Quadratic Optimization Algorithm Research Articles

A data assimilation algorithm for predicting rain

AbstractConvective‐scale data assimilation uses high‐resolution numerical weather prediction models and temporally and spatially dense observations of relevant atmospheric variables. In addition, it requires a data assimilation algorithm that is able to provide initial conditions for a state vector of large size with one third or more of its components containing prognostic hydrometeors variables whose non‐negativity needs to be preserved. The algorithm also needs to be fast as the state vector requires a high updating frequency in order to catch fast‐changing convection. A computationally efficient algorithm for quadratic optimization (QO, or formerly QP) is presented here, which preserves physical properties in order to represent features of the real atmosphere. Crucially for its performance, it exploits the fact that the resulting linear constraints may be disjoint. Numerical results on a simple model designed for testing convective‐scale data assimilation show accurate results and promising computational cost. In particular, if constraints on physical quantities are disjoint and their rank is small, further reduction in computational costs can be achieved.

Optimal control allocation for the parallel interconnection of buck converters

This paper presents a control algorithm for the parallel interconnection of heterogeneous power converters. A single resistive load is assumed to be fed by an arbitrary number of buck converters via a common DC bus. The approach is based on control allocation theory and a constrained quadratic optimization algorithm. The strategy achieves a fast voltage response with an optimal current distribution among the converters, while taking into account the current limits, the dynamic response, and the efficiency of the individual converters. An interesting by-product of the approach is the ability to put converters in and out of service through trivial adjustments of the code. The benefits of the approach are assessed through simulations and an experimental evaluation.

An Approach to QP-based Thrust Allocation considering Inflow

Abstract One essential subtask in Dynamic Positioning is the optimal thrust distribution onto all available propulsors - the thrust allocation. Current thrust allocation algorithms support a variety of different propulsor types, but usually only under bollard pull conditions, hence ignoring water inflow. However, there are marine control tasks in which severe relative motion through water is present. In such conditions zero-inflow models may suggest wrong thrust vectors, which may lead to degraded positioning performance. In this paper an approach for dynamic thrust allocation is presented that utilizes available information on water inflow. The method is inspired by stochastic optimization and uses a set of achievable thrust points to construct convexified constraints for an underlying Quadratic Programming optimization algorithm. The workflow of the proposed method as well as simple simulations are shown on the example of thrust generation with cycloidal propellers.

Sequential Quadratic Optimization for Nonlinear Equality Constrained Stochastic Optimization

Sequential quadratic optimization algorithms are proposed for solving smooth nonlinear optimization problems with equality constraints. The main focus is an algorithm proposed for the case when the...

Privacy-Preserving Computation for Large-Scale Security-Constrained Optimal Power Flow Problem in Smart Grid

In this paper, we present a distributed privacy-preserving quadratic optimization algorithm to solve the Security Constrained Optimal Power Flow (SCOPF) problem in the smart grid. The SCOPF problem seeks the optimal dispatch subject to a set of postulated constraints under the normal and contingency conditions. However, due to the large problem size and real-time requirement, a fast and robust technique is required to solve this problem. Moreover, due to privacy concerns, it is important that the data remains confidential and processed on local computers. Therefore, a fully privacy-preserving algorithm is proposed which performs computation directly over the encrypted SCOPF problem. The SCOPF is decomposed into smaller subproblems corresponding to individual pre-contingency and post-contingency cases using the Alternating Direction Method of Multipliers (ADMM) and gradient projection algorithms. Both algorithms are presented for solving the SCOPF problem in a privacy-preserving and distributed manner. Security analysis shows that our algorithm can preserve both system confidentiality and data privacy. Performance evaluations validate the correctness and effectiveness of the proposed algorithm.

