Quadratic Programming Optimization Problem Research Articles

A Joint Array Parameters Design Method Based on FDA-MIMO Radar

Frequency diverse array (FDA)-multiple-input and multiple-output (MIMO) radar is characterized by a range-angle-dependent beampattern owing to extra frequency offset across the transmit array elements. In this respect, the ideal beamforming performance can be obtained by designing the transmit and receive array parameters. On this basis, this paper aims to design the ideal beampattern for FDA-MIMO radar by introducing a joint array parameters optimization design method including receive filter (RF) and transmit frequency offset-receive element spacing (TFO-RS). The cyclic iteration is introduced, and this joint optimization method is divided into three sub-problems, including RF, TFO, and RS design. As for the TFO and RS design subproblems, function scaling is applied to transform the objection function to the quadratic form. Furthermore, the quadratic programming (QP) optimization problem with linear constraints can be constructed. The simulation results show that the proposed optimization design method can improve the ability of FDA-MIMO radar to detect multiple targets at the same time compared with the given conventional TFO and RS schemes.

Linear Parameter-Varying Model Predictive Control for Hydraulic Wind Turbine

Wind speed uncertainty and measurement noise affect the control effect in hydraulic wind turbine systems. This paper proposes a model predictive control (MPC) method with a dynamic Kalman filter (KF) based on a linear parameter-varying (LPV) model to address this problem. First of all, the LPV model for a nonlinear system of a hydraulic wind turbine is established using function substitution. Then, a LPV-based KF is introduced into the MPC to provide more precise estimated results and improve the anti-interference ability of the system. According to the current condition of the hydraulic wind turbine, the method updates the Kalman state estimator at each sampling instant and computes the optimal control input by solving a quadratic programming (QP) optimization problem. The performance and the efficiency of the proposed method is validated in simulation and compared with other methods.

Multistage power and energy management strategy for hybrid microgrid with photovoltaic production and hydrogen storage

For several years, microgrids (MGs) integrated with smart grids have been presented as one of the promising solutions for better integration of intermittent renewable energy sources (RES). As a result, the interest for the development of MGs has increased. Due to the variability of RES as well as the non-synchronization of intermittent RES production and energy consumption, new storage systems have emerged. The integration of hydrogen produced via water electrolysis powered by RES, the production of electricity through fuel cells (FCs) and the storage of hydrogen are becoming more and more attractive. In this paper, a multistage power and energy management strategy (MSPEMS) is presented for a MG with photovoltaic (PV) as a RES and a battery energy storage system, a FC and an Electrolyzer. The objective is to solve a unit commitment problem considering the different constraints of the MG components. The power management system (PMS) is based on a Distributed explicit model predictive control (DeMPC), whereas the energy management system (EMS) relies on a mixed-integer quadratic programming (MIQP) optimization problem. The interaction between the power management system (PMS) and the energy management system (EMS) is analyzed in order to improve their effectiveness. The PMS and the EMS are almost always developed separately and their interaction is not investigated. This point is an important contribution to the scientific community and the development of hybrid installations with intermittent sources, especially for hydrogen technologies. The performance of the power and energy management strategy (PEMS) is evaluated using simulation results and different predefined key performance indicators (KPI). The performance analysis shows that the proposed MSPEMS avoid inadequate start-up of the FC and the Electrolyzer.

Neural-Dynamics Optimization and Repetitive Learning Control for Robotic Leg Prostheses

Rapid development in robotics and bionics makes it possible for robotic leg prostheses to help amputees while imposing challenges on duplicating the motion characteristics of the amputees’ healthy leg. One critical problem in prosthetic control is joint angle drift problem, that is, a repetitive motion trajectory in task space cannot guarantee that the generated motion trajectories in joint space are also repetitive. In order to solve this problem, in this article, we propose neural-dynamics optimization for robotic leg prostheses to generate the repetitive joint trajectories in real time. Our proposed method duplicates the self-selected walking speed of the amputees’ healthy leg. The online motion generation is formulated as a constrained quadratic programming (QP) optimization problem whose objective function adopts the kinetic energy and joint displacement performance criterion. The varying parameter convergent differential neural network is developed as a real-time QP solver which can globally converge to the optimal solution of the constrained QP problem. Then, a repetitive learning controller is designed for robotic leg prostheses to reduce the tracking errors while following the repetitive motion. Through the physical experiments on the developed two-degree-of-freedom robotic leg prosthesis worn on an amputee, the neural-dynamics optimization is substantiated to be a remedy of online motion generation, and the effectiveness of repetitive learning control for reducing the prosthetic tacking errors is verified.

