Quadratic Programming Research Articles

Dynamic Modelling and Optimal Sliding Mode Control of the Wearable Rehabilitative Bipedal Cable Robot with 7 Degrees of Freedom

Although robot-assisted physiotherapy has gained increasing attention in recent years, the use of wearable rehabilitation robots for lower limbs has shown reduced efficiency due to additional equipment and motors located at the center of the joint, increasing complexity and load on disabled patients. This paper proposes a novel rehabilitation approach by eliminating motors and equipment from the center of joints and placing them on a fixed platform using cable-based power transmission. A proposed model of a 14 cable-driven bipedal robot with 7 degrees of freedom has been used to model a lower limb rehabilitation robot corresponding to it. The dynamic equations of the robot are derived using the Euler-Lagrange method. The sliding mode control technique is utilized to offer accurate control for tracking desired trajectories, ensuring smoothness despite disturbances, and reducing tracking errors. This approach is employed to help prevent patients from falling and support them in maintaining balance during rehabilitative exercises. To ensure that cables exert positive tension, the sliding mode controller was combined with quadratic programming optimization, minimizing path error while constraining the controller input torque to be non-negative. The performance of the proposed controller was assessed by considering several control gains resulting in K = 10 identified as the most effective one. The feasibility of this approach to rehabilitation is demonstrated by the numerical results in MATLAB simulation, which show that the RMSE amount of the right and left hip and thigh angles are 0.29, 0.37, 0.31, and 0.44, respectively which verified an improved rehabilitation process. Also, the correlation coefficient between the Adams and MATLAB simulation results for motor torque was found to be 0.98, indicating a high degree of correlation between the two simulation results.

Design of evolutionary computational intelligent solver for nonlinear corneal shape model by Mexican Hat and Gaussian wavelet neural networks

In this study, an integrated computational intelligence algorithm is implemented for the numerical treatment of the two-point boundary value problems that arise in the nonlinear corneal shape (NCS) model through the exploitation of wavelet neural networks including Mexican-Hat (MHWNNs) and Gaussian-wavelet (GWNNs) through global genetic algorithms (GAs) then hybridization with local sequential quadratic programming (SQP) solvers, i.e. MHWNNs-GAs, GWNNs-GAs, MHWNNs-GA-SQP, and GWNNs-GA-SQP respectively. The GWNNs and MHWNNs are applied to calculate the mean squared error of mathematical modeling of the proposed problem through objective functions while optimization of the fitness functions is initially conducted with an efficiency of global search GAs and then the efficacy of local search technique SQP for fine-tuning. A comparison of the proposed solutions of MHWNNs-GAs, GWNNs-GAs, MHWNNs-GA-SQP, and GWNNs-GA-SQP solvers with a reference solution of Adam’s method shows that the proposed schemes have better accuracy, stability, efficiency consistency on an independent number of runs analyzed through complexity analysis and different statistical operators.

Application of ANN control algorithm for optimizing performance of a hybrid ORC power plant

Hybrid systems for generating electricity from multiple sources are becoming an increasingly popular subject of analysis in science and industry. This paper presents a validated model of a hybrid ORC plant powered by solar and geothermal energy. A key challenge in optimizing the operating parameters over time was the variability of solar conditions, which was the main energy source of the system. The operation of the ORC plant is simulated using a complex model with Multiple Input Multiple Output (MIMO) variables, which is nonlinear. The input variables represent the system’s operational parameters, while the output variables describe the plant’s performance indicators. The main objective of this paper is to optimize the year-round performance of the ORC installation through different computational techniques. The first approach involves the application of the gradient-based optimization method that is known as sequential quadratic programming (SQP). With the use of SQP, two distinct simulation runs (SQP-N and SQP-Q/N) of the system are performed, each with a specific objective function to be optimized. The second approach is based on reinforcement learning principles and leverages the method known as Deep Deterministic Policy Gradient (DDPG) algorithm. The main advantage of DDPG over SQP is that DDPG does not require knowledge of the model. This improves the algorithm flexibility, making it well-adapted to fluctuating environmental conditions. Overall, three optimization runs (two using SQP, one using DDPG) have been performed, aiming at identifying the optimal year-round control strategy for the installation. The results revealed that under the control of DDPG, the hybrid system has produced the highest amount of electricity (4993.4 MWh), outperforming in this matter SQP-N and SQP-Q/N optimization variants by 16.83 % and 10.49%, respectively.

