Nonlinear Programming Algorithm Research Articles

Fault-Tolerant Control of Autonomous Underwater Vehicle Actuators Based on Takagi and Sugeno Fuzzy and Pseudo-Inverse Quadratic Programming under Constraints.

Autonomous Underwater Vehicles (AUVs) play a significant role in ocean-related research fields as tools for human exploration and the development of marine resources. However, the uncertainty of the underwater environment and the complexity of underwater motion pose significant challenges to the fault-tolerant control of AUV actuators. This paper presents a fault-tolerant control strategy for AUV actuators based onTakagi and Sugeno (T-S) fuzzy logic and pseudo-inverse quadratic programming under control constraints, aimed at addressing potential actuator faults. Firstly, considering the steady-state performance and dynamic performance of the control system, a T-S fuzzy controller is designed. Next, based on the redundant configuration of the actuators, the propulsion system is normalized, and the fault-tolerant control of AUV actuators is achieved using the pseudo-inverse method under thrust allocation. When control is constrained, a quadratic programming approach is used to compensate for the input control quantity. Finally, the effectiveness of the fuzzy control and fault-tolerant control allocation methods studied in this paper is validated through mathematical simulation. The experimental results indicate that in various fault scenarios, the pseudo-inverse combined with a nonlinear quadratic programming algorithm can compensate for the missing control inputs due to control constraints, ensuring the normal thrust of AUV actuators and achieving the expected fault-tolerant effect.

A Reentry Trajectory Planning Algorithm via Pseudo-Spectral Convexification and Method of Multipliers

The reentry trajectory planning problem of hypersonic vehicles is generally a continuous and nonconvex optimization problem, and it constitutes a critical challenge within the field of aerospace engineering. In this paper, an improved sequential convexification algorithm is proposed to solve it and achieve online trajectory planning. In the proposed algorithm, the Chebyshev pseudo-spectral method with high-accuracy approximation performance is first employed to discretize the continuous dynamic equations. Subsequently, based on the multipliers and linearization methods, the original nonconvex trajectory planning problem is transformed into a series of relaxed convex subproblems in the form of an augmented Lagrange function. Then, the interior point method is utilized to iteratively solve the relaxed convex subproblem until the expected convergence precision is achieved. The convex-optimization-based and multipliers methods guarantee the promotion of fast convergence precision, making it suitable for online trajectory planning applications. Finally, numerical simulations are conducted to verify the performance of the proposed algorithm. The simulation results show that the algorithm possesses better convergence performance, and the solution time can reach the level of seconds, which is more than 97% less than nonlinear programming algorithms, such as the sequential quadratic programming algorithm.

The use of complex structure splines in roadway design

Objectives. The aim of the work is to develop the theory of spline-approximation of a sequence of points on a plane for using compound splines with a complex structure. In contrast to a simple spline (e.g., polynomial), a compound spline contains repeating bundles of several elements. Such problems typically arise in the design of traces for railroads and highways. The plan (projection on the horizontal plane) of such a trace is a curve consisting of a repeating bundle of elements “line + clothoid + circle + clothoid ...,” which ensures continuity not only of curve and tangent but also of curvature. The number of spline elements, which is unknown, should be determined in the process of solving the design problem. An algorithm for solving the problem with respect to the spline, which consists of arcs conjugated by straight lines, was implemented and published in an earlier work. The approximating spline in the general case is a multivalued function, whose ordinates may be limited. Another significant factor that complicates the problem is the presence of clothoids that are not expressed analytically (in a formula). The algorithm for determining the number of elements of a spline with clothoids and constructing an initial approximation was also published earlier. The present work considers the next stage of solving the spline approximation problem: optimization using a nonlinear programming spline obtained at the first stage by means of the dynamic programming method.Methods. A new mathematical model in the form of a modified Lagrange function is used together with a special nonlinear programming algorithm to optimize spline parameters. In this case, it is possible to calculate the derivatives of the objective function by the spline parameters in the absence of its analytical expression through these parameters.Results. A mathematical model and algorithm for optimization of compound spline parameters comprising arcs of circles conjugated by clothoids and lines have been developed.Conclusions. The previously proposed two-step scheme for designing paths of linear structures is also suitable for the utilization of compound splines with clothoids.

RECONSTRUCTION OF THE CORNEAL SURFACE OF THE HUMAN EYE USING A COMPUTATIONAL EVOLUTIONARY ALGORITHM. PRACTICAL APPLICATION IN NON-PATHOLOGICAL CASES

Increasingly, the use of geometric modelling techniques in Applied Ophthalmology is significant in the characterization of important pathologies of the cornea, such as Keratoconus. This article presents a novel method for the geometric reconstruction of the corneal surface from optical topography using a genetic algorithm. Traditionally, mathematical programming methods such as the least squares method have been used to obtain the coefficients of the corneal surface function, such as Navarro model or Zernike polynomials. This new method uses non-dominated multivariable genetic algorithm optimization to obtain the surface function coefficients from the point cloud obtained with corneal topographer device. Once the reconstruction is performed, the surface is represented using CAD software, and morphogeometric parameters are obtained. The experimental sample consisted in 33 healthy patients eyes, aged from 11 to 63, and without previous ocular surgeries or pathologies. Topographic data were obtained using a Scheimpflug Sirius tomographer (CSO, Italy). The computational optimization was executed under Matlab software environment (Mathworks, USA). The new method provides a lower mean squared error (MSE) than those obtained by the least squares or the nonlinear programming algorithms. Thus, the morphogeometric parameters obtained from the patient's corneas fit better, allowing for a better analysis of real clinical conditions.