A practical trajectory tracking control of autonomous vehicles using linear time-varying MPC method

With the rapid development and implementation of autonomous vehicles (AVs), the simultaneous and accurate trajectory tracking problem for such AVs has become a popular research topic. This paper proposes a comprehensive linear time-varying model predictive controller (LTV-MPC) design for a type of AV, aiming to achieve good trajectory tracking in a practical driving scenario. First, a two-degree-of-freedom kinematic model of an AV is established. Next, an error model of the AV’s trajectory tracking system is constructed using linear time-varying theory. A successive linearization is introduced to linearize the nonlinear tracking error model, and a quadratic programming optimization problem is then formulated. Thus, the control sequence for this AV is incorporated into the predictive control framework, and the desired controller can be solved with a relatively higher computational efficiency and lower computational cost. Finally, the effectiveness and performance of the proposed controller are validated via a comparison of simulations conducted using MATLAB software and experiments conducted using a self-established test platform. The results demonstrate that the proposed LTV-MPC method can track the prescribed reference road trajectories with high precision and stability for an AV under various driving conditions.

Multi-objectivization inspired metaheuristics for the sum-of-the-parts combinatorial optimization problems

Multi-objectivization is a term used to describe strategies developed for optimizing single-objective problems by multi-objective algorithms. This paper focuses on multi-objectivizing the sum-of-the-parts combinatorial optimization problems, which include the traveling salesman problem, the unconstrained binary quadratic programming and other well-known combinatorial optimization problem. For a sum-of-the-parts combinatorial optimization problem, we propose to decompose its original objective into two sub-objectives with controllable correlation. Based on the decomposition method, two new multi-objectivization inspired single-objective optimization techniques called non-dominance search and non-dominance exploitation are developed, respectively. Non-dominance search is combined with two metaheuristics, namely iterated local search and iterated tabu search, while non-dominance exploitation is embedded within the iterated Lin–Kernighan metaheuristic. The resultant metaheuristics are called ILS+NDS, ITS+NDS and ILK+NDE, respectively. Empirical studies on some TSP and UBQP instances show that with appropriate correlation between the sub-objectives, there are more chances to escape from local optima when new starting solution is selected from the non-dominated solutions defined by the decomposed sub-objectives. Experimental results also show that ILS+NDS, ITS+NDS and ILK+NDE all significantly outperform their counterparts on most of the test instances.

Relaxed multi-view clustering in latent embedding space

Although many multi-view clustering approaches have been developed recently, one common shortcoming of most of them is that they generally rely on the original feature space or consider the two components of the similarity-based clustering separately (i.e., similarity matrix construction and cluster indicator matrix calculation), which may negatively affect the clustering performance. To tackle this shortcoming, in this paper, we propose a new method termed Multi-view Clustering in Latent Embedding Space (MCLES), which jointly recovers a comprehensive latent embedding space, a robust global similarity matrix and an accurate cluster indicator matrix in a unified optimization framework. In this framework, each variable boosts each other in an interplay manner to achieve the optimal solution. To avoid the optimization problem of quadratic programming, we further propose to relax the constraint of the global similarity matrix, based on which an improved version termed Relaxed Multi-view Clustering in Latent Embedding Space (R-MCLES) is proposed. Compared with MCLES, R-MCLES achieves lower computational complexity with more correlations between pairs of data points. Extensive experiments conducted on both image and document datasets have demonstrated the superiority of the proposed methods when compared with the state-of-the-art.

Jerk Control of Floating Base Systems With Contact-Stable Parameterized Force Feedback

Nonlinear controllers for floating base systems in contact with the environment are often framed as quadratic programming (QP) optimization problems. Common drawbacks of such QP-based controllers are: the control input often experiences discontinuities; no force feedback from force/torque (FT) sensors installed on the robot is taken into account. This article attempts to address these limitations using jerk-based control architectures. The proposed controllers assume the rate-of-change of the joint torques as control input, and exploit the system position, velocity, accelerations, and contact wrenches as measurable quantities. The key ingredient of the presented approach is a one-to-one correspondence between free variables and an inner approximation of the manifold defined by the contact stability constraints. More precisely, the proposed correspondence covers completely the contact stability manifold except for the socalled friction cone, for which there exists a unique correspondence for more than 90% of its elements. The correspondence allows us to transform the underlying constrained optimization problem into one that is unconstrained. Then, we propose a jerk control framework that exploits the proposed correspondence and uses FT measurements in the control loop. Furthermore, we present Lyapunov stable controllers for the system momentum in the jerk control framework. The approach is validated with simulations and experiments using the iCub humanoid robot.