Safety-critical formation control of switching uncertain Euler-Lagrange systems with control barrier functions

This paper investigates the safety-critical formation control problem with disturbance rejection for switching uncertain EL MASs in the presence of multiple stationary/moving obstacles. A safety-critical control method is proposed for achieving a collision-free formation for a group of EL systems subject to safety constraints, model uncertainties, and external disturbances. Specifically, a distributed adaptive nominal control law is designed to accomplish the formation control task. Then, based on ISSf-CBF derived safety constraints, a distributed quadratic programming problem is established for computing the optimal control input subject to safety constraints. The safety and stability of the closed-loop control system have been demonstrated. Finally, one exemplary application to safety-critical formation control of some practical multiple mechanical systems is provided to illustrate the effectiveness of the main result.

Research on performance seeking control of turbofan engine in minimum hot spot temperature mode

Abstract The uneven temperature distribution at the combustion chamber outlet seriously affects the working life of the engine. In order to reduce the heat spot temperature at the combustion chamber outlet, a performance optimization control method of the engine minimum heat spot temperature pattern is proposed. Firstly, based on CFD method, the temperature distribution characteristics of combustion chamber outlet under different working conditions were obtained, and a component-level model of turbofan engine was established to characterize the heat spot temperature at combustion chamber outlet. Secondly, the high precision and high real-time engine on-board model is established by deep neural network. Compared with the component-level model, the average relative error of each performance parameter is less than 0.3 %, and the real-time performance is improved by 12 times. Finally, based on the feasible sequential quadratic programming algorithm, the performance optimization control of the minimum hot spot temperature model in the typical flight envelope is simulated and verified. The simulation results show that under the condition of ensuring the safe and stable operation of the engine and constant thrust, the heat spot temperature at the combustion chamber outlet decreases by 21 K maximum. Compared with the conventional minimum turbine front temperature optimization mode, the minimum heat spot temperature mode significantly reduces the heat spot temperature at the combustion chamber outlet.

Deep neural network accelerated-group African vulture optimization algorithm for unit commitment considering uncertain wind power

The unit commitment (UC) of power systems serves to plan out the starting and shutdown of units and the power generation of units for a future period of time. However, the UC problem for large-scale systems faces the problems of long solution time and insufficiently accurate solution. Uncertainty in wind power generation poses a great challenge in solving the unit combination problem. This work proposes a deep neural network accelerated-double layer optimization method (DNNA-DOM) to improve the solution efficiency, accuracy, and economy of UC. The outer layer of DNNA-DOM utilizes the proposed deep neural network accelerated-group African vulture optimization algorithm (DNNA-GAVOA) to optimize the on-off condition of conventional coal-fired power units. The inner layer of DNNA-DOM adopts quadratic programming to optimize the solution of the economic dispatch problem of load distribution. The GAVOA optimizes the simulated African vultures in four groups to obtain the optimal solution after diverse exploration, exploitation, and exploitation activities, with low complexity and high accuracy. This work first evaluates the performance of GAVOA by solving seven unimodal functions. Furthermore, the 10-unit simulation by incorporating wind power curves and related constraints is optimized through the DNNA-DOM. The results show that GAVOA outperforms the African vulture optimization algorithm (AVOA) and traditional metaheuristics like the particle swarm algorithm and gray wolf algorithm in terms of lower operating cost and optimization stability. The DNNA-DOM combined with DNNA-GAVOA in the outer layer results in an average daily cost reduction of $36.30 and a 45.1997 % speed increase compared to AVOA in the outer layer.