Optimal Design of a Novel Large-Span Cable-Supported Steel–Concrete Composite Floor System

This paper optimizes the design of a novel large-span cable-supported steel–concrete composite floor system in a simply supported single-span, single-strut configuration, aiming for cost-effective solutions and minimal steel consumption. The optimization considers various cross-sectional dimensions, adhering to building standards and engineering practices, and is based on a non-linear programming (NLP) algorithm. Parameters of live loads ranging from 2 to 10 kN/m2 and spans from 20 to 100 m are considered. The optimization results show that cable-supported composite floors with a single strut exhibit robust economic feasibility for spans of less than 80 m and live loads under 8 kN/m2. Compared to conventional composite floors with welded I-beams, the cable-supported system offers more cost-effective cross-sections and reduces steel consumption. The savings in economically equivalent steel consumption range from 20% to 60%. Discussion on the area ratio of cables to steel beam in the optimal cross-section reveals that the secondary load-bearing system (i.e., bending of the main beam with an effective span length of L/2) may require more steel in cases of ultra-large spans. Therefore, the economical efficiency of cable-supported composite beams with multiple struts and smaller effective span lengths warrants further exploration in future studies.

Efficiency Optimization Strategies for Wind-Solar Driven Hydrogen Energy Storage Systems

This research focuses on optimizing wind-solar driven hydrogen energy storage systems. It addresses efficiency challenges through mathematical modeling and optimization. The study establishes mathematical representations, including probability distribution models for energy inputs, and defines output efficiency linked to electrolysis and fuel cell processes. Various optimization strategies, such as linear programming, nonlinear programming, and genetic algorithms, are explored. Case analysis and numerical simulations demonstrate the strategy's effectiveness. The study concludes by highlighting its practical implications and the promising future of wind-solar driven hydrogen energy storage systems.

PV/Hydrogen DC microgrid control using distributed economic model predictive control

The integration of hydrogen energy into a photovoltaic-dominated microgrid is now becoming a promising approach to improve the photoconversion efficiency and enhance the operating reliability. However, the energy management and power regulation of the Photovoltaic/Hydrogen DC microgrid face challenges due to the intermittency of photovoltaic (PV) power generation and the randomness of load. In this paper, a distributed economic model predictive control (DEMPC) scheme is developed for a PV/Hydrogen DC microgrid, which integrates the energy management, economic optimization, and power regulation into one optimal control framework. Based on the developed distributed converter-based mathematical model, three local controllers are designed to achieve the economic targets of PV subsystem, alkaline electrolyzer subsystem, and proton exchange membrane fuel cell subsystem respectively, which cooperate with each other through the communication network to realize the power supply–demand balance, DC bus voltage stability, and economic optimization. A mixed integer nonlinear programming algorithm utilizing the finite converter switching states is embedded into the DEMPC to solve the non-convex local optimization problems efficiently. The effectiveness and superiority of the proposed DEMPC scheme are verified by simulations under varying irradiance and load conditions, indicating that the DEMPC can achieve a comparable overall dynamic economic performance with a significantly reduced computation burden and power oscillation, compared to the centralized economic model predictive control (CEMPC).

Dynamic optimal control of flow front position in injection molding process: A control parameterization-based method

High dynamic and precise control of process variables within permissible limits is the key to high product quality in the injection molding industry. Among these variables, the injection flow rate of molten polymer is particularly significant. In this paper, an effective optimal open-loop and state feedback controller design method is designed to realize the optimal tracking control of the melt polymer flow front position flow of melt polymer fluid during injection molding. To this end, the dynamic model of the filling process is firstly established, taking into account the nonlinearity of hydraulic control system and the effect of molten polymer flow on the dynamics of the injection ram, and then the dynamic optimal tracking control problem of flow front position of molten polymer in injection molding machine is proposed. Then, an open-loop controller and a multi-level feedback control law are well designed, wherein the control signal and the control feedback kernels are parameterized by control parameterization. The controller design problems are transformed into sequential optimal parameter decision problems. The explicit expressions of the gradient information of the objective function and constraints on the parameters of the decision variables are solved by using the state sensitivity equation analysis method, and the gradient information is combined with the nonlinear programming algorithm to solve the optimization problems efficiently. Finally, the viability and effectiveness of the proposed design method are verified by numerical simulations.

