optimization calculation. The results indicate that the structurally lightened design can attain higher strength and stiffness. [ABSTRACT FROM AUTHOR]

This paper proposes a cost-based stochastic optimal energy management framework for a renewable energy-assisted isolated microgrid system. These microgrids encourage the integration of multiple distributed energy sources, including the penetration of renewable energy. For this purpose, the optimal day-ahead dispatch of the connected energy resources is obtained for an economically viable system by solving a nonlinear constrained optimization problem. The renewable energy and the load demand data forecasting are accomplished using the Gaussian process regression learning model in the MATLAB/SIMULINK® environment for obtaining the day-ahead dispatch. The optimal problem is solved through sequential quadratic programming and a hybrid function approach incorporating particle swarm optimization for a comprehensive techno-economical analysis. A comparative assessment of the results is accomplished to obtain a more feasible and economical system operation corresponding to different time horizons and other critical factors such as fast iterations, computational accuracy, solution feasibility, convergence rate, etc. [ABSTRACT FROM AUTHOR]

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

SOLNP \(+\) is a derivative-free solver for constrained nonlinear optimization. It starts from SOLve Nonlinear Programming (SOLNP) proposed in 1989 by Ye. The main ideas are to use finite difference to approximate the gradient of the objective function and constraints, and use augmented Lagrangian method and sequential quadratic programming to deal with nonlinear constraints. We incorporate the techniques of implicit filtering, a new restart mechanism, and a modern quadratic programming solver into this new version with an ANSI C implementation. The algorithm exhibits a great advantage in running time and robustness under noise compared with the old version implemented in MATLAB. The numerical experiments show that SOLNP \(+\) is comparable with two widely used solvers, COBYLA and NOMAD. SOLNP \(+\) is available at https://github.com/COPT-Public/SOLNP_plus. [ABSTRACT FROM AUTHOR]

A distributionally robust model predictive control (DRMPC) scheme is proposed based on neural network (NN) modeling to achieve the trajectory tracking control of robot manipulators with state and control torque constraints. First, an NN is used to fit the motion data of robot manipulators for data-driven dynamic modeling, converting it into a linear prediction model through gradients. Then, by statistically analyzing the stochastic characteristics of the NN modeling errors, a distributionally robust model predictive controller is designed based on the chance constraints, and the optimization problem is transformed into a tractable quadratic programming (QP) problem under the distributionally robust optimization (DRO) framework. The recursive feasibility and convergence of the proposed algorithm are proven. Finally, the effectiveness of the proposed algorithm is verified through numerical simulation. [ABSTRACT FROM AUTHOR]

In the big data era, subsampling or sub-data selection techniques are often adopted to extract a fraction of informative individuals from the massive data. Existing subsampling algorithms focus mainly on obtaining a representative subset to achieve the best estimation accuracy under a given class of models. In this article, we consider a semi-supervised setting wherein a small or moderate sized "labeled" data is available in addition to a much larger sized "unlabeled" data. The goal is to sample from the unlabeled data with a given budget to obtain informative individuals that are characterized by their unobserved responses. We propose an optimal subsampling procedure that is able to maximize the diversity of the selected subsample and control the false selection rate (FSR) simultaneously, allowing us to explore reliable information as much as possible. The key ingredients of our method are the use of predictive inference for quantifying the uncertainty of response predictions and a reformulation of the objective into a constrained optimization problem. We show that the proposed method is asymptotically optimal in the sense that the diversity of the subsample converges to its oracle counterpart with FSR control. Numerical simulations and a real-data example validate the superior performance of the proposed strategy. for this article are available online. [ABSTRACT FROM AUTHOR]

In this paper, we look into the rotated quadratic cone and analyze its algebraic structure. We construct an algebra associated with this cone and show that this algebra is a Euclidean Jordan algebra (EJA) with a certain inner product. We also demonstrate some spectral and algebraic characteristics of this EJA. The rotated quadratic cone is then proven to be the cone of squares of the generated EJA. The obtained results can help optimization researchers improve specialized interior-point algorithms for rotated quadratic cone programming based on the generated EJA. Additionally, since it is known that the rotated quadratic cone is a special case of the power cone, another reason for this study may be to open the door to understanding the algebraic structure of the general power cone in the future. [ABSTRACT FROM AUTHOR]