Intuitionistic fuzzy twin proximal SVM with fuzzy hyperplane and its application in EEG signal classification

Twin support vector machine (TSVM) is a contemporary machine learning technique to tackle classification and regression problems. However, TSVM lacks the ability to differentiate between support vectors and noises since it neglects the positional information of input data samples, and hence it is sensitive to noises. Additionally, it fails to consider uncertainties associated with the data, which reduces its capacity for generalization. To address these drawbacks, we propose a novel fuzzy hyperplane based intuitionistic fuzzy twin proximal support vector machine. The first significant feature of the proposed approach is that it gives an intuitionistic fuzzy number based on the relevance to each data vector. This efficiently reduces the impact of noise and outliers by leveraging the local neighborhood information within the data points by incorporating membership and non-membership weights. Secondly, all the parameters present in the model are fuzzy variables, including the offset term and the elements of the normal vector. The suggested fuzzy hyperplane successfully reflects the inherent ambiguity prevalent in real-world categorization problems by reflecting vagueness in the input data through the use of fuzzy variables. The model’s efficiency is enhanced by solving two systems of linear equations to obtain two non-parallel classifiers rather than solving two quadratic programming problems as in standard TSVM. Utilizing non-linear kernel functions within the feature space enables the method to effectively identify complex patterns or non-linear relationships within the datasets. In order to demonstrate the effectiveness of the suggested approach, extensive computer experiments have been conducted on a set of eighteen benchmark datasets with both linear and non-linear kernels. In addition, rigorous statistical analysis, including Friedman and post-hoc Nemenyi tests, have been employed to assess the significance of the observed performance differences. Furthermore, we also performed numerical experiments utilizing linear, Gaussian, and polynomial kernels to classify electroencephalogram (EEG) signals. The outcomes of the experiment are analyzed in terms of average accuracy, processing time, and F-measure. The results demonstrate that the proposed method outperforms existing methods and achieves better generalization.

A Two-steps Fixed-point Method for the Simplicial Cone Constrained Convex Quadratic Optimization

In this paper, we deal with the resolution of the simplicial cone constrained convex quadratic optimization (abbreviated SCQO). It is known that the optimality conditions of SCQO is only a standard linear complementarity problem (LCP). Under a suitable condition, the solution of LCP is equivalent to find the solution of an absolute value equations AVE. For its numerical solution, we propose an efficient two-steps fixed point iterative method for solving the AVE. Moreover, we show that this method converges globally linear to the unique solution of the AVE and which is in turn an optimal solution of SCQO. Some numerical results are reported to demonstrate the efficiency of the proposed algorithm. Keywords: Quadratic programming, simplicial cones, absolute value equations, linear complementarity problem, Picard’s fixed point iterative method.

Robust data‐driven dynamic optimization using a set‐based gradient estimator

AbstractThis article presents an extremum‐seeking control (ESC) algorithm for unmodeled nonlinear systems with known steady‐state gain and generally non‐convex cost functions with bounded curvature. The main contribution of this article is a novel gradient estimator, which uses a polyhedral set that characterizes all gradient estimates consistent with the collected data. The gradient estimator is posed as a quadratic program, which selects the gradient estimate that provides the best worst‐case convergence of the closed‐loop Lyapunov function. We show that the polyhedral‐based gradient estimator ensures the stability of the closed‐loop system formed by the plant and optimization algorithm. Furthermore, the estimated gradient provably produces the optimal robust convergence. We demonstrate our ESC controller through three benchmark examples and one practical example, which shows our ESC has fast and robust convergence to the optimal equilibrium.

