Sequential Quadratic Programming Research Articles

Predictive control of interlinked water-energy microgrids

Although water and energy systems are interdependent, they are still designed individually due to their complexity. This paper proposes a multiple input multiple output (MIMO) model predictive control (MPC) for demand management of an integrated water distribution system (WDS) supplied by an islanded microgrid (MG) system, offering an additional opportunity for energy-saving at the WDS. This strategy benefits the island and remote communities, which have limited access to the centralized electric grid. The existing literature either used an open-loop approach for energy management of water-energy microgrids or ignored the interconnected nature and MIMO nature of these systems. Compared to that, the proposed closed-loop energy management system is developed to address the detailed dynamics of assets, the inherent interconnections between water and energy networks, and to provide resilience as well as energy saving and demand management capabilities. The integrated MPC algorithm is designed in discrete time, utilizing a state-space model and sequential quadratic programming (SQP) as the solution method. Considering the intensive use of electricity by the pumps in WDS, their energy consumption is accommodated by an islanded microgrid system that incorporates a diesel generator, renewable energy sources (wind and solar), and a battery bank that serves as an energy source and a storage device. The proposed approach is investigated using base water demand from a real-world community, Telford, in Pennsylvania. Several case studies, such as variations in renewable energy contributions and increments of the control actions, are carried out to demonstrate the feasibility and reliability of the integrated MPC to provide efficient water and energy demand management concurrently.

Advanced Bio-Inspired computing paradigm for nonlinear smoking model

Smoking has emerged as one of the leading global factors that is the source of health issues. It damages almost all of the body's organs. It damages various muscles and causes lung cancer. Additionally, it causes ulcers, pulmonary disease, and vascular deterioration. Except for the financial benefit to tobacco companies, manufacturers, and marketing companies, smoking has no advantages. Due to these factors, the present study exploited a feed forward neural networking based global optimization procedure with a local scheme to solve a mathematical model of smoking. A genetic based algorithm and sequential quadratic programming (GA-SQP) are utilized as hybridized global and local strategies. The model is categorized into five classes: potential smokers, occasional smokers, smokers, temporary quit, and permanent quit smokers. An objective optimization function is constructed to minimize the mean square error using the designed smoking model in form of feed forward neural networking. The comparative evaluation of hybrid GA-SQP and Adam numerical scheme is also assessed to authenticate the precision and correctness of the solution of the smoking model. The robustness, perfection, and convergence stability of GA-SQP are verified by establishing various statistical performance indicators. The quantitative analysis provides the minimum, mean, and semi-inter quartile range values for absolute errors up to 6 to 13 decimal places, demonstrating the worthiness and precision of the proposed GA-SQP.

Multi-objective optimization configuration of redundant electromagnetic actuators in fault-tolerant control of active magnetic bearing system

Fault-tolerant control of active magnetic bearing (AMB) systems with redundant electromagnetic actuators (EMAs) based on generalized bias current linearization has become a practical technique to address EMA/amplifier faults. In this method, the configuration of multi-channel EMAs involves solving a high-dimensional and nonlinear problem containing complex constraints offline. This article develops a general framework for the EMAs multi-objective optimization configuration (MOOC) by combining the non-dominated sorting genetic algorithm III (NSGA-III) and the sequential quadratic programming (SQP) with the designing of objectives, handling of constraints, consideration of the iterative efficiency and the diversity of solutions. The numerical simulation results confirm the feasibility of the framework for searching the non-inferior configurations and reveal the function mechanism that intermediate variables of the nonlinear optimization model on AMB performance. Finally, the best configurations identified using the technique for order preference by similarity to an ideal solution (TOPSIS) are applied to the 4-DOF AMB experimental platform. Experiments further indicate that the work in this paper provides a novel way with good performance and high reliability for solving the EMAs MOOC problem in fault-tolerant control of AMB systems.