In this study, the stiffener geometry was optimized using curvilinear 3D printing to enhance the buckling resistance. A bio-inspired skin/stiffener composite that mimicked spider-web structures was generated. A dataset was formulated for the regression analysis, covering buckling stresses under distinct feature values. The regression equations, crafted using a deep neural network trained on the dataset, were evaluated. The derived regression equation was subjected to sequential quadratic programming, a mathematical optimization, to determine the optimal value of the explanatory variable. This was aimed at maximizing the buckling stress-to-stiffener volume ratio, which is the objective variable. The optimized arrangement exhibited significantly improved buckling resistance, with approximately 163% higher buckling stress than conventionally designed structures with straight stiffeners of similar weight. [ABSTRACT FROM AUTHOR]

We show that KKT-type conditions are necessary and sufficient for global optimality for some quadratically constrained (possibly nonconvex) quadratic programming QCQP problems in Hilbert space. The key property is the convexity of an image-type set, called generalized image set, related to the functions appearing in the formulation of the problem. The proof of the main result relies on a generalized version of the (Jakubovich) S-Lemma in Hilbert spaces. As an application, we consider the class of QCQP problems with a special form of the quadratic terms of the constraints. [ABSTRACT FROM AUTHOR]

High-speed autonomous vehicles can effectively improve the performance of obstacle-avoidance trajectory-planning and tracking control through integration with existing electronic control systems. However, relatively little research has been conducted in this field. This paper proposes a novel methodology of obstacle-avoidance trajectory-planning and tracking control based on active front-wheel steering integrated with tilting technology that can tilt the vehicle body toward the inside of the curve via active suspension when turning. The controller is designed using hierarchical control, in which the upper layer uses the point-mass vehicle model to design the trajectory-planning algorithm based on model predictive control. The lower layer uses the nonlinear vehicle model to design obstacle-avoidance tracking nonlinear model predictive control based on active steering integrated with tilt control. Then, the constrained nonlinear model predictive control problem is transformed into a constrained nonlinear programming problem, which is solved by sequential quadratic programming. Finally, simulations were performed using the CarSim/Simulink co-simulation platform. Two other hierarchical obstacle-avoidance tracking nonlinear model predictive controllers were designed as comparison objects. The simulation results show that the planning trajectory of the proposed integrated controller is closest to the obstacle. This controller effectively improves the vehicle obstacle-avoidance trajectory-tracking performance, handling stability, and maneuverability. [ABSTRACT FROM AUTHOR]

This paper focuses on the development and position control of a robotic system specifically designed for passive rehabilitation. The system is a two-degree-of-freedom robot, dedicated to elbow and a wrist joints. The objective of this research is to create a robotic rehabilitation emulation test that allows therapists to implement their therapeutic programs smoothly and efficiently while minimizing any excessive movements or overshooting. The real-time experiments were conducted to compare the performances of four controllers: model predictive controller (MPC), proportional–integral (PI) controller, RST controller, and constrained MPC (CMPC). Sinusoidal and filtered trajectories were studied to determine the optimal controller for energy efficiency. The obtained results demonstrate that the embedded MPC outperforms the other two controllers. The constrained model predictive control design is employed to address the stringent constraints of the robot. Using a rapid quadratic programming solver based on the Hildreth method ensures compliance with the short real-time implementation sampling time. This approach achieves reduced computational costs while balancing control effort against closed-loop performance. [ABSTRACT FROM AUTHOR]

As the environmental aspects become increasingly important, the disassembly problems have become the researcher's focus. Multiple criteria do not enable finding a general optimization method for the topic, but some heuristics and classical formulations provide effective solutions. By highlighting that disassembly problems are not the straight inverses of assembly problems and the conditions are not standard, disassembly optimization solutions require human control and supervision. Considering that Reinforcement learning (RL) methods can successfully solve complex optimization problems, we developed an RL-based solution for a fully formalized disassembly problem. There were known successful implementations of RL-based optimizers. But we integrated a novel heuristic to target a dynamically pre-filtered action space for the RL agent (dlOptRL algorithm) and hence significantly raise the efficiency of the learning path. Our algorithm belongs to the Heuristically Accelerated Reinforcement Learning (HARL) method class. We demonstrated its applicability in two use cases, but our approach can also be easily adapted for other problem types. Our article gives a detailed overview of disassembly problems and their formulation, the general RL framework and especially Q-learning techniques, and a perfect example of extending RL learning with a built-in heuristic. [ABSTRACT FROM AUTHOR]