Radial basis kernel harmony in neural networks for the analysis of MHD Williamson nanofluid flow with thermal radiation and chemical reaction: An evolutionary approach

The current investigative exploration exemplifies the conceptualization of a novel design intelligent computing paradigm based on artificial neural networks (ANNs) by utilizing radial basis function (RBF) to analyze magnetohydrodynamic (MHD) Williamson nanofluid two-dimensional flow along a stretchable sheet under the effect of chemical reaction as well as thermal radiation in a porous medium. This newly designed technique is an amalgam of a well-known reliable global solver named genetic algorithms (GAs) and a swift convergence generated local solver named sequential quadratic programming (SQP) used in ANNs by taking RBF as a kernel function i.e. ANNs-RBF-GASQP solver. The PDEs demonstrating the current nanofluid problem flow are transformed into the system of non-linear ODEs through a relevant similarity transformation and subsequently solved using ANNs-RBF-GASQP solver to investigate thermohydraulic properties by manipulating the values of various system parameters present in the ODEs. Moreover, the simulation results show that increasing the heat source parameter leads to a significant decrease in temperature. Additionally, an increase in the porosity parameter causes a decrease in the velocity of nanofluid, as a higher value of porosity increases fluid permeability and greater resistance to flow. The efficacy of the suggested solver is scrutinized through various statistical and convergence analyses.

Optimization of robot manipulator configuration calibration by using Zhang neural network for repetitive motion

High precision and low complexity control algorithm plays an important role in the developing of the end-effector instrumentation of different robot manipulators. In order to reduce the kinetic energy and the high-speed drift phenomenon of the repetitive motion tracking task, the robot manipulator needs to calibrate its configuration. In this paper, we formulate the configuration calibration of the robot manipulator for the repetitive motion task as a future quadratic programming optimization problem constrained with equality constraints, which is also regarded as a fundamental problem in artificial intelligence and modern control engineering. Zhang neural network, which is a canonical method, can be adopted to deal with the continuous form of the future optimization problem, named as temporally dependent quadratic programming problem with equality constraints. In order to overcome the issue of temporally dependent inverse computing, a novel Zhang neural network model and its uncertain disturbance tolerant model, which are termed as filtered reciprocal-kind Zhang neural network model and uncertain disturbance tolerant filtered reciprocal-kind Zhang neural network model, respectively, are proposed by integrating the energy-type cost function and Zhang neural network design formula for solving the temporally dependent quadratic programming problem with equality constraints in this paper. Based on the Euler discrete formula and the models, the discrete filtered reciprocal-kind Zhang neural network and the discrete uncertain disturbance tolerant filtered reciprocal-kind Zhang neural network algorithms are proposed for solving the future quadratic programming problem with equality constraints and the robot manipulator configuration calibration problem of repetitive motion. The convergence properties of the reciprocal-kind Zhang neural network model and its corresponding uncertain disturbance tolerant model are obtained by Lyapunov stability theory of nonlinear system and its corresponding perturbed system, while the convergence property of the filtered reciprocal-kind Zhang neural network model is analyzed by the limit thinking. For the repetitive motion task, three experiments for solving the configuration calibration problem of PUMA560, Kinova Jaco2, and Franka Emika Panda robot manipulators are performed to illustrate the effectiveness, robustness and superiority of our proposed discrete filtered reciprocal-kind Zhang neural network algorithms.

Fully Stochastic Trust-Region Sequential Quadratic Programming for Equality-Constrained Optimization Problems

Fully Stochastic Trust-Region Sequential Quadratic Programming for Equality-Constrained Optimization Problems

Optimization investigation on variable-density multi-layer insulation coupled with vapor-cooled shield for liquid hydrogen tank based on sequential quadratic programming