Small-signal stability constrained unit commitment based on decomposition and SQP-GS

This paper proposes a small-signal stability constrained unit commitment(SSSC-UC) model to ensure that the solution of SCUC can provide a sufficient small-signal stability margin. To solve the model, Benders decomposition (BD) is applied to separate the problem into a SCUC master problem, which is a mixed-integer linear programming problem, and a series of subproblems to check the AC power flow constraint and small-signal stability constraint. The small-signal stability check subproblems are non-smooth and non-linear programming problems, which are solved by Sequential Quadratic Programming with Gradient Sampling (SQP-GS). When the subproblem checks do not pass, cuts formed by the sensitivity of the spectral abscissa with respect to generator output are added to the master problem for the next iteration of the SCUC. The iteration process continues until all AC power flow and small-signal constraint violations are eliminated and a SCUC solution is found. Simulations on the New England 10-machine 39-bus system and the IEEE 54-machine 118-bus system show that our proposed SSSC-UC can guarantee small-signal stability for all time periods while SCUC cannot. Furthermore, the proposed parallel technique can speed up the computation up to 5 and 11 times respectively for the two test systems.

Multi-objective optimization of subsurface $$\text {CO}_{2}$$ capture, utilization, and storage using sequential quadratic programming with stochastic gradients

Multi-objective optimization of subsurface $$\text {CO}_{2}$$ capture, utilization, and storage using sequential quadratic programming with stochastic gradients

Cooperative distributed MPC via decentralized real-time optimization: Implementation results for robot formations

Distributed model predictive control (DMPC) is a flexible and scalable feedback control method applicable to a wide range of systems. While the stability analysis of DMPC is quite well understood, there exist only limited implementation results for realistic applications involving distributed computation and networked communication. This article approaches formation control of mobile robots via a cooperative DMPC scheme. We discuss the implementation via decentralized optimization algorithms. To this end, we combine the alternating direction method of multipliers with decentralized sequential quadratic programming to solve the underlying optimal control problem in a decentralized fashion with nominal convergence guarantees. Our approach only requires coupled subsystems to communicate and does not rely on a central coordinator. Our experimental results showcase the efficacy of DMPC for formation control and they demonstrate the real-time feasibility of the considered algorithms.

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

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

Seismic Bearing Capacity Solution for Strip Footings in Unsaturated Soils with Modified Pseudo-Dynamic Approach

In engineering mathematics, the unsaturated nature of soil has a significant impact on the seismic bearing capacity solution. However, it has generally been neglected in the published literature to date. Based on the kinematic approach of limit analysis, the present study proposes a method for calculating the bearing capacity of shallow strip footings located in unsaturated soils, taking four common types of soils as examples. The modified pseudo-dynamic (MPD) approach is used to calculate the seismic forces varying with time and space, and the layerwise summation method is used to derive the power generated by the seismic forces. In the calculation of internal energy dissipation, this paper introduces the effective stress based on the suction stress to derive the cohesion expression at different depths. The analytical formula of bearing capacity is obtained by the principle of virtual work, and its value is optimized by the Sequential Quadratic Programming (SQP) algorithm. In order to verify the validity of the proposed method, the present results are compared with the solutions published so far and a good agreement is obtained. Finally, a parametric study is performed to investigate the influence of different types of parameters on the bearing capacity.

Design of a Highly Compatible Underwater Wireless Power Transfer Station for Seafloor Observation Equipment

Conventional cabled seafloor observatories (CSOs) power in-situ instruments via wet-mated or dry-mated direct electrical contact (DEC) connectors to achieve long-term and real-time observation. However, the DEC connectors have high risks of water leakage and short circuits in power feeding, especially under high water pressure. This paper proposes a highly compatible underwater station based on inductive wireless power transfer (IPT) technology to address the above reliability issue. A novel energy transmitter with runway-structure coils is applied to the proposed underwater station to cover a sufficient power feeding area so that various in-situ equipment can be powered with desirable misalignment tolerance. The magnetic field distribution is analyzed by both derivation and finite element analysis (FEA) methods, and the principal parameters of the transmitter are further optimized and compared with both the mixed-integer sequential quadratic programming (MISQP) algorithm and the evolutionary algorithm (EA) for better performance. The same results show a reliable optimization process. The WPT circuit characteristics are also investigated to power different loads and improve the power transmission efficiency. The output power decreases, and the transmission efficiency rises and then decreases as the load increases. In addition, receivers with higher mutual inductance have better transmission performance. A prototype of the underwater station has been tested both in air and in water, and the experimental results have proven it can power multiple seafloor observation instruments stably and achieve compatibility requirements. The maximum output power of the station prototype for testing is 100 W, and the maximum overall transmission efficiency is 61%.

