Quadratic Programming Approach Research Articles

Research on Trajectory Planning of Autonomous Vehicles in Constrained Spaces.

This paper addresses the challenge of trajectory planning for autonomous vehicles operating in complex, constrained environments. The proposed method enhances the hybrid A-star algorithm through back-end optimization. An adaptive node expansion strategy is introduced to handle varying environmental complexities. By integrating Dijkstra's shortest path search, the method improves direction selection and refines the estimated cost function. Utilizing the characteristics of hybrid A-star path planning, a quadratic programming approach with designed constraints smooths discrete path points. This results in a smoothed trajectory that supports speed planning using S-curve profiles. Both simulation and experimental results demonstrate that the improved hybrid A-star search significantly boosts efficiency. The trajectory shows continuous and smooth transitions in heading angle and speed, leading to notable improvements in trajectory planning efficiency and overall comfort for autonomous vehicles in challenging environments.

Whole-body control of redundant hybrid cable-driven robot with manipulator: hierarchical quadratic programming approach

Whole-body control of redundant hybrid cable-driven robot with manipulator: hierarchical quadratic programming approach

Robust Contact Computation in Non-Rigid Variation Simulation

Abstract Geometric variation is an inevitable element of any fabrication process. To secure the geometric quality of the assembled products, variation simulation is performed to control compliance with the set geometric requirements. In non-rigid variation simulation, contact modeling is used to avoid the virtual penetration of the components in the adjacent areas, enhancing the simulation accuracy. For frictionless contact models, numerical errors and convergence issues due to the deformation behavior of the interacting surfaces are still limiting the computational efficiency of solving this optimization problem. The optimization problem associated with a contact model is often large-scale, and in practice, fast and robust methods for achieving convergence are required. Previous implementations of contact modeling for non-rigid variation simulation have been prominently based on the Iterative or Penalty Methods. In this paper, a quadratic programming approach has been introduced, based on the Lagrangian multiplier method, for robust contact modeling in non-rigid variation simulation, and the performance of the proposed approach has been compared to the previously applied Iterative and Interior Point Method. The methods have been compared on three industrial reference cases, and the convergence and time-efficiency of each method are compared. The results show that robust optimization of the quadratic program associated with the contact model is highly dependent on the reduced stiffness matrix condition. Furthermore, it has been shown that robust and efficient contact modeling in non-rigid variation simulation is achievable through the proposed quadratic programming method.

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

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

PAPR reduction using polynomial based compressing with Rapp model in GFDM

Generalized Frequency Division Multiplexing (GFDM) has been considered as an attractive candidate to replace Orthogonal Frequency Division Multiplexing (OFDM) for the fifth generation (5 G) mobile networks. GFDM system has better spectral characteristics compared to the OFDM system due to the usage of properly selected pulse shaping filters. Non-causal ideal filters, such as the raised cosine (RC), are commonly used in the GFDM systems. Here, Generalized frequency division multiplexing is a promising candidate to deploy. However, as an intrinsic property of multi-carrier modulation, the high signal amplitude fluctuation can cause several degradation effects when the signal is affected by nonlinearities. The pulse shaping filters are designed using the computationally efficient quadratic programming (QP) approach. Therefore, the aim of this paper is to evaluate the performance of Generalized frequency division multiplexing systems undergoing nonlinear amplification. We evaluate the bit error ratio using high power amplifier, namely the Rapp model. The results show that the fault rate is apparently affected according to the particular high power amplifier model and its transmission parameters.

Intelligent Vehicle Path Based on Discretized Sampling Points and Improved Cost Function: A Quadratic Programming Approach

Intelligent Vehicle Path Based on Discretized Sampling Points and Improved Cost Function: A Quadratic Programming Approach

A Gudermannian neural network performance for the numerical environmental and economic model

The present work is to exploit the Gudermannian neural network (GNN) using the global competency of genetic algorithm (GA) and quick local refinements of sequential quadratic programming approach (SQPA), i.e., GNN-GA-SQPA for the nonlinear economic and environmental system. The differential form of the nonlinear system depends upon three classes, system capability of industrial elements, implementation cost of control values and a new diagnostics technical elimination cost. An error-based fitness function is constructed using the differential system and then optimized by using the hybrid competency of the GA-SQPA. Ten numbers of neurons, a merit Gudermannian function, and the suitable weight vectors are presented in the neural network construction. The accuracy of the GNN-GA-SQPA is assessed through the comparisons and the negligible performances of absolute error. The statistical observations using single and multiple trials validate the stability of the scheme.

