Sequential Quadratic Programming Research Articles

Iterative distributed model predictive control for nonlinear systems with coupled non‐convex constraints and costs

AbstractThis paper proposes a distributed model predictive control (DMPC) algorithm for dynamic decoupled discrete‐time nonlinear systems subject to nonlinear (maybe non‐convex) coupled constraints and costs. Solving the resulting nonlinear optimal control problem (OCP) using a DMPC algorithm that is fully distributed, termination‐flexible, and recursively feasible for nonlinear systems with coupled constraints and costs remains an open problem. To address this, we propose a fully distributed and globally convergence‐guaranteed framework called inexact distributed sequential quadratic programming (IDSQP) for solving the OCP at each time step. Specifically, the proposed IDSQP framework has the following advantages: (i) it uses a distributed dual fast gradient approach for solving inner quadratic programming problems, enabling fully distributed execution; (ii) it can handle the adverse effects of inexact (insufficient) calculation of each internal quadratic programming problem caused by early termination of iterations, thereby saving computational time; and (iii) it employs distributed globalization techniques to eliminate the need for an initial guess of the solution. Under reasonable assumptions, the proposed DMPC algorithm ensures the recursive feasibility and stability of the entire closed‐loop system. We conduct simulation experiments on multi‐agent formation control with non‐convex collision avoidance constraints and compare the results against several benchmarks to verify the performance of the proposed DMPC method.

Optimizing heat source distribution in sintering molds: Integrating response surface model with sequential quadratic programming

The sintering mold imposes strict requirements for temperature uniformity. The mold geometric parameters and the power configuration of heating elements exert substantial influence. In this paper, we introduce an optimization approach that combines response surface models with the sequential quadratic programming algorithm to optimize the geometric parameters and heating power configuration of a heating system for sintering mold. The response surface models of the maximum temperature difference, maximum temperature, and minimum temperature of the sintering area are constructed utilizing the central composite design method. The model's reliability is rigorously confirmed through variance analysis, residual analysis, and generalization capability validation. The models demonstrate remarkable predictive accuracy within the design space. A nonlinear constrained optimization model is established based on the response surface models, and the optimal parameters are obtained after 9 iterations using the sequential quadratic programming algorithm. Under the optimal parameters, the maximum temperature difference is maintained at less than 5 °C, confirming exceptional temperature uniformity. We conduct parameter analysis based on standardized effects to determine the main influencing factors of temperature uniformity, revealing that the distance between adjacent heating rods and the power density of the inner heating rods exert significant influence. Enhanced temperature uniformity can be achieved by adopting a larger distance between heating rods and configuring the power density of the heating rods to a relatively modest level. This work introduces a practical approach to optimize the heating systems for sintering molds, with potential applications in various industrial mold optimization.

A Robot Positional Error Compensation Method Based on Improved Kriging Interpolation and Kronecker Products

This paper proposes a stable and high-accuracy model-free calibration method for unopened robotic systems, which can significantly improve the robot positional accuracy. Two improvements are made to the existing kriging-based error compensation method to achieve robustness/practicality enhancement goals: (1) The semi-variogram model is solved using the sequential quadratic programming (SQP) algorithm, and the distance weight coefficients are added to the objective function. The accuracy of semi-variogram modeling is guaranteed, thereby improving the performance and stability of error compensation. (2) The hand-eye (the pose matrix between the robot base and the laser tracker) and the tool center point (TCP) position are calibrated based on Kronecker products without relying on the spatial analyzer (SA) software to construct the robot base coordinate system separately. Thus, the calibration accuracy and efficiency are significantly improved. Experiments have been conducted, and the results reveal that the proposed method can significantly reduce the robot positional error. Furthermore, the proposed approach performs better than the existing kriging-based error compensation method without Kronecker products. The maximum, mean, and root mean square (RMS) values of the absolute positional errors are reduced by 34.48%, 8.09%, and 10.05%, respectively.