Energy-Efficient Configuration and Control Allocation for a Dynamically Reconfigurable Underwater Robot

A dynamically reconfigurable underwater robot, which can vary its configuration during a mission, would be useful for confined environment exploration and docking because of its versatility. A mission can be performed by choosing among different configurations, and the energy cost may increase, owing to the reconfigurability of the robot. Energy saving is the critical issue in long-range missions with underwater robots. Moreover, control allocation must be considered for a redundant system and input constraints. We propose an approach for an energy-efficient configuration and control allocation for a dynamically reconfigurable underwater robot that is built for karst exploration. The proposed method is based on sequential quadratic programming, which minimizes an energy-like criterion with respect to robotic constraints, i.e., mechanical limitations, actuator saturations, and a dead zone. The optimization problem is solved in each sampling instant. Two popular tasks for underwater robots, i.e., path-following and station-keeping (observation) problems, are simulated, and the simulation results show the efficiency of the method. Moreover, an experiment is carried out to highlight the results.

Minimax design of two-channel critically sampled graph QMF banks

We address here the issue of designing high spectral selectivity graph filter banks, which require high-degree polynomial approximation. To achieve sharp transition band roll required for high-selectivity, the minimax criterion is used in the design formulation. A constraint optimization method is used for the design process, and a spectral transformation is employed to circumvent the numerical problems that arise with high-degree polynomials. Using the transformation, approximation problem can be recast as an approximation problem with trigonometric polynomials. The transformed constraint optimization problem can be solved using the readily available sequential quadratic programming (SQP) method. High order filters, with low maximum approximation error (MAE) and low maximum reconstruction error (MRE), can be designed with this method. An algorithm is also developed that allows the user to choose design parameters that will give the lowest possible MRE. The method can also be adapted to trade-off between reconstruction quality and spectral selectivity of the resulting filter bank. The suite of techniques presented allow the user to easily shape the spectral response of the filters, to suit the application at hand. Numerous examples, with comparisons, will be presented to demonstrate the versatility of the proposed techniques. Applications to nonlinear approximation and denoising of graph signal will also be considered.

Determination of Energy-Saving Drying Modes in Vibrofluidized Bed Apparatus

The traditional pectin production technology is highly energy-intensive and environmentally unsafe. One of the possible ways to improve the technological process of pectin production is to dry directly the petine hydrolyzate before it is precipitated with ethyl alcohol. The most effective method of drying pectin hydrolyzate is drying in a vibrofluidized layer of an inert material, which provides high productivity in terms of evaporated moisture per unit volume of the chamber and the quality of the resulting dry product. This paper proposes a method for optimizing the drying process of pectin hydrolyzatein the apparatus of a vibrofluidized layer of an inert material, which makes it possible to determine the values of regime parame- ters at which the drying process proceeds with minimal costs for thermal and electrical energy. The technique is based on the experimentally obtained relationship between the specific productivity of the drying unit and the following operating parameters of the drying process: the air velocity in the drying chamber, the initial air temperature, the specific load related to the area of the gas distribution grid, the initial concentration for dry substances. On the basis of this experimental dependence, the criteria for assessing the reduced costs for heat and electric energy are formalized. A complex criterion for optimizing the drying process in a vibrofluidized bed is formulated, the minimization of which makes it possible to increase the efficiency of the drying process. Restrictions on the ranges of variation of the operating parameters of the drying process are formulated as well. The posed problem of optimization of the drying process in a vibrofluidized bed is solved numerically using the method of sequential quadratic programming and recommendations are formulated on the values of operating parameters for conducting the process in the optimal mode.

Receding Horizon D-Optimal Input Design for Identification of Wireless Power Transfer Systems

This paper develops a method of input design for the identification of wireless power transfer (WPT) systems based on receding horizon D-optimization. The dynamic behavior of the system is characterized by a discrete-time, Single-Input, Single-Output (SISO) model, and the associated model parameters are estimated by a recursive least-squares method. To improve the quality of the parameter estimates, the excitation signal of the system is designed based on receding horizon D-optimization. To improve the convergence and efficiency of the input design process, the Sequential Quadratic Programming (SQP) method is employed to solve the receding horizon D-optimization. Numerical and experimental results are presented to demonstrate the effectiveness of the proposed method.