Quadratic Programming Approach in the Non-Negatif Matrix Factorization

Non-negative Matrix Factorization is an iteration optimization algorithm. ie to decipher one matrix into several non-negative component matrices. Non-negative Matrix Factorization (FMN) serves to obtain a picture of non-negative data. There is a problem in the Non-negative Matrix Factorization that is optimization at the constraint boundary, where in the optimization solution on the constraint boundary it is necessary to do long iteration and of course very difficult and conquers a long time. Quadratic Programing is an approach to solving linear optimization problems where the constraint is linear function and its purpose function is the square of the decision variable or multiplication of the two decision variables. This method is considered to be an effective method to overcome the optimization in the Non-negative Matrix Factorization.

Vehicle-to-grid system optimization for electric vehicle – a review

The transportation industry is a major contributor to global greenhouse gas emissions, and the adoption of electric vehicles (EVs) presents a viable solution to this problem. The implementation of vehicle-to-grid (V2G) systems has significantly enhanced energy supply and utilization efficiency, particularly through the integration of renewable energy sources such as solar and wind. However, the complexity of the V2G system necessitates addressing multiple objectives and constraints. Previous research has employed optimization methods to refine the V2G system. However, traditional linear and quadratic programming approaches are limited to simple and linear objectives, while non-linear programming methods encounter challenges when dealing with uncertain variables. Consequently, there is a pressing need for a more dependable optimization method capable of managing uncertain variables in this intricate system, particularly in the context of renewable energy source integration. This paper reviews the feasible and reliable optimization approaches utilized by scholars and researchers, examining the multiple objective functions and constraints required for optimizing the V2G system.

Adjoint-based aerodynamic shape optimization with hybridized discontinuous Galerkin methods

We present a discrete adjoint approach to aerodynamic shape optimization (ASO) based on a hybridized discontinuous Galerkin (HDG) discretization. Our implementation is designed to tie in as seamlessly as possible into a solver architecture written for general balance laws, thus adding design capability to a tool with a wide range of applicability. Design variables are introduced on designated surfaces using the knots of a 2D spline-based geometry representation, while gradients are computed from the adjoint solution using a difference approximation of residual perturbations. A suitable optimization algorithm, such as an in-house steepest descent or the Preconditioned Sequential Quadratic Programming (PSQP) approach from the pyOpt framework, is then employed to find an improved geometry. We present verification of the implementation, including drag or heat flux minimization in compressible flows, as well as inverse design.

Testing for complementarity between the use of continuous no-till and cover crops: An application of entropy approach

The carbon sequestration and overall crop production sustainability benefits of no-till (NT) farming are fully realized only when NT is used continuously over several years. Research shows that most U.S. farmers do not use the practice continuously. One of the commonly suggested reasons for intermittent tillage is the risk of a significant yield penalty during the first several years after converting to continuous no-till (CNT). Agronomic research suggests that continuous cover crops (CCR) can be both an economical and biological answer to the risk of yield reduction associated with the use of CNT, as CCR accelerates the processes of converting and storing nitrogen in the soil and improves soil structure and water infiltration. However, whether farmers consider the complementary benefits of CNT and CCR is largely unknown. The objective of this study is to test the complementarity between the uses of the two conservation practices in the State of Indiana, U.S. We combine Quadratic Programming and Entropy approaches to estimate 1st-order Markov transition matrices for tillage and cover crops dynamic models, respectively. Then, we apply Bayes' theory to test the complementarity. The data used for the analysis come from the Conservation Tillage Information Center and Indiana Tillage and Cover Crops Transect, 1992–2019. The findings show that there is no evidence supporting complementarity between the use of CNT and CCR in Indiana. The results also show that the use of CCR in the State is growing steadily at a rate of approximately 30% during 2011–2015 and then stabilize during 2016–2019, whereas the share of land allocated to CNT remains flat in the same period. In addition to being the first formal test of the complementarity between the uses of the two sustainable crop production practices, the novelty of our contribution relates to the econometric methodology and the data. We introduce an approach for estimating dynamic models of farmers' yearly choices and demonstrate the possibility of testing for complementarity between the choices with very limited – aggregated and missing – data.

Operation of The Hybrid Energy Resources with Storage System Participation

This paper focused on the optimal operation of the hybrid energy resources in the off-grid state considering energy storage participation. The hybrid energy resources consist of wind turbine (WT), photovoltaic (PV), diesel generator (DG), and energy storage system for supplying energy to DC and AC load demand with maximum reliability. The operation of the proposed energy system based on energy control and energy optimization is modeled. The energy optimization and energy control are implemented by heuristic and nonlinear quadratic programming approaches via optimal power flow on the resources side. The energy control is done based on the weight sum method in different operation states of the system. Also, the impact of the energy storage system on the hybrid energy resources is considered as backup resources. The energy control modeling is implemented via mathematical simulation and numerical analysis in the two operation states in the summer and winter seasons for verifying the proposed approaches. Finally, the results of the energy control show optimal states of the energy system in supplying demand with considering the energy storage system.