Bending Deformation of Bio-tensegrity Model at Different Deployable Schemes

Tensegrity structures consist of multiple struts or cables that are interconnected and ideal for deployable structures. Given the challenges of controlling the strut’s deformation, active cables are more preferred and commonly studied in the deployment of tensegrities. The selection of the active cables becomes important as the deployment of tensegrities is highly dependent on the construction cost and computational time. This paper presents three different deployable schemes considering different sets of active cables. The deployable schemes were studied in this study to investigate the bending deformation of a human spine-inspired bio-tensegrity model. The shape change strategy involves a computational approach based on sequential quadratic programming to optimise the cable force elongation. A total of nine shape change analysis cases were conducted on the bio-tensegrity model to undergo deformation under three different schemes and three uni-directional targeted coordinates. The bending ability of bio-tensegrity models, the convergence curve, and axial forces were all discussed. It was found that the deployment scheme S3 is the most efficient scheme for the model to achieve different targets in uni-directional mode. This study is useful for applications such as deployable structures, automation, and robots

Design of metamaterial-based heat manipulators using isogeometric level-set topology optimization

We exploit level-set topology optimization to find the optimal material distribution for metamaterial-based heat manipulators. The level-set function, geometry, and solution field are parameterized using the Non-Uniform Rational B-Spline (NURBS) basis functions to take advantage of easy control of smoothness and continuity. In addition, NURBS approximations can produce conic geometries exactly and provide higher efficiency for higher-order elements. The values of the level-set function at the control points (called expansion coefficients) are utilized as design variables. For optimization, we use an advanced mathematical programming technique, Sequential Quadratic Programming. Taking into account a large number of design variables and the small number of constraints associated with our optimization problem, the adjoint method is utilized to calculate the required sensitivities with respect to the design variables. The efficiency and robustness of the proposed method are demonstrated by solving three numerical examples. We have also shown that the current method can handle different geometries and types of objective functions. In addition, regularization techniques such as Tikhonov regularization and volume regularization have been explored to reduce unnecessary complexity and increase the manufacturability of optimized topologies.

A fast and accurate domain decomposition nonlinear manifold reduced order model

This paper integrates nonlinear-manifold reduced order models (NM-ROMs) with domain decomposition (DD). NM-ROMs approximate the full order model (FOM) state in a nonlinear-manifold by training a shallow, sparse autoencoder using FOM snapshot data. These NM-ROMs can be advantageous over linear-subspace ROMs (LS-ROMs) for problems with slowly decaying Kolmogorov n-width. However, the number of NM-ROM parameters that need to be trained scales with the size of the FOM. Moreover, for “extreme-scale” problems, the storage of high-dimensional FOM snapshots alone can make ROM training expensive. To alleviate the training cost, this paper applies DD to the FOM, computes NM-ROMs on each subdomain, and couples them to obtain a global NM-ROM. This approach has several advantages: Subdomain NM-ROMs can be trained in parallel, involve fewer parameters to be trained than global NM-ROMs, require smaller subdomain FOM dimensional training data, and can be tailored to subdomain-specific features of the FOM. The shallow, sparse architecture of the autoencoder used in each subdomain NM-ROM allows application of hyper-reduction (HR), reducing the complexity caused by nonlinearity and yielding computational speedup of the NM-ROM. This paper provides the first application of NM-ROM (with HR) to a DD problem. In particular, this paper details an algebraic DD reformulation of the FOM, training a NM-ROM with HR for each subdomain, and a sequential quadratic programming (SQP) solver to evaluate the coupled global NM-ROM. Theoretical convergence results for the SQP method and a priori and a posteriori error estimates for the DD NM-ROM with HR are provided. The proposed DD NM-ROM with HR approach is numerically compared to a DD LS-ROM with HR on the 2D steady-state Burgers’ equation, showing an order of magnitude improvement in accuracy of the proposed DD NM-ROM over the DD LS-ROM.