In this paper, constraint-oriented coordination control of a first-order multi-robot system has been considered in a leaderless consensus where rectangular velocity components of participating robots are subject to constraints while also avoiding inter-robots collisions. The desired formation control of different robots and their inter-robots collision avoidance in a team of robots are achieved by solving an optimization problem based on control barrier functions whereas graph theory concepts are used to represent the interaction relations among robots. A devised quadratic programme subject to the velocity and safety conditions, minimizes the desired cost function encoded in the control barrier function and generates separate control inputs for each robot. The rectangular components of the velocity against each robot are kept constrained during the entire operation of the formation control. The optimization-technique-based decentralized controllers were simulated in MATLAB and the corresponding results were recorded. The robots in the team successfully attained the desired formation in a leaderless consensus, deploying themselves in a plane under constrained rectangular velocities without colliding with each other. Several simulation examples with different values of velocity constraints have been shown to illustrate the operation of constrained controllers while ensuring that the desired leaderless-consensus-based formation remains attainable in a safe manner. [ABSTRACT FROM AUTHOR]

We consider the algorithm by Ferson et al. (Reliab Comput 11(3):207--233, 2005) designed for solving the NP-hard problem of computing the maximal sample variance over interval data, motivated by robust statistics. The formulation can be written as a nonconvex quadratic optimization problem with a specific structure. First, we design a new version of the algorithm improving its original time bound O (n 2 · 2 ω) to O (n log n + n · 2 ω) , where n is the size of input data and ω is the clique number in a certain intersection graph. Then, we treat input data as random variables and introduce a natural probabilistic data generating model. We get 2 ω = O (n 1 / log log n) on average. This results in average computing time O (n 1 + ϵ) for ϵ > 0 arbitrarily small, which may be considered as surprisingly good average-time complexity for solving an NP-hard problem. We also prove the following tail bound on the distribution of computation time: hard instances, forcing the algorithm to compute in time 2 Ω (n) , occur rarely, with probability tending to zero at rate e - n log log n . The main result admits a smoothed-complexity interpretation: the average computing time can be bounded by n 1 + O (1 / σ) log log n , where σ measures the dispersion of the distribution of data perturbation. [ABSTRACT FROM AUTHOR]

The marine environment is highly complex and variable, featuring obstacles such as islands, buoys, and vessels. Safe navigation of the surface agent (SA) fleet is crucial for ensuring the safety of the SA fleet, enhancing operational efficiency, and guaranteeing the smooth execution of the fleet's mission. Regarding the problem of formation obstacle avoidance for SA fleets encountering complex obstacles during navigation, this chapter presents a fixed-time-based safe navigation algorithm for the SA fleet based on streamline traction. Firstly, to precisely position each SA at the designated location within the formation, a highly malleable leader–follower formation mode is introduced. Based on an enhanced interfered fluid dynamical system (EIFDS) obstacle avoidance algorithm, the virtual Leader is guided to evade static obstacles and determine a trajectory of the designated position. Secondly, a first-order fixed-time control Lyapunov function (FTCLF) is designed based on the EIFDS obstacle avoidance algorithm to guide the angular velocity constraint. The optimal guiding angular velocity signal is obtained through quadratic programming, ensuring that the SA steers towards the designated position while avoiding obstacles. Next, for the guiding velocity amplitude signal, a first-order fixed-time control barrier function (FTCBF) is designed based on the streamline formation scheme and the inter-boat safety distance to guide the velocity amplitude constraint. The optimal guiding velocity amplitude signal is obtained through quadratic programming, guaranteeing that each SA maintains the formation while avoiding collisions with adjacent vessels. Finally, the simulation results indicate the effectiveness, superiority, and stability of the proposed fixed-time-based safe navigation guidance algorithm for the SA fleet based on streamline traction. [ABSTRACT FROM AUTHOR]