A Large-Scale Identification Approach for Thermal Parameters of Multichips IGBT Modules Based on LLSO-SQP Algorithm

This paper proposes a large-scale optimization approach for identifying thermal parameters of multi-chip IGBT modules. State-space equation, in which the coefficient matrix comprises the thermal resistance and capacitance, is provided to represent the compact three-dimensional thermal network model. Then, the level-based learning swarm optimization (LLSO) algorithm is firstly utilized to identify large-scale thermal parameters. Additionally, to solve the inefficient convergence problem, the optimization results obtained from the LLSO is provided as the initial value of the sequential quadratic programming (SQP) algorithm to find the global optimal solution. Hence, the proposed LLSO-SQP algorithm can identify the large-scale thermal parameters efficiently and accurately. The training dataset for the algorithm is derived from the transient temperature response of a finite element model (FEM) of the IGBT module under power step excitation. Since only one-time simulation is in-demand, this approach needs less computational effort than others. The identified thermal network model is utilized to estimate junction temperature profiles taking a two-level inverter as a case study. In comparison to that of the experiment and FEM, the results validate the feasibility and accuracy of the junction temperature estimation method based on the compact three-dimensional thermal network model.

Likelihood Maximization of Lifetime Distributions With Bathtub-Shaped Failure Rate

Equipment lifetime distributions with bathtub-shaped failure rate can be fitted to data by the maximum likelihood criterion. In the literature, a commonly used method is to find a point in the parameter space where the partial derivatives of the log-likelihood function are zero. As the log-likelihood function is typically nonconvex, this approach may yield a suboptimal fit. In this work, we maximize the log-likelihood function, using a multistart of 100 optimization procedures, by three nonlinear optimization algorithms: 1) Nelder–Mead with adaptive parameters; 2) sequential least squares quadratic programming (SLSQP); 3) limited-memory Broyden–Fletcher–Goldfarb–Shanno algorithm with box constraints (L-BFGS-B). We perform a systematic study of refitting ten key lifetime distributions with bathtub-shaped failure rate from the literature to two widely studied datasets. The multistart nonlinear optimization yields better fits than those reported in the literature in 14 out of 19 distribution-dataset pairs, for which reference parameters are available. Based on the results, if gradient information of the log-likelihood function is available, our recommended optimization algorithm for the purpose is SLSQP.

Optimal Maneuvers Around Binary Asteroids Using Particle Swarm Optimization and Machine Learning

Designing optimal transfer trajectories and reference orbit tracking in binary asteroid systems is both challenging and computationally expensive. This paper proposes a method of bypassing the high computational overhead by leveraging a collection of known techniques. Indeed, the proposed framework is based on the combination of artificial intelligence techniques, such as the particle swarm optimization and neural networks, along with the inverse dynamics and the B-splines approximation of the trajectory. The real irregular shapes of the asteroids are considered in the free dynamics of the system, which are obtained via the mutual polyhedral model. The gravitational accelerations of the single asteroids acting on the spacecraft are approximated by using two single-layer neural networks trained via an extreme learning machine. By using a combination of these techniques, the computational time of the whole optimization is decreased from hours to minutes. The proposed approach is applied to the optimal trajectory design around the binary asteroid system, 1999 KW4, showing the feasibility of the proposed optimization approach, reducing the computational effort and time, and increasing the reliability of the obtained results. It is shown through a Monte Carlo analysis that our optimization strategy yields more accurate solutions than other optimization algorithms, such as the interior point and sequential quadratic programming methods, when a random initial guess is provided. Finally, the proposed optimization approach can be used in combination with other techniques to provide a feasible and reliable initial guess for a better solution refinement.t

Upper Limit Analysis for the Ultimate Bearing Capacity of a Multilayer Slope with Horizontal Stratification