Multi-Energy Flow Integrated Energy System Considering Economic Efficiency Targets: Capacity Allocation and Scheduling Study

An integrated energy system (IES) breaks down barriers between different energy subsystems, enhancing energy reliability and efficiency. However, issues such as uneven equipment capacity allocation and suboptimal scheduling persist in multi-energy flow IES. To maximize economic benefits while ensuring energy balance and the operational characteristics of the equipment, a capacity matching optimization and scheduling strategy model for IES was developed. Firstly, mathematical models for the electricity, gas, and thermal networks within the IES were established. Secondly, considering the efficiency of energy conversion between different forms and constraints of energy storage in the electricity–thermal–gas interconnected energy system, optimization solutions were obtained using regional contraction algorithms and sequential quadratic programming methods. Finally, case studies conducted in a real park demonstrated that, through optimized capacity matching, unit prices for electricity, heat, and gas decreased by 39.9%, 90.5%, and 74.2%, respectively, effectively improving the economic viability of the system.

A GPU-accelerated 3dBEM supporting the optimization of actively morphing flapping-foil thrusters with application to AUV propulsion

In recent years, flapping thrusters have been getting attention as an eco-friendly alternative to conventional propellers for autonomous underwater vehicles (AUVs) mainly due to their low-frequency operation, advanced maneuverability, and high efficiency. Their operating principle mimics the thrust-producing kinematics found among efficient swimmers in the aquatic environment. The present work focuses on the analysis and optimization of flapping systems with active morphing features for increased performance. The two optimization studies refer to a realistic AUV propulsion scenario for a wing thruster with active hydrofoil-section adjustment, spanwise bend and twist morphing capabilities. A gradient descent approach based on sequential quadratic programming (SQP) is used for optimal tuning of design variables (planform shape, kinematics) targeting efficiency maximization under thrust and effective angle of attack constraints. For the evaluation of each candidate thruster the unsteady boundary element solver 3dBEM is developed and used for wing performance prediction. The solver exploits GPU parallel computation techniques to reduce computational time and enable fast optimization. Results indicate that the optimal thruster with chordline/spanwise bending is 25% more efficient, whereas the same result for the wing with spanwise bending and twist profiles is up to 8.8%. The 3dBEM solver can support the preliminary design process of morphing flapping-foil thrusters.

Optimization of surface texture distribution on the thrust bearing using the mass-conserving cavitation boundary condition: Theory and experiments

This study developed a numerical optimization model for the texture distribution in thrust bearings, employing the flat-headed chevron and circular dimple, and utilizing a mass-conserving cavitation boundary. A hybrid of the genetic algorithm and sequential quadratic programming algorithm is utilized. The results indicate the highest load-carrying capacity can be obtained by optimizing the texture distribution based on the flat-headed chevron. The primary mechanism is that the optimal distribution can efficiently harness the collective effect of texture, thereby effectively building up pressure. The optimal distributions of the flat-headed chevron and circular dimples exhibit asymmetric chevron and herringbone shapes, respectively. Furthermore, verification experiments show that the optimal distribution can shift the transition point to a lower rotation speed and higher normal load.

Minimizing Urban Flooding by Optimal Design of Drainage System Using Sequential Least Squares Quadratic Programming and Spatial Datasets

Urban flooding is caused due to poor drainage design and excessive rain. It severely affects the road infrastructure. Existing hydrologic software tools to examine the extent of urban flooding primarily require walking through a series of manual steps and address each study area individually, preventing a collective review of poor storm-drains in an efficient manner. Previous methods for optimal drainage design were inefficient and lacked the ability of solving the underlying optimization problem due to the inherent nonlinearity of the decision variables. In this paper, we develop a nonlinear optimization formulation to minimize urban flooding using underground pipe size as a decision variable. We propose a solution algorithm using sequential least squares quadratic programming and spatial datasets. The proposed method eliminates the need to examine each study area manually using existing hydrologic tools. An example using the storm-drain system for the Baltimore County is performed. The results show that the model is effective in identifying storm-drain deficiencies and correcting them by choosing appropriate storm-drain inlet types to minimize flooding. Future works may include using large datasets and a more sophisticated modeling approach for estimating rainfall intensity based on extreme weather patterns. The method can be applied to other jurisdictions if relevant hydrological and underdrain piping network data were available.