For { B H (t) = (B H , 1 (t) , ... , B H , d (t)) ⊤ , t ≥ 0 } , where { B H , i (t) , t ≥ 0 } , 1 ≤ i ≤ d are mutually independent fractional Brownian motions, we obtain the exact asymptotics of P (∃ t ≥ 0 : A B H (t) - μ t > ν u) , u → ∞ , where A is a non-singular d × d matrix and μ = (μ 1 , ... , μ d) ⊤ ∈ R d , ν = (ν 1 , ... , ν d) ⊤ ∈ R d are such that there exists some 1 ≤ i ≤ d such that μ i > 0 , ν i > 0. [ABSTRACT FROM AUTHOR]

With the increasing demand for autonomous driving, ensuring safe and efficient lane-changing behavior in multi-lane traffic scenarios has become a key challenge. This paper proposes an algorithm for active lane-changing decision-making and trajectory planning designed for intelligent vehicles in such environments. The lane-changing intent is evaluated using fuzzy logic, followed by an assessment of lane-changing feasibility based on a lane utility evaluation function. A hierarchical model for path and speed planning is established. Path clusters are generated using quintic polynomials. With a multi-objective cost function designed to ensure collision safety, smoothness, road boundaries, and trajectory continuity, dynamic programming (DP) and quadratic programming (QP) are employed to obtain the trajectory with the minimum cost among the trajectory set fitted by fifth-order polynomials, which is the optimal lane-changing trajectory. For speed planning, obstacles are projected onto the S–T coordinate system, which is a coordinate system with time as the horizontal axis and the distance(s) of the planned path as the vertical axis, and multi-objective cost functions for speed, acceleration, and speed continuity are designed. The speed curve is optimized using DP followed by QP under given constraints. Simulation results show that the proposed algorithm makes safe and effective lane-changing decisions based on traffic conditions, vehicle distances, and speeds. The model generates smooth and stable paths while ensuring the safe and efficient execution of lane changes. This process meets real-time requirements and verifies the reliability of the algorithm. [ABSTRACT FROM AUTHOR]

The auxiliary unmanned ground vehicle (AUGV) for physical education can significantly enhance the continuity and safety of training and competitions. However, obstacles and area boundary constraints present substantial challenges to the efficiency of the AUGV. This paper proposes an anti-disturbance target tracking control strategy for AUGV, enabling rapid tracking of out-of-bounds balls. In the guidance layer, we design safety constraints based on the exponentially stabilizing control Lyapunov function (ES-CLF) position constraint and control barrier function (CBF), and solve the expected convergence velocity guidance law through quadratic programming. Additionally, the expected motion direction of AUGV is determined using the expected combined velocity. In the control layer, we employ a nonlinear tracking differentiators (NLTD) to achieve finite-time estimation of the derivative of the guidance velocity signal, and observed the model parameter uncertainty and external environmental disturbances through a fixed time disturbance observer. Finally, a fixed-time control strategy is developed to achieve precise target tracking. Stability analysis and simulation results confirm the effectiveness of the proposed AUGV target tracking control strategy and the safety collision avoidance method. [ABSTRACT FROM AUTHOR]

In this paper, we propose a method for solving constrained nonsmooth multiobjective optimization problems which is based on a Sequential Quadratic Programming (SQP) type approach and the Gradient Sampling (GS) technique. We consider the multiobjective problems with noncovex and nonsmooth objective and constraint functions. The problem functions are assumed to be locally Lipschitz. Such problems arise in important applications, many having (weak) Pareto solutions at points of nondifferentiability of the problem functions. In our algorithm, a penalty function is applied to regularize the constraints, GS is employed to overcome the subdifferential calculation burden and make the search direction computation effective in nonsmooth regions, and SQP is used for getting a local linearization. We prove the global convergence properties of our algorithm to the stationary points which approximate (weak) Pareto front. Furthermore, we illustrate the ability and efficiency of the proposed method via a MATLAB implementation on several tests problems and compare it with some existing algorithms. [ABSTRACT FROM AUTHOR]

This paper introduces a framework for implementing log-domain interior-point methods (LDIPMs) using inexact Newton steps. A generalized inexact iteration scheme is established that is globally convergent and locally quadratically convergent towards centered points if the residual of the inexact Newton step satisfies a set of termination criteria. Three inexact LDIPM implementations based on the conjugate gradient (CG) method are developed using this framework. In a set of computational experiments, the inexact LDIPMs demonstrate a 24–72% reduction in the total number of CG iterations required for termination relative to implementations with a fixed termination tolerance. This translates into an important computation time reduction in applications such as real-time optimization and model predictive control. [ABSTRACT FROM AUTHOR]