Extreme Learning Regression for nu Regularization

ABSTRACTExtreme learning machine for regression (ELR), though efficient, is not preferred in time-limited applications, due to the model selection time being large. To overcome this problem, we reformulate ELR to take a new regularization parameter nu (nu-ELR) which is inspired by Schölkopf et al. The regularization in terms of nu is bounded between 0 and 1, and is easier to interpret compared to C. In this paper, we propose using the active set algorithm to solve the quadratic programming optimization problem of nu-ELR. Experimental results on real regression problems show that nu-ELR performs better than ELM, ELR, and nu-SVR, and is computationally efficient compared to other iterative learning models. Additionally, the model selection time of nu-ELR can be significantly shortened.

Cooperative Delay-Constrained Cognitive Radio Networks: Delay-Throughput Trade-Off With Relaying Full-Duplex Capability

In this paper, the problem of maximizing the secondary user (SU) throughput under a primary user (PU) quality of service (QoS) delay requirement is studied. Moreover, the impact of having a full-duplex capability at the SU on the network performance is investigated compared to the case of a SU with half-duplex capability. We consider a cooperative cognitive radio (CR) network in which the receiving nodes have multi-packet reception (MPR) capabilities. In our proposed model, the SU not only benefits from the idle time slots (i.e. when PU is idle), but also chooses between sharing the channel or cooperating with the PU in a probabilistic manner. We formulate our optimization problem to maximize the SU throughput under a PU QoS, defined by a delay constraint; the optimization is performed over the transmission modes selection probabilities of the SU. The resultant optimization problem is found to be a non-convex quadratic constrained quadratic programming (QCQP) optimization problem, which is, generally, an NP-hard problem. We devise an efficient approach to solve it and to characterize the network stability region under a delay constraint set on the PU. Numerical results, surprisingly, reveal that the network performance when full-duplex capability exists at the SU is not always better compared to that of a half-duplex SU. In fact, we demonstrate that a full-duplex capability at the SU can, in some cases, adversely influence the network stability performance, especially if the direct channel conditions between the SU and the destinations are worse than that between the PU and the destinations. In addition, we formulate a multi-objective programming (MOP) optimization problem to investigate the trade-off between the PU delay and the SU throughput. Our MOP approach allows for assigning relative weights for our two conflicting performance metrics, i.e., PU delay and SU throughput. Numerical results also demonstrate that our cooperation policy outperforms conventional cooperative and non-cooperative policies presented in previous works.

Cooperative Kinematic Control for Multiple Redundant Manipulators Under Partially Known Information Using Recurrent Neural Network

In this study, we investigate the problem of cooperative kinematic control for multiple redundant manipulators under partially known information using recurrent neural network (RNN). The communication among manipulators is modeled as a graph topology network with the information exchange that only occurs at the neighbouring robot nodes. Under partially known information, four objectives are simultaneously achieved, i.e, global cooperation and synchronization among manipulators, joint physical limits compliance, neighbor-to-neighbor communication among robots, and optimality of cost function. We develop a velocity observer for each individual manipulator to help them to obtain the desired motion velocity information. Moreover, a negative feedback term is introduced with a higher tracking precision. Minimizing the joint velocity norm as cost function, the considered cooperative kinematic control is built as a quadratic programming (QP) optimization problem integrating with both joint angle and joint speed limitations, and is solved online by constructing a dynamic RNN. Moreover, global convergence of the developed velocity observer, RNN controller and cooperative tracking error are theoretically derived. Finally, under a fixed and variable communication topology, respectively, application in using a group of iiwa R800 redundant manipulators to transport a payload and comparison with the existing method are conducted. Among the simulative results, the robot group synchronously achieves the desired circle and rhodonea trajectory tracking, with higher tracking precision reaching to zero. When joint angles and joint velocities tend to exceed the setting constraints, respectively, they are constrained into the upper and lower bounds owing to the designed RNN controller.