Nonlinear model predictive control for trajectory-planning and tracking based on tilting technology to achieve vehicle obstacle avoidance

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

Hybrid Renewable Production Scheduling for a PV–Wind-EV-Battery Architecture Using Sequential Quadratic Programming and Long Short-Term Memory–K-Nearest Neighbors Learning for Smart Buildings

Electricity demand in residential areas is generally met by the local low-voltage grid or, alternatively, the national grid, which produces electricity using thermal power stations based on conventional sources. These generators are holding back the revolution and the transition to a green planet, being unable to cope with climatic constraints. In the residential context, to ensure a smooth transition to an ecological green city, the idea of using alternative sources will offer the solution. These alternatives must be renewable and naturally available on the planet. This requires a generation that is very responsive to the constraints of the 21st century. However, these sources are intermittent and require a hybrid solution known as Hybrid Renewable Energy Systems (HRESs). To this end, we have designed a hybrid system based on PV-, wind-turbine- and grid-supported battery storage and an electric vehicle connected to a residential building. We proposed an energy management system based on nonlinear programming. This optimization was solved using sequential quadrature programming. The data were then processed using a long short-term memory (LSTM) model to predict, with the contribution and cooperation of each source, how to meet the energy needs of each home. The prediction was ensured with an accuracy of around 95%. These prediction results have been injected into K-nearest neighbors (KNN), random forest (RF) and gradient boost (GRU) repressors to predict the storage collaboration rates handled by the local battery and the electric vehicle. Results have shown an R2_score of 0.6953, 0.8381, and 0.739, respectively. This combination permitted an efficient prediction of the potential consumption from the grid with a value of an R²-score of around 0.9834 using LSTM. This methodology is effective in allowing us to know in advance the amount of energy of each source, storage, and excess grid injection and to propose the switching control of the hybrid architecture.

An efficient solver for the inverse kinematics of cable-driven manipulators with pure rolling joints using a geometric iterative approach

The inverse kinematics (IK) problem of cable-driven manipulators with pure rolling joints (CDM-PRJs) presents unique challenges due to the equal angle constraints and strict joint limits. These factors render existing IK solvers ineffective or result in substantial degradation of their performance. To address these challenges, we propose a three-phase geometric iterative method to efficiently solve the IK problem for CDM-PRJs, which is a variant of the forward and backward reaching inverse kinematics method. Our method begins by establishing a surrogate model for CDM-PRJs to handle the equal angle constraints. Subsequently, we introduce a geometric iterative approach comprising a forward reaching phase, a backward reaching phase, and a state update phase. Additionally, we devise two novel measures, the random disturbance measure and the branch change measure, to effectively address deadlock situations and asymmetric joint limits, respectively. Simulation results demonstrate that our method surpasses the inverse Jacobian method and the sequential quadratic programming method in terms of success rate and computational efficiency. Furthermore, our method exhibits generality across various CDM-PRJs.

A framework for the analysis of skin sores disease using evolutionary intelligent computing approach

The most common and contagious bacterial skin disease i.e. skin sores (impetigo) mostly affects newborns and young children. On the face, particularly around the mouth and nose area, as well as on the hands and feet, it typically manifests as reddish sores. In this study, a neuro-evolutionary global algorithm is introduced to solve the dynamics of nonlinear skin sores disease model (SSDM) with the help of an artificial neural network. The global genetic algorithm is integrated with local sequential quadratic programming (GA-LSQP) to obtain the optimal solution for the proposed model. The designed differential model of skin sores disease is comprised of susceptible (S), infected (I), and recovered (R) categories. An activation function based neural network modeling is exploited for skin sores system through mean square error to achieve best trained weights. The integrated approach is validated and verified through the comparison of results of reference Adam strategy with absolute error analysis. The absolute error results give accuracy of around 10 − 11 to 10 − 5 , demonstrating the worthiness and efficacy of proposed algorithm. Additionally, statistical investigations in form of mean absolute deviation, root mean square error, and Theil’s inequality coefficient are exhibited to prove the consistency, stability, and convergence criteria of the integrated technique. The accuracy of the proposed solver has been examined from the smaller values of minimum, median, maximum, mean, semi-interquartile range, and standard deviation, which lie around 10 − 12 to 10 − 2 .