Parameter estimation of the photovoltaic (PV) array model is able to improve the accuracy of model parameter setting, and also obtain a model consistent with actual situations. It plays a very important role in the maximum power point tracking of PV array and the improvement of micro‐grid and at the same time further affects the sustainable development of new energy sources. In order to reduce the impact of gross errors on the results of parameter estimation, Correntropy based parameter estimation for PV array model under partial shading conditions is structured for robust estimation. In view of the fact that traditional particle swarm optimization (PSO) algorithm tends to converge prematurely and has poor local optimization capabilities and it is hard to resolve nonlinear parameter estimation problems with many nonlinear constraints, an algorithm (IPSO_SQP) that combines the improved particle swarm optimization (IPSO) algorithm with sequential quadratic programming (SQP) is proposed to identify the parameters of photovoltaic (PV) arrays under partial shading conditions. to recognize the parameters of PV array under partial shading conditions. The algorithm optimizes the performance of conventional algorithms by introducing nonlinear dynamic updating of inertia weights and learning factors, as well as the Cauchy mutation operator. It is reflected in the use of improved nonlinear iterative formulations to balance the global and local search capabilities of the algorithm, followed by the introduction of the Cauchy mutation operator to avoid the algorithm from falling into local optima and satisfy the nonlinear constraints to obtain a better solution. After simulation and experimental tests, the results indicate that the IPSO_SQP algorithm has high performance and precision in the robust parameter estimation of PV array model under partial shading conditions. © 2024 Institute of Electrical Engineers of Japan and Wiley Periodicals LLC. [ABSTRACT FROM AUTHOR]

Inverse kinematics of redundant robots presents a challenging problem for real-time applications due to the lack of uniqueness of solution and the low computational efficiency caused by redundancy and hard limits. In this work, a general and efficient method for addressing the real-time optimized inverse kinematics of redundant robots is proposed, taking into account hard limits in joint and Cartesian space that can never be violated. The proposed method proceeds by using constrained linear programming instead of quadratic programming to solve the inverse kinematics problem. Various hard limits such as joint range, bounds on velocity and acceleration are handled explicitly as inequality constraints. This method resolves the redundancy in real-time and enable to simultaneously guarantee that the additional motion constraints will never be violated. Its performance allows real-time kinematic control of redundant robots executing sensor-driven online tasks. The effectiveness of this method is demonstrated through simulations and experiments conducted on a 7-DOF KUKA IIWA robot, showcasing its ability to control redundant robots executing sensor-driven tasks in dynamic environments with numerous hard limits. [ABSTRACT FROM AUTHOR]

Maritime collisions are a leading cause of accidents at sea, causing severe casualties, economic losses, and environmental damage. Although numerous methods have been developed to mitigate collisions, existing research primarily emphasises decision-making and path planning, often overlooking motion planning methods that incorporate dynamic constraints and ship-specific kinematics. This paper presents a motion planning method that takes into account ship dynamics to minimise jerk, the acceleration change rate, during ship acceleration and deceleration. The paper demonstrates the differential flatness property of the 3-DOF ship motion model, which allows for the direct use of flat outputs to implement motion planning and facilitate the addition of dynamic constraints. The front-end path search is performed using the traditional A* algorithm. To represent the trajectory as a piecewise Bézier curve, we use the Bernstein polynomial basis function. Based on this curve, we propose a motion planning method that employs jerk as the cost function and includes necessary constraints. This transforms the problem into a typical convex quadratic programming problem, ensuring the solvability of the optimisation problem. Finally, simulations are carried out to evaluate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

ABSTRACT This paper presents a nonsingular fast terminal sliding mode control for the PAR 4 parallel robot, focusing on workspace optimization and trajectory planning. First, an analytical inverse kinematic model is derived to calculate the workspace, which is then extended using parameter optimization techniques. Next, a trajectory planning method based on the S‐curve approach is proposed to generate the desired path, with special attention to reducing the cycle time of pick‐and‐place operations using sequential quadratic programming method. Finally, a nonsingular fast terminal sliding mode control strategy is suggested to enable the robot to accurately track the generated trajectory. The stability of the closed‐loop system is analyzed using Lyapunov theory, and the effectiveness of the controller is validated through simulation results. [ABSTRACT FROM AUTHOR]