Inverse Kinematics of Redundant Manipulators Formulated as Quadratic Programming Optimization Problem Solved Using Recurrent Neural Networks: A Review

SUMMARYThe Inverse Kinematics (IK) problem of manipulators can be divided into two distinct steps: (1)Problem formulation,where the problem is developed into a form which can then be solved using various methods. (2)Problem solution,where the IK problem is actually solved by producing the values of different joint space variables (joint angles, joint velocities or joint accelerations). The main focus of this paper is concentrated on the discussion of the IK problem of redundant manipulators, formulated as a quadratic programming optimization problem solved by different kinds of recurrent neural networks.

Distributed Reactive Model Predictive Control for Collision Avoidance of Unmanned Aerial Vehicles in Civil Airspace

Safety in the operations of UAVs (Unmanned Aerial Vehicles) depends on the current and future reduction of technical barriers and on the improvements related to their autonomous capabilities. Since the early stages, aviation has been based on pilots and Air Traffic Controllers that take decisions to make aircraft follow their routes while avoiding collisions. RPA (Remotely Piloted Aircraft) can still involve pilots as they are UAVs controlled from ground, but need the definition of common rules, of a dedicated Traffic Controller and exit strategies in the case of lack of communication between the Ground Control Station and the aircraft. On the other hand, completely autonomous aircraft are currently banned from civil airspace, but researchers and engineers are spending great effort in developing methodologies and technologies to increase the reliability of fully autonomous flight in view of a safe and efficient integration of UAVs in the civil airspace. This paper deals with the design of a collision avoidance system based on a Distributed Model Predictive Controller (DMPC) for trajectory tracking, where anticollision constraints are defined in accordance with the Right of Way rules, as prescribed by the International Civil Aviation Organization (ICAO) for human piloted flights. To reduce the computational burden, the DMPC is formulated as a Mixed Integer Quadratic Programming optimization problem. Simulation results are shown to prove the effectiveness of the approach, also in the presence of a densely populated airspace.

Real-time optimal energy management strategy for a dual-mode power-split hybrid electric vehicle based on an explicit model predictive control algorithm

To improve fuel economy and reduce online computation time and microprocessor hardware resources, a real-time implementable energy management strategy for a dual-mode power-split hybrid electric vehicle (HEV) based on an explicit model predictive control (EMPC) method is proposed in this paper. The proposed strategy includes an accurate control-oriented model and a dynamic process coordination control algorithm. The energy management optimal control problem is formulated as a multiparameter quadratic programming optimization problem, and the EMPC control laws are obtained by solving the multiparameter quadratic programming problem offline. The laws are then used online to realize real-time control. A traditional model predictive control (MPC)-based control strategy, DP-based control strategy and rule-based control strategy are considered benchmark strategies for verification of the proposed EMPC-based energy management strategy. The simulation results indicate the EMPC controller has far lower microprocessor hardware costs than the MPC controller but equivalent control performance. As the prediction horizon increases, fuel consumption remains nearly the same between the MPC-based control strategy and EMPC-based control strategy. The consumption time of the MPC-based control strategy increases significantly, while the consumption time of the EMPC-based control strategy is nearly unchanged. Compared with the benchmark algorithms, the elapsed time of the EMPC controller maximum reduced by 97.46%, and the fuel economy improved by 23.37%.

An iterative model predictive control algorithm for constrained nonlinear systems

AbstractAn iterative model predictive control (MPC) scheme for constrained nonlinear systems is presented. The idea of the method is to detour from the solution of a non‐convex optimization problem using a time‐variant linearization of the nonlinear system model that is adjusted iteratively by solving an iterative quadratic programming optimization problem at each sampling time. The main advantage is the faster resolution of the optimization problem by using quadratic programming instead of non‐convex programming and yet, properly describing the nonlinear dynamics of the process being controlled. In this article, a general framework of the method is presented together with a discussion on the conditions under which the iterations converge and on the uncertainty of its results due to the linearization used, as well as some practical considerations about its implementation. The performance of the proposed controller is illustrated via two examples.