MIMO radar partially correlated waveform design based on chirp rate diversity

Waveform design is a significant topic in multiple-input-multiple-output (MIMO) radar. In this paper, we address the problem of waveform design for colocated narrowband MIMO radar transmit beampattern synthesis. The existing methods have not comprehensively considered the transmit beampattern synthesis under multiple practical constraints, such as constant modulus constraint, Doppler tolerance, high range resolution and low auto-correlation sidelobe. We consider these practical constraints and propose a novel chirp rate diversity-based linear frequency modulated (CRD-LFM) waveform design for approximating the desired MIMO radar transmit beampattern. To tackle the problem, we improve the classical two-step approach. Firstly we design the covariance matrix using the existing closed-form solution. Then we model the problem of obtaining the waveforms from the covariance matrix as a nonlinear optimization problem, and we utilize the Sequential Quadratic Programming (SQP) algorithm to solve it. The simulations demonstrate that the waveforms obtained by this method can well approximate the desired transmit beampattern and have higher range resolution. Furthermore, we verify that the suppression of auto-correlation sidelobe can be achieved using amplitude weighting, which is easily realizable in practical engineering.

Research on optimization method for flyby observation mission adapted to satellite on-board computation

In this paper, the optimization problem of orbital transfer strategy for orbital flyby observation missions is studied. A hybrid optimization method is proposed, which is improved to make it more suitable for satellite on-board computing. This new algorithm is designed to solve the initial value sensitivity problem of the sequential quadratic programming algorithm (SQP). It is consisted of the depth-first search algorithm (DFS) and the SQP algorithm and thus has the characteristics of fast convergence, high reliability, and good robustness. With this method, the DFS with a large step size is calculated first, and then the optimal value in the calculation result is used as the initial value of the SQP algorithm for further optimization. This method can obtain the approximate optimal solution available in engineering. The numerical simulation of an orbital transfer optimization problem is set to verify the effectiveness of the new hybrid algorithm. The simulation results compared with the genetic algorithm (GA) show that the proposed hybrid algorithm can effectively reduce the on-board resource occupation when getting similar results and thus can meet the needs of satellite on-board computing.

Design, optimization and verification of a conical guiding origami mechanism for underwater docking station

Underwater docking station requires a conical guiding device with a large tolerance capacity and smaller volume to recover unmanned underwater vehicles (UUVs). Here, this paper innovatively introduces a conical guiding origami mechanism designed by an array and rotation approach based on a rigid origami mechanism. The Jacobian matrix method systematically calculates the degree of freedom (DOF) of the device. The variation function of dihedral angle in the folding process of the origami mechanism is derived, and the kinematics model is established within the Cartesian coordinate system. Based on this model, we established a mathematical model for optimizing the origami mechanism by considering number of units and unit volume as the design variables, subject to minimizing the underwater flow area and length. The sequential quadratic programming algorithm is employed to identify the optimum design variables. Subsequently, based on optimized results, collision simulation is carried out, and a conical guiding device tailored for an underwater docking station is successfully designed. The proposed device can be used as an underwater docking station to recover UUVs for ocean exploration. The proposed device has a large tolerance capacity, minimal shrinkage state cross-sectional area and length, excellent hydrodynamic performance, and a high spatial utilization rate.