The ultimate bearing capacity is one of the most important mechanical parameters in the mining and geotechnical fields and has a vital influence on the stability of slopes and the safety of constructions and structures. The determination of the ultimate bearing capacity has become a controversial issue in slope engineering. This study proposes a way to obtain the ultimate bearing capacity of a multilayer slope with horizontal stratification. According to limit analysis theory, three typical multiblock sliding failure modes for a multilayer slope with horizontal stratification are established. The upper limit solution of the ultimate bearing capacity of a multilayer slope, considering the influence of horizontal stratification, is derived. The optimization procedure is carried out to obtain the optimal value of the ultimate bearing capacity by using the sequential quadratic programming algorithm. The accuracy of the present method is proven based on a comparison of calculation results using other analytical methods and the numerical simulation method. The influence analysis of the parameters, involving the slope angle, soil strength, and distance of the foundation from the slope shoulder, is performed. The results indicate that the error between the calculated results of the present method and those of numerical simulation, as well as the error between the calculated results of the present method and those of other existing methods, is less than 10%. The ultimate bearing capacity linearly decreases with increasing slope angle, while it linearly increases with increasing distance of the foundation from the slope shoulder. The analytical method provides a method to analyze the ultimate bearing capacity of a multilayer slope, which effectively solves the problem of heterogeneity of soil layers observed in the natural slope. The results from this study can be used as a guide to estimate the stability of the slope and design of the foundation on a slope considering the load action near the slope.

Pattern-Reconfigurable Sparse Linear Array Synthesis Under Minimum Element Spacing Control by Alternating Sequential Quadratic Programming

A new method called alternating sequential quadratic programming (ASQP) is proposed to synthesize pattern-reconfigurable sparse linear arrays with minimum element spacing control. The method can find the common element positions and multiple sets of excitations for generating multiple reconfigurable patterns which accurately meet their given upper and lower pattern bounds. In addition, by introducing auxiliary weighting coefficients and collective excitation coefficient vectors and choosing them as optimization variables alternately, the proposed method can appropriately incorporate the minimum element spacing constraint into the pattern synthesis. Synthesized results show that the proposed method can give satisfactory reconfigurable pattern performance but save much more elements compared with some existing methods.

Vehicle Control Strategy Evaluation Based on the Driving Stability Region

Vehicle stability control strategies can improve driving safety effectively; however, there is still a lack of unified evaluation criteria for different control strategies. This paper proposes a vehicle control strategy evaluation method based on the driving stability region and is analyzed by using direct yaw moment control (DYC) and four-wheel steering (4WS) as examples. Firstly, the five-degree-of-freedom (5DOF) vehicle system models including DYC and 4WS are established, and the effectiveness of the control strategies is verified by nonlinear analysis methods; the dynamic characteristics of the system are also analyzed. Following this, a hybrid algorithm combining the Genetic Algorithm (GA) and Sequential Quadratic Programming (SQP) methods is used to solve the system equilibrium points, and the driving stability regions under different control strategies are obtained. Finally, the driving stability regions are tested based on the CarSim and Simulink simulations, and the control performance is evaluated. The results indicate that DYC and 4WS can improve vehicle stability and expand the range of driving stability regions. When the initial longitudinal velocity is below 30 m/s, the driving stability regions under DYC and 4WS expand to different extents compared to the original driving stability region. The expanded driving stability regions show that the stability region of the vehicle with DYC is larger than that of 4WS; thus, the control effect of DYC is better than that of 4WS. The proposed method can be used to evaluate the effective range of different control strategies.

Dynamic Optimization of Variable Load Process for Combined Heat and Power Unit Based on Sequential Quadratic Programming and Interior Point Method Alternating Solution Method

Aiming at the problem that the modeling and solving method of combined heat and power (CHP) unit variable load control process is challenging to meet the demand for efficient analysis of complex systems, this paper proposes a method based on sequential quadratic programming and interior point method (SQP-IPM) alternating solution for dynamic optimization of the CHP unit variable load process. Firstly, by constructing the CHP unit mechanism model, multi-variable coordination control constraints, and output variable process constraints, the dynamic optimization proposition of the CHP unit variable load control process is formed. Then, the large-scale nonlinear programming (NLP) problem formed by using the orthogonal configuration method to discrete the state and control variables is optimally solved using the IPM-SQP alternating solution method. Further, from the perspective of balancing the accuracy of the solution and computational efficiency, the flexible convergence depth control (CDC) strategy is introduced into the alternative solution method to improve the real-time performance of the algorithm. Finally, the variable load control process of 300MW extraction CHP unit is simulated to verify that the proposed method reduces the calculation time for 12 consecutive variable load scenarios by about 70%, effectively improving the real-time performance of scenario applications.