Image reconstruction of ECT based on second-order hybrid sensitivity matrix and fuzzy nonlinear programming

In the derivation of the sensitivity matrix of electrical capacitance tomography, only the linear portion of the sensitivity coefficient is usually retained, while the neglected nonlinear part also contains important imaging information. In order to improve the accuracy of image reconstruction, a second-order hybrid sensitivity matrix is presented based on the capacitance normalization model and second-order item of sensitivity coefficients in this paper. Then, a fuzzy nonlinear programming algorithm based on the second-order hybrid sensitivity matrix (SHS-FNP) is proposed. Simulation and experiments are carried out. Reconstructed images using the presented method are compared with those of the Tikhonov algorithm, first-order hybrid Landweber algorithm, second-order hybrid Landweber algorithm, and fuzzy linear programming algorithm. The experimental results show that the SHS-FNP algorithm considerably enhances the quality of the reconstructed image.

Spread and control of medical rumors in a social network: A generalized diffusion model with a highly asymmetric network structure

Medical rumors have become a threat to modern society. To study the spread and control of rumors, nonlinear differential equations modeling with the well‐mixed assumption is commonly used. However, this approach ignores the underlying network structure which plays an important role in information spreading. We establish a generalized differential equations model to study the spread and control of medical rumors in a highly asymmetric social network. In our model, each node represents a group of people and a “weighted” and “directed” network describes the communications between these nodes. This network can be generated from real‐world data by community detection algorithms. We provide methods to numerically calculate the final size of a rumor in each node and its derivatives with respect to each parameter. With these methods, if the government has resources to influence the parameters subject to certain constraints or cost functions, one can obtain the optimal resources allocation easily through nonlinear programming algorithms. We show that the implications on the government's resources allocation from the well‐mixed special case in the literature or conventional wisdom may become inapplicable in the general situation. Therefore, the underlying network should not be ignored. Because the final size of a medical rumor is not always the best measure of its damage, we extend our results to a wide class of objectives and show that different objectives result in very different implications. While the lack of a rule of thumb may sound negative, our flexible framework provides a powerful workhorse for interested parties to work out the details in their specific situations. Finally, we provide a sufficient condition for no outbreak of rumors. This condition can serve as a heuristic that a government with abundant resources can use to prevent the outbreak of rumors.

Matheuristics approaches for the satellite constellation design problem

In this paper, we propose two novel matheuristic algorithms, i.e., heuristics based on mathematical formulations of the problem, in order to find a good feasible solution to the satellite constellation design problem for discontinuous coverage with a constrained revisit time. This problem consists in searching for a constellation able to periodically observe several targets at the Earth surface with the smallest number of satellites achievable. A Feasibility Pump approach is described: we specifically adapt the Feasibility Pump procedure to our design problem and we report results highlighting the benefits of this approach compared to the base Mixed Integer Nonlinear Programming (MINLP) algorithm it is derived from. Then, we propose a second matheuristic based on the discretized Mixed Integer Linear Programming (MILP) formulation of the problem, which outperforms the plain MILP formulation.

Piston Detection of Optical Sparse Aperture Systems Based on an Improved Phase Diversity Method

The piston error has a significant effect on the imaging resolution of the optical sparse aperture system. In this paper, an improved phase diversity method based on particle swarm optimization and the sequential quadratic programming algorithm is proposed, which can overcome the drawbacks of the traditional phase diversity method and particle swarm optimization, such as the instability that results from polychromatic light conditions and premature convergence. The method introduces factor β in the stage of calculating the objective function, and combines the advantages of a heuristic algorithm and a nonlinear programming algorithm in the optimization stage, thus enhancing the accuracy and stability of piston detection. Simulations based on a dual-aperture optical sparse aperture system verified that the root mean square error obtained by the method can be guaranteed to be within 0.001λ (wavelength), which satisfies the requirement of practical imaging. An experimental test was also conducted to demonstrate the performance of the method, and the test results showed that the quality of the image after piston detection and correction improved significantly compared to images with the co-phase error.

An economic model predictive control-based flexible power point tracking strategy for photovoltaic power generation

In a high solar-power-penetration power grid, photovoltaic (PV) power generation requires to run in a flexible power point tracking (FPPT) mode. However, traditional hierarchical control-based FPPT strategy ignores the dynamic economic performance of PV power generation. To address this issue, an advanced FPPT strategy based on economic model predictive control (EMPC) is proposed to achieve higher dynamic economic performance. This strategy integrates the PV voltage reference calculation, PV voltage control, and pulse width modulation into one optimal control framework, utilizing the economic indices of the PV power generation system (PVPGS) as the cost function to achieve its economic optimization and power tracking. Due to the strong nonlinearity in the PVPGS, the EMPC optimization problem is non-convex, leading to a local optimum. A mixed integer nonlinear programming algorithm is developed, which utilizes a finite number of converter switching states for obtaining the global optimum. Simulations demonstrate that the EMPC-based FPPT strategy enhances the dynamic economic performance compared to the hierarchical control-based FPPT strategy.

A nonlinear programming algorithm for finite element limit analysis using feasible arc searching technique

AbstractThis article presents a nonlinear programming algorithm for finite element limit analysis (FELA) based on feasible arc searching technique (FAST). The proposed algorithm has the potential to significantly reduce the iteration numbers required for convergence, making it a valuable tool for solving