A projected-search interior-point method for nonlinearly constrained optimization

AbstractThis paper concerns the formulation and analysis of a new interior-point method for constrained optimization that combines a shifted primal-dual interior-point method with a projected-search method for bound-constrained optimization. The method involves the computation of an approximate Newton direction for a primal-dual penalty-barrier function that incorporates shifts on both the primal and dual variables. Shifts on the dual variables allow the method to be safely “warm started” from a good approximate solution and avoids the possibility of very large solutions of the associated path-following equations. The approximate Newton direction is used in conjunction with a new projected-search line-search algorithm that employs a flexible non-monotone quasi-Armijo line search for the minimization of each penalty-barrier function. Numerical results are presented for a large set of constrained optimization problems. For comparison purposes, results are also given for two primal-dual interior-point methods that do not use projection. The first is a method that shifts both the primal and dual variables. The second is a method that involves shifts on the primal variables only. The results show that the use of both primal and dual shifts in conjunction with projection gives a method that is more robust and requires significantly fewer iterations. In particular, the number of times that the search direction must be computed is substantially reduced. Results from a set of quadratic programming test problems indicate that the method is particularly well-suited to solving the quadratic programming subproblem in a sequential quadratic programming method for nonlinear optimization.

Simultaneous Trajectory and Speed Planning for Autonomous Vehicles Considering Maneuver Variants

The paper presents a technique of motion planning for autonomous vehicles (AV) based on simultaneous trajectory and speed optimization. The method includes representing the trajectory by a finite element (FE), determining trajectory parameters in Frenet coordinates, composing a model of vehicle kinematics, defining optimization criteria and a cost function, forming a set of constraints, and adapting the Gaussian N-point scheme for quadrature numerical integration. The study also defines a set of minimum optimization parameters sufficient for making motion predictions with smooth functions of the trajectory and speed. For this, piecewise functions with three degrees of freedom (DOF) in FE’s nodes are implemented. Therefore, the high differentiability of the trajectory and speed functions is ensured to obtain motion criteria such as linear and angular speeds, acceleration, and jerks used in the cost function and constraints. To form the AV roadway position, the Frenet coordinate system and two variable parameters are used: the reference path length and the lateral displacement perpendicular to reference line’s tangent. The trajectory shape, then, depends only on the final position of the AV’s mass center and the final reference’s curvature. The method uses geometric, kinematic, dynamic, and physical constraints, some of which are related to hard restrictions and some to soft restrictions. The planning technique involves parallel forecasting for several variants of the AV maneuver followed by selecting the one corresponding to a specified criterion. The sequential quadratic programming (SQP) technique is used to find the optimal solution. Graphs of trajectories, speeds, accelerations, jerks, and other parameters are presented based on the simulation results. Finally, the efficiency, rapidity, and prognosis quality are evaluated.

Using Constrained Convex Optimization in Parameter Estimation of Process Dynamics with Dead Time

Abstract This paper proposes the usage of constrained convex optimization in improving the quality of the parameter estimates of a typical process plant with dead time from its time response data by incorporating system-specific constraints that are not considered in standard estimation methods. As the majority of the process plants are identified as second-order plus dead time (SOPDT) systems, the proposed method uses the same for establishing the optimization process. Traditional methods for parameter estimation in SOPDT systems have often relied on heuristic approaches or simplified assumptions, leading to suboptimal results. The proposed methodology augments the accuracy of the estimated values by leveraging the power of constrained convex optimization techniques, using Newton's Quadratic Model and Sequential Quadratic Programming, which provide a rigorous mathematical framework for parameter estimation. By incorporating system constraints, such as bounds on the parameters or stability requirements, it is ensured that the obtained parameter estimates adhere to physical and practical limitations. The proposed approach is demonstrated using simulations and on a real-time system, and the results show that it is effective not only in accurately estimating the parameters of the underdamped SOPDT systems but also works efficiently for parameter estimation of SOPDT systems in the presence of measurement noise. The efficacy of the proposed algorithm is verified by comparing it with similar published methods.