Portfolio Selection Strategies in Bursa Malaysia Based on Quadratic Programming

The study aims to select the efficient portfolio on stock listed in Bursa Malaysia by using the quadratic programming method. It can help the investors to gain expected returns from the diversification portfolio. However, there are some problems that should be considered such as the measurement of inputs for Mean-Variance Models (MVM), use of portfolio models through time and consistency with management objectives in the portfolio. These problems will affect the performance of selected portfolio and cause the loss problem. Therefore, this study implements a quadratic programming approach to select an efficient portfolio on stocks listed in Bursa Malaysia. The study will choose 15 potential companies which have the best performance in the Bursa Malaysia. Quadratic programming (QP) model can solve any type of mathematical optimisation problem in the study. Therefore, investors can optimise the investment portfolio returns by using QP methods. However, we can observe the efficient frontier which is a graph that representing a list of portfolios that optimising expected return for a different level of portfolio risk so can help the investors make a good decision. The findings of this study will give important inputs, especially to the investors to maximise their portfolio return at different level of risks.

Prescribed-Time Safety Filter for a 7-DOF Robot Manipulator: Experiment and Design

In this research effort, we formulate a prescribed-time safety filter (PTSf) for the case of a redundant manipulator performing a fixed-duration task. This formulation, which is based on a quadratic programming approach, yields a filter that is capable of avoiding multiple obstacles in a minimally invasive manner with bounded joint torques, while simultaneously allowing the nominal controller to converge to positions located on the boundary of the safe set by the end of the fixed-duration task. To demonstrate the efficacy of the proposed method, we performed a series of simulations and experiments on Baxter, a seven-DOF collaborative robot manipulator. In these simulations and experiments, Baxter must follow a 6-s parabolic trajectory as closely as possible while navigating around a large spherical obstacle blocking its path and place an object precisely on the surface of a table without overshoot by the end of the 6 s. The results of our simulations and experiments demonstrated the ability of the PTSf to enforce safety throughout the 6-s task, while allowing the robot manipulator to make contact with the table and thus achieve the desired goal position by the end of the task. Furthermore, when compared with the exponential safety filter (ESf), which is the state-of-the-art in current literature, our proposed method yielded consistently lower joint jerks. Thus, for tasks with a fixed duration, the proposed PTSf offers performance benefits over the exponential filters currently present in literature.

Time-flexible min completion time variance in a single machine by quadratic programming

In the context of job scheduling, the time required to complete a task is related not only to the intrinsic difficulty of the task, but also to the operator’s willingness to speed up (or slow down) its execution. In fact, service operators are sometimes authorized to flexibly calibrate job processing times when this is beneficial for the efficient design of services and production plans. In this paper, we show that some forms of time flexibility have major consequences on the operator’s ability to efficiently solve the problem of scheduling non-preemptive jobs to minimize the variance of their completion times. In fact, although this remains a challenging combinatorial problem, authorizing forms of processing time flexibility allows for solving it up to optimality by convex quadratic programming approaches, with a view to tackling large-scale instances, where no exact algorithm can be applied. Our contribution allows establishing a form of least flexibilization of job processing times while guaranteeing the solvability of the resulting problem by convex quadratic programming approaches. To this end, we provide novel bounding conditions for the characterization of an optimal sequence that strengthen and integrate state-of-the-art dominance properties. Our numerical tests indicate that this new methodology is capable of approaching the solution of the original min completion time variance problem with a max relative difference of about 0.05% (on average), with respect to the time-flexible solution.

Zero-order optimization for Gaussian process-based model predictive control

By enabling constraint-aware online model adaptation, model predictive control using Gaussian process (GP) regression has exhibited impressive performance in real-world applications and received considerable attention in the learning-based control community. Yet, solving the resulting optimal control problem in real-time generally remains a major challenge, due to (i) the increased number of augmented states in the optimization problem, as well as (ii) computationally expensive evaluations of the posterior mean and covariance and their respective derivatives. To tackle these challenges, we employ (i) a tailored Jacobian approximation in a sequential quadratic programming (SQP) approach and combine it with (ii) a parallelizable GP inference and automatic differentiation framework. Reducing the numerical complexity with respect to the state dimension nx for each SQP iteration from O(nx6) to O(nx3), and accelerating GP evaluations on a graphical processing unit, the proposed algorithm computes suboptimal, yet feasible, solutions at drastically reduced computation times and exhibits favorable local convergence properties. Numerical experiments verify the scaling properties and investigate the runtime distribution across different parts of the algorithm.