MODEL REFERENCE ADAPTIVE CONTROL-BASED GENETIC ALGORITHM DESIGN FOR HEADING SHIP MOTION

In this paper, the heading control of a large ship is enhanced with a specific end goal, to check the unwanted impact of the waves on the actuator framework. The Nomoto model is investigated to describe the ship’s guiding progression. First and second order models are considered here. The viability of the models is examined based on the principal properties of the Nomoto model. Different controllers are proposed, these are Proportional Integral Derivative (PID), Linear Quadratic Regulator (LQR) and Model Reference Adaptive Control Genetic optimization Algorithm (MRAC-GA) for a ship heading control. The results show that the MRAC-GA controller provides the best results to satisfy the design requirements. The Matlab/Simulink tool is utilized to demonstrate the proposed arrangement in the control loop.

Design of an Adaptive Neural Predictive Nonlinear Controller for Nonholonomic Mobile Robot System Based on Posture Identifier in the Presence of Disturbance

This paper proposes an adaptive neural predictive nonlinear controller to guide a nonholonomic wheeled mobile robot during continuous and non-continuous gradients trajectory tracking. The structure of the controller consists of two models that describe the kinematics and dynamics of the mobile robot system and a feedforward neural controller. The models are modified Elman neural network and feedforward multi-layer perceptron respectively. The modified Elman neural network model is trained off-line and on-line stages to guarantee the outputs of the model accurately represent the actual outputs of the mobile robot system. The trained neural model acts as the position and orientation identifier. The feedforward neural controller is trained off-line and adaptive weights are adapted on-line to find the reference torques, which controls the steady-state outputs of the mobile robot system. The feedback neural controller is based on the posture neural identifier and quadratic performance index optimization algorithm to find the optimal torque action in the transient state for N-step-ahead prediction. General back propagation algorithm is used to learn the feedforward neural controller and the posture neural identifier. Simulation results show the effectiveness of the proposed adaptive neural predictive control algorithm; this is demonstrated by the minimised tracking error and the smoothness of the torque control signal obtained with bounded external disturbances.

Monotone Splitting Sequential Quadratic Optimization Algorithm with Applications in Electric Power Systems

In this paper, we propose a new sequential quadratic optimization algorithm for solving two-block nonconvex optimization with linear equality and generalized box constraints. First, the idea of the splitting algorithm is embedded in the method for solving the quadratic optimization approximation subproblem of the discussed problem, and then, the subproblem is decomposed into two independent low-dimension quadratic optimization subproblems to generate a search direction for the primal variable. Second, a deflection of the steepest descent direction of the augmented Lagrangian function with respect to the dual variable is considered as the search direction of the dual variable. Third, using the augmented Lagrangian function as the merit function, a new primal–dual iterative point is generated by Armijo line search. Under mild conditions, the global convergence of the proposed algorithm is proved. Finally, the proposed algorithm is applied to solve a series of mid-to-large-scale economic dispatch problems for power systems. Comparing the numerical results demonstrates that the proposed algorithm possesses superior numerical effects and good robustness.

Multislope PI Modeling and Feedforward Compensation for Piezoelectric Beam

The hysteresis nonlinearity greatly reduces the tracking precision of piezoceramic actuators for expected displacement in a high-accuracy positioning system. In order to effectively compensate the hysteresis for piezoelectric ceramics, a novel modeling method, namely, multislope PI (Prandtl–Ishlinskii) was proposed. In view of the minimum mean square error (MSE) criterion, the weights of an improved PI model were identified by the quadratic programming optimization algorithm. For verifying the accuracy of the proposed multislope PI hysteresis model, a feedforward compensation control for piezoceramic beam was achieved. The corresponding experimental system was established, and the displacement tracking experiments were carried out. The results indicated that the mean tracking error was 0.2828 μm and within 1% of full scale, as well as the MSE was 0.3100 μm. Compared with the conventional PI model, the proposed multislope PI model demonstrated a significant improvement in positioning performance for the piezoceramic beam.