Robust Tube-Based Predictive Control for Visual Servoing of Constrained Differential-Drive Mobile Robots

This paper proposes a control strategy for the vision-based control problem of a nonholonomic constrained differential-drive mobile robots with bounded disturbance by using robust tube-based model predictive control (MPC) method. The proposed control strategy mainly consists of an ancillary state feedback controller and an MPC control for a nominal robotic system. First, the state-error kinematics of the nominal system is converted into a chained form system, and then its MPC optimization is computed to deal with a quadratic programming optimization problem by integrating a linear variable inequality-based primal-dual neural network (LVI-PDNN). Next, the gain scheduling of the ancillary state feedback is obtained via solving robust pole assignment using LVI-PDNN. An optimal state trajectory is thus generated for the nominal robotic system by the MPC without various uncertainties, the ancillary state feedback control forces the state variables to be constrained within an invariant designed tube. Finally, extensive experimental results on stabilization control of the nonholonomic mobile robot are provided to verify the effectiveness of the proposed robust tube-based MPC.

Nonlinear model predictive control based on piecewise linear Hammerstein models

This paper develops a nonlinear model predictive control (MPC) algorithm for dynamic systems represented by piecewise linear (PWL) Hammerstein models. At each sampling instant, the predicted output trajectory is linearized online at an assumed input trajectory such that the control actions can be easily calculated by solving a quadratic programming optimization problem, and such linearization and optimization may be repeated a few times for good linear approximation accuracy. A three-step procedure is developed to linearize a PWL function, where the derivatives of a PWL function are obtained by a computationally efficient look-up table approach. Unlike many existing MPC algorithms for Hammerstein systems, it does not require the inversion of static nonlinearity and can directly cope with input constraints even in multivariable systems. Two benchmark chemical reactors are studied to illustrate the effectiveness of the proposed algorithm.

Actuator allocation for integrated control in tokamaks: architectural design and a mixed-integer programming algorithm

Plasma control systems (PCS) in tokamaks need to fulfill a number of control tasks to achieve the desired physics goals. In present-day devices, actuators are usually assigned to a single control task. However, in future tokamaks, only a limited set of actuators is available for multiple control tasks at the same time. The priority to perform specific control tasks may change in real-time due to unforeseen plasma events and actuator availability may change due to failure. This requires the real-time allocation of available actuators to realize the requests by the control tasks, also known as actuator management.In this paper, we analyze possible architectures to interface the control tasks with the allocation of actuators inside the PCS. Additionally, we present an efficient actuator allocation algorithm for Heating and Current Drive (H&CD) actuators. The actuator allocation problem is formulated as a Mixed-Integer Quadratic Programming optimization problem, allowing to quickly search for the best allocation option without the need to compute all allocation options. The algorithms performance is demonstrated in examples involving the full proposed ITER H&CD system, where the desired allocation behavior is successfully achieved. This work contributes to establishing integrated control routines with shared actuators on existing and future tokamaks.

General Projection Neural Network Based Nonlinear Model Predictive Control for Multi-Robot Formation and Tracking

For controlling the multi-robot formation system, a general projection neural network based nonlinear model predictive control (NMPC) strategy is proposed in this paper. The multi-robot formation system consists of the trajectory tracking of leader robot and the leader-follower formation controlling. Their kinematic error systems can be reformulated as a convex nonlinear minimization problem by the NMPC method and can be transformed into a constrained quadratic programming (QP) optimization problem. To solve this QP problem online efficiently, a general projection neural network (GPNN) is applied to obtain the optimal solution, which includes the optimal inputs of the formation system. Compare to other existing leader-follower approaches, the proposed nonlinear MPC method can take the input and state constraints of system into consideration. In the end of this work, simulations of the trajectory tracking and multi-robot formation are performed to verify the effectiveness of the developed strategy.

Natural Color Satellite Image Mosaicking Using Quadratic Programming in Decorrelated Color Space

Generating mosaics of orthorectified remote sensing images is a challenging task because of the colorimetric differences between adjacent images introduced by land use, surface illumination, atmospheric conditions, and sensor. Most of the existing color correction methods involve pairwise techniques, which are limited when the collection of images is large with numerous overlaps. Besides, available techniques do not operate in a color space suited for true-color processing. This paper presents a simple and robust method to perform the global colorimetric harmonization of multiple overlapping remote sensing images in natural colors (RGB). Our parameter-free method deals simultaneously with any number of images, with any spatial layout, and without any single reference image. It is based on the resolution of a quadratic programming (QP) optimization problem. It operates in the lαβ decorrelated color space, which is well suited for human vision of natural scenes. The results obtained from the mosaicking of 132 RapidEye color orthoimages over mainland France demonstrate good potential for performing colorimetric harmonization automatically and effectively.