The MLI (multi-layer insulation), commonly used in liquid hydrogen tank, acts to reduce HLF (heat leakage flux) into the tank and slow down tank pressurization. It is usually optimally designed into three or four regions, with the same RS spacing in every region, which is regarded as the discontinuous variable density and called VDMLI (variable-density multi-layer insulation). However, the VCS (vapor-cooled shield) and P-O (para-to-ortho hydrogen conversion) in VDMLI are not considered in the optimal design of VDMLI. Therefore, a kind of nonlinear programming algorithm named SQP (sequential quadratic programming), in which HLF solver of liquid hydrogen tank is embedded, is firstly introduced to obtain the optimized distribution of RS (radiative shield) spacing to minimize HLF of liquid hydrogen storage tank. The HLF solver is a numerical model of VDMLI coupled with VCS and P-O, and SQP can be regarded as the optimization process of searching for an optimal solution in high dimensional space, under inequality constraints. The calculation results show that the best SN (serial number) of RS for SVCS (single vapor-cooled shield) setting to minimize HLF, in three cases of before optimization with P-O, after optimization with P-O, and after optimization without P-O is 16, 11, and 14 respectively. With P-O, the minimum HLF after optimization is reduced by 8.45% compared with the minimum HLF before optimization. When SVCS is set at the 4th RS, P-O leads to the most decreasing range of HLF, which is 28.3%, while the optimization process leads to the most decreasing range of 48.1% under condition that SVCS is set at the 2nd RS and P-O is coupled. Under condition of no P-O, after optimization, the minimum HLF occurs when the SN of RS where DVCS (double vapor-cooled shield) is set is (8,21), and the minimum HLF is reduced by 9.0%, compared to that before optimization with DVCS, and is reduced by 50.43% compared to that after optimization with SVCS.

Solving a class of Thomas–Fermi equations: A new solution concept based on physics-informed machine learning

This paper presents a novel physics-informed machine learning approach, designed to approximate solutions to a specific category of Thomas–Fermi differential equations. To tackle the inherent intricacies of solving Thomas–Fermi equations, we employ the quasi-linearization technique, which transforms the original non-linear problem into a series of linear differential equations. Our approach utilizes collocation least-squares support vector regression, leveraging fractional Chebyshev functions for finite interval simulations and fractional rational Chebyshev functions for semi-infinite intervals, enabling precise solutions for linear differential equations across varied spatial domains. These selections facilitate efficient simulations across both finite and semi-infinite intervals. Key contributions of our approach encompass its versatility, demonstrated through successful approximation of solutions for diverse Thomas–Fermi problem types, including those featuring non-local integral terms, Bohr radius boundary conditions, and isolated neutral atom boundary conditions defined on semi-infinite domains. Furthermore, our method exhibits computational efficiency, surpassing classical collocation methods by solving a sequence of positive definite linear equations or quadratic programming problems. Notably, our approach showcases precision, as evidenced by experiments, including the attainment of the initial slope of the renowned Thomas–Fermi equation with an impressive 39-digit precision.

Enhancing Power Supply Flexibility in Renewable Energy Systems with Optimized Energy Dispatch in Coupled CHP, Heat Pump, and Thermal Storage

The use of renewable energy by converting it into heat is an important form of storing energy in a usable form and improving the energy supply flexibility; therefore, the electricity–heating system (EHS) can cope with load fluctuations. However, relevant research is lacking on improving the energy supply limitations by the optimal dispatch of energy flow at the typical EHS, such as the coupled CHP–heat pump–thermal storage system (CCHTS). Based on the study of the energy supply characteristics of the CCHTS for extending the energy supply limitation, this study develops an optimal dispatch method using a heat pump (HP) and the thermal storage (TS) of heating networks to improve the flexibility of the CCHTS and the accommodation capacity of renewable energy. The maximum and minimum energy supply limitation model of the CCHTS and the output power characteristic model are established. Based on the piecewise power supply constraint, the energy flow of the EHS is optimized by using the quadratic programming algorithm. The CCHTS can significantly improve the energy supply flexibility; both coupled combined heat and power (CHP) + HP and coupled CHP + TS can improve the power supply flexibility, but the enhanced effect of CHP + HP is better than that of CHP + TS. An increase of 7.6% in wind power consumption is achieved. The consumption of renewable energy increases by 17.9% in the energy flow optimization results.