A Two-Stage Optimization Approach for Healthcare Facility Location- Allocation Problems With Service Delivering Based on Genetic Algorithm.

Objective: This study assesses a multi-period capacitated maximal-covering location-allocation model for healthcare services, taking interservice referral as well as equity access into account. Methods: A two-stage optimization strategy is used to formulate the model. In the first stage, facilities are located to maximize covered demand, and in the second stage, patients are allocated to capacitated facilities based on their radius of coverage over multiple time periods. The problem, which belongs to the NP-hard class of optimization problems, is solved using a linear mixed-integer programming (MILP) model. Results: A numerical example is presented to evaluate the efficiency of the proposed model. In addition, to identify near-optimal solutions for large instances, a hybrid genetic-sequential quadratic programming approach (GA-SQP) is developed. To examine the performance and efficiency of the GA-SQP, we employed several randomly generated test instances of various sizes and compared them to those obtained using the exact method. Conclusion: The proposed model has demonstrated an excellent ability in locating healthcare facilities and allocating health services while taking shortage and equity into account during each time period.

Robust Optimal Impulsive Blood Glucose Control Exploiting a Direct Searching Algorithm

In spite of numerous developments in blood glucose control based on the artificial pancreas, multiple daily injections (MDIs) are still the most applicable method in insulin-dependent diabetes mellitus (IDDM) subjects. These patients measure their blood glucose level (BGL) regularly and inject insulin in multiple dosages. In the present study, an efficient, robust optimal impulsive control approach is introduced to attain a safe range of blood glucose considering everyday life factors, including exercise, food intake, and circadian rhythms. This article assumes the dosages of the MDIs as control design parameters and addresses an appropriate approach for optimal dosage determination. The BGL regulation problem by the MDI program is characterized as a robust optimal impulsive control problem with uncertainties, and it is required to minimize the BGL error as the objective function. To achieve this, the polytopic form of the nonlinear glucose-insulin system is derived, and the feasible region for MDI is determined using a direct searching algorithm. Then, the optimal MDI is found by a sequential quadratic programming (SQP) approach. Regarding several uncertainties and the impulsive nature of insulin injection dosages, the proposed approach efficiently solves the BGL regulation problem. The proposed approach is evaluated by a simulated model of the blood-glucose insulin system in two regular and overfeeding scenarios with (mild, moderate) and without physical activity. The results show that the proposed method reduces the amount of injected insulin from 14% to 20% compared to a state-of-the-art approach and, simultaneously, reduces the severe hyperglycemia risk from 15% to 25% for overeating in three injection scenarios.

Consensus fuzzy clustering by sequential quadratic programming approach

Existing fuzzy clustering ensemble approaches do not consider dependability. This causes those methods to be fragile in dealing with unsuitable basic partitions. While many ensemble clustering approaches are recently introduced for improvement of the quality of the partitioning, but lack of a median partition based consensus function that considers more participate reliable clusters, remains unsolved problem. Dealing with the mentioned problem, an innovative weighting fuzzy cluster ensemble framework is proposed according to cluster dependability approximation. For combining the fuzzy clusters, a fuzzy co-association matrix is extracted in a weighted manner out of initial fuzzy clusters according to their dependabilities. The suggested objective function is a constrained nonlinear objective function and we solve it by sparse sequential quadratic programming (SSQP). Experimentations indicate our method can outperform modern clustering ensemble approaches.

A Quadratic-Programming Approach for the Real-Time Control of the Fingers Position in Industrial Pneumatic Grippers

Industrial grippers are generally either electric or pneumatic, with the latter being preferred as their air-based functioning guarantees many advantages such as cost effectiveness and reduced encumbrance. Despite the very large employment, pneumatic grippers do not yet offer performance beyond the open/closed behavior in the majority of cases. Pneumatic grippers mounted on industrial robotic arms are commonly rigid as high forces might be required during the grasping operations. The poorness of the control strategies for the grasping force, as well as for the fingers position, does not match the great advancement that robotics obtained in the last years. Therefore, this letter intends to deliver a new control algorithm for the control of pneumatic grippers. The proposed algorithm permits to finely control the position of the gripper fingers, exploiting a quadratic-programming function to minimize the controller output. Different experiments are shown to demonstrate the algorithm effectiveness.