Fast Quadratic Programming for Mean-Variance Portfolio Optimization

In this paper, a vectorized quadratic convex optimization algorithm based on Matlab's quadprog built-in function is proposed. We target specifically a classic problem confronted by portfolio analysts, that of optimizing asset allocation when choosing among several asset classes, in the context of Markowitz's modern portfolio theory. Simulating return trajectories for several asset classes, we formulate the optimization routine in such a way that is able to handle multiple scenarios at the same time, instead of on a one-by-one basis, reducing computational times significantly, without introducing observable estimation errors. A sensitivity analysis is offered with respect to the optimal batch size.

AN INPUT LIMITED REPETITIVE LEARNING CONTROL OF FLEXIBLE-BASE TWO-FLEXIBLE-LINK AND TWO-FLEXIBLE-JOINT SPACE ROBOT WITH INTEGRATION OF MOTION AND VIBRATION

In order to analyze the dynamic simulation and movement control of space robot under the influence of full flexible of base, links and joints, as well as the active vibration suppression of base, links and joints, an input limited repetitive learning controller with integration of motion and vibration is proposed. The design of the algorithm is not based on the system model information. The flexible base and the flexible joints are regarded as linear spring and torsion springs. The flexible links are analyzed by the Eulerian Bernoulli model, and the dynamic equation is established by the Lagrange equation and the assumed mode method. Based on the singular perturbation theory, the model is decomposed into a slow subsystem including the system rigid variables and the link flexible vibration, and a fast subsystem including the base and joint flexible vibration. The corresponding sub controllers are designed for the slow and fast subsystems to form the general controller with joint flexible compensation. For the slow subsystem, an input limited repetitive learning controller is proposed, which is composed of hyperbolic tangent function, saturation function and repetitive learning term. The hyperbolic tangent function and saturation function realize the requirement of limited input torque. The repetitive learning term compensates the periodic system error to complete the gradual stable tracking of the expected trajectory of base attitude and joint. However, in order to suppress the flexible vibration of the links of the slow subsystem, a hybrid trajectory reflecting the flexible vibration of the links and the rigid motion of the system is constructed by using virtual force conception, and an input limited repetitive learning controller on virtual force conception is proposed to ensure the accurate tracking of the trajectory of the base and joint, while actively suppressing the flexible vibration of the links. For the fast subsystem, the linear quadratic optimal control algorithm is used to suppress the flexible vibration of the base and joints. The simulation results show that the controller is suitable for general flexible nonlinear system, meets the requirements of limited input torque, realizes high-precision tracking of periodic signal, effectively suppresses the flexible vibration of base, links and joints, and verifies the feasibility of the algorithm.

Trajectory tracking control of an amphibian robot with operational capability

Although the traditional amphibious robot has the ability of multi-space motion, it has the disadvantage of low power utilization and no operational capability. In order to make it competent in an extremely complex environment, we studied the structural design and control of amphibian robot with operational capability. First, in order to make the robot have the ability of flying in the sky, moving on land, and swimming in the water, a “bevel variant” mechanism for power switching is designed. Then, taking the uncertainty of the kinetic parameters and external influences into account, the kinetic and kinematic models of the system are established. Next, a sliding mode controller that outputs control force for the system and a quadratic calculation optimization algorithm for inverse kinematics solution are designed. Finally, the simulation platform for the system is built based on MATLAB. The simulation results show that when the system is in the land and air flight stages, the vehicle position and orientation tracking error are within ±0.05 m and ±2°, respectively. When the system is in the underwater stage, the end effector position and orientation tracking error are within ±0.15 m and ±3.0°, respectively.

Critical elastic parameters motivating divergence instability of frictional composite infinitely long media

The current study addresses the occurrence of smooth dynamic paths which rapidly diverge the mechanical system away from equilibrium configuration in an exponentially (non-oscillatory) path. The explored paths begin arbitrarily in the neighborhood of equilibrium states of an infinite orthotropic composite elastic layer. The subject treated here is handled from both the analytical and the numerical models. The divergence instability problem is reformulated as a nonlinear constrained optimization problem. Fortran implementation of sequential quadratic programming optimization algorithm for finding the minimum coefficient of friction for the onset of instability and the corresponding parameters is exploited. A finite element model is worked out to approximate the continuum. The results of several sets of numerical experiments for finding the minimum coefficient of friction for the onset of instability and the corresponding parameters are presented. The finite element method results were computed and compared with the analytic solutions: A very good matching between numerical and analytical results was obtained. It is concluded that, for normal relationships among elastic material properties and specific orthotropic directions, significantly surprising very low thresholds of the coefficient of friction were required for the onset of divergence instability.

Optimal active power dispatch for wind farm based on the improved fatigue load sensitivity

Reasonable active power dispatch for wind farms can reduce the dynamic fatigue loads of wind turbines (WTs) and prolong the service lives of the WTs. An active power dispatch method for wind farms based on the improved fatigue load sensitivity of WT is proposed. According to the WT operating parameters, the fatigue load sensitivity to the power reference value is improved. The analytical equations of the fatigue load sensitivity are rederived, and the accuracies of the fatigue load sensitivity calculations are improved. The wind farm fatigue load minimization is taken as the target, the tracking power reference value is taken as the constraint, and the active power distribution model is established. The quadratic programming optimization algorithm is used to calculate the power reference of each WT. Case studies were conducted with wind farm control for different turbulent winds. The effectiveness of the proposed method is verified by comparing the rainflow cycles and the damage equivalent load.

A robust classification framework with mixture correntropy

In this paper, we define a mixture correntropy criterion where two different kernel functions are combined. We induce a more general nonconvex robust loss function by this heterogenous mixture correntropy. The proposed mixture correntropy is also a local similarity measure that not only improves the limitations of correntropy under a single kernel, but also handles heterogeneous data more flexibly and stably. The induced loss amalgamates the superiors of the state-of-the-art robust loss functions and is more effective. What’s more, we verify the Fisher consistency of the induced loss and analyze the robustness from the view point of robust estimation. With this induced loss, we propose a robust support vector machine (SVM) framework and adopt half quadratic optimization algorithm to handle the nonconvexity and further improve convergent rate. Furthermore, we generate heterogenous structured artificial datasets and impose different levels of label noise on benchmark datasets. Implements on these two types of datasets show the superior flexibility and effectiveness of the proposed framework.

Integrated hierarchical control strategy of active suspension and differential assisted steering system for electric-wheel vehicle

In order to solve the performance decrease of riding comfort and handling stability caused by the increase of unsprung mass for the electricwheel vehicle, an integrated hierarchical control strategy is proposed based on differential assisted steering system (DASS) and active suspension system (ASS). Here, the upper controller is designed to coordinate the overall control strategy and determine the control weight of the two subsystems by the fuzzy control algorithm. Afterwards, for the lower controllers, the linear quadratic optimal algorithm is taken in the differential steering system to determine the additional yaw moment, and the active disturbance rejection control is used in the active suspension system to suppress body vibration and improve riding comfort. The simulation results show that the proposed hierarchical control can effectively improve the riding comfort and handling stability of the electric-wheel vehicle.

Simplex QP-based methods for minimizing a conic quadratic objective over polyhedra

We consider minimizing a conic quadratic objective over a polyhedron. Such problems arise in parametric value-at-risk minimization, portfolio optimization, and robust optimization with ellipsoidal objective uncertainty; and they can be solved by polynomial interior point algorithms for conic quadratic optimization. However, interior point algorithms are not well-suited for branch-and-bound algorithms for the discrete counterparts of these problems due to the lack of effective warm starts necessary for the efficient solution of convex relaxations repeatedly at the nodes of the search tree. In order to overcome this shortcoming, we reformulate the problem using the perspective of the quadratic function. The perspective reformulation lends itself to simple coordinate descent and bisection algorithms utilizing the simplex method for quadratic programming, which makes the solution methods amenable to warm starts and suitable for branch-and-bound algorithms. We test the simplex-based quadratic programming algorithms to solve convex as well as discrete instances and compare them with the state-of-the-art approaches. The computational experiments indicate that the proposed algorithms scale much better than interior point algorithms and return higher precision solutions. In our experiments, for large convex instances, they provide up to 22x speed-up. For smaller discrete instances, the speed-up is about 13x over a barrier-based branch-and-bound algorithm and 6x over the LP-based branch-and-bound algorithm with extended formulations. The software that was reviewed as part of this submission was given the Digital Object identifier https://doi.org/10.5281/zenodo.1489153 .

Optimal Control of the Vehicle Path Following by Using Image Processing Approach

Nowadays, the importance of the vehicles and its dramatic effects on human life is no secret. The use of trailers with multiple axels for transporting bulky and heavy equipment is essential. Increase in trailers axles which results increment of wheels, needs considerations in order to increase in transporting speed, maneuverability, safety, better control and path following accurately. Therefore, in this paper dynamic modeling and control of a 5 axial trailer was studied. As well as to increase maneuverability and speed up, steering 3 axles was considered. Also, by using image processing trailer path following in desired path with the highest accuracy was achieved. In this study, first a 14 DoF model for a 5 axial trailer with 3 steering axles was considered and its characteristics were described. Then, dynamic equations including kinematic and kinetic of trailer was obtained. Then, with checking trailers behavior a linear quadratic optimal control algorithm was designed. To evaluate the performance of the control algorithm, control problem simulation for 3 maneuver; single lane change, double lane change and overtaking; was done. The results confirmed the performance of designed control algorithm and image processing accuracy in trailer path following.

Using artificial neural network and quadratic algorithm for minimizing entropy generation of Al2O3-EG/W nanofluid flow inside parabolic trough solar collector

Abstract Entropy generation minimization approach, quadratic optimization algorithm and artificial neural network (ANN) have been applied to find optimal condition of the turbulent Al2O3-60:40% EG/W nanofluid flow inside the absorber tube of a parabolic trough solar collector (PTSC). A three-input ANN has been employed for predicting optimal volume fraction ( ϕ opt ). The process is carried out for optimizing nanoparticle concentration, nanoparticle diameter, nanofluid average flow temperature and Reynolds number. Results show that the rate of the entropy generation decreases by decreasing volume fraction, increasing particle diameter and increasing average flow temperature. Adding the nanoparticles to the base-fluid increases frictional entropy generation and decreases thermal entropy generation. It causes an improvement in heat transfer but an increase in viscous irreversibility too. Finally, it was observed that for each particle sizes and average flow temperatures, there is a specific amount of optimal volume fraction, ϕ opt ; which is not dependent on the Re number. There is an optimal volume fraction for all Re numbers at constant particle size and mean flow temperature. Also, the optimum values of nanoparticle size, nanofluid average flow temperature and Reynolds number are found to be 90 nm, 360 K and 4000, respectively.

Successive Lagrangian relaxation algorithm for nonconvex quadratic optimization

Optimization problems whose objective function and constraints are quadratic polynomials are called quadratically constrained quadratic programs (QCQPs). QCQPs are NP-hard in general and are important in optimization theory and practice. There have been many studies on solving QCQPs approximately. Among them, a semidefinite program (SDP) relaxation is a well-known convex relaxation method. In recent years, many researchers have tried to find better relaxed solutions by adding linear constraints as valid inequalities. On the other hand, the SDP relaxation requires a long computation time, and it has high space complexity for large-scale problems in practice; therefore, the SDP relaxation may not be useful for such problems. In this paper, we propose a new convex relaxation method that is weaker but faster than SDP relaxation methods. The proposed method transforms a QCQP into a Lagrangian dual optimization problem and successively solves subproblems while updating the Lagrange multipliers. The subproblem in our method is a QCQP with only one constraint for which we propose an efficient algorithm. Numerical experiments confirm that our method can quickly find a relaxed solution with an appropriate termination condition.