Bi-level robust planning of hydrogen energy system for integrated electricity–heat–hydrogen energy system considering multimode utilization of hydrogen

This paper proposes a bi-level robust planning model to address the rational configuration of a hydrogen energy system, accounting for the impact of wind power uncertainty in an integrated electricity–heat–hydrogen energy system (IEHHES) with the increasing wind power penetration. The upper-level problem aims to determine the capacity of the hydrogen energy system in this system, whereas the lower-level problem is formulated as a two-stage robust optimization model to simulate the typical daily operational scheme of the system, considering uncertain wind turbine output and the on/off switching of devices. This model considers multiple hydrogen utilization modes and the physical characteristics of various hydrogen storage tanks. The complex bi-level robust model is intractable directly. Therefore, this bi-level robust planning model is initially decomposed into planning and operation subproblems. These subproblems are then can be solved in parallel using the alternating direction method of multipliers (ADMM) algorithm; the planning subproblem, a quadratic programming model, is solved using a commercial solver; the operating subproblem, a two-stage robust optimization model, is solved using the column and constraint generation algorithm. Finally, case studies validate the advantages and effectiveness of the developed model and algorithm.

A Fusion Approach for UAV Onboard Flight Trajectory Management and Decision Making Based on the Combination of Enhanced A* Algorithm and Quadratic Programming

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.

A quadratic programming based simultaneous impact model (QPSIM) for mechanisms

A quadratic programming based simultaneous impact model (QPSIM) for mechanisms

Trajectory Planning and Tracking Using Decoupled CBF-QPs for Safe Navigation of Quadrotors

Abstract Control barrier function-based quadratic program (CBF-QP) provides an avenue for agile and numerically efficient obstacle avoidance algorithms. However, the CBF-QP methods may lead to lengthy detours and undesirable avoidance maneuvers. This paper proposes a bi-level CBF-QP for the safe navigation of quadrotors. A Planning-QP is proposed to create a safe reference trajectory that shadows the actual reference trajectory with prescribed avoidance acceleration, velocity, distance, and direction during the avoidance maneuver. A control Lyapunov function (CLF) ensures that modified reference closely matches the actual reference outside the avoidance regions and multiple control barrier functions (CBFs) ensure the safety and smoothness of the avoidance trajectory. Model uncertainties can undermine the safety of the quadrotor while tracking the modified reference. Hence, a Tracking-QP is designed to achieve accurate tracking with ensured safe maneuvering around obstacles, where a new CBF is constructed to prevent actuator saturation. Prescribed attitude bounds are ensured via additional acceleration constraints in the Tracking-QP. The proposed method is validated using numerous experiments involving various static obstacles where the quadrotor carries different payloads.

Active Fault Tolerant Nonsingular Terminal Sliding Mode Control for Electromechanical System Based on Support Vector Machine

Effective fault diagnosis and fault-tolerant control method for aeronautics electromechanical actuator is concerned in this paper. By borrowing the advantages of model-driven and data-driven methods, a fault tolerant nonsingular terminal sliding mode control method based on support vector machine (SVM) is proposed. A SVM is designed to estimate the fault by off-line learning from small sample data with solving convex quadratic programming method and is introduced into a high-gain observer, so as to improve the state estimation and fault detection accuracy when the fault occurs. The state estimation value of the observer is used for state reconfiguration. A novel nonsingular terminal sliding mode surface is designed, and Lyapunov theorem is used to derive a parameter adaptation law and a control law. It is guaranteed that the proposed controller can achieve asymptotical stability which is superior to many advanced fault-tolerant controllers. In addition, the parameter estimation also can help to diagnose the system faults because the faults can be reflected by the parameters variation. Extensive comparative simulation and experimental results illustrate the effectiveness and advancement of the proposed controller compared with several other main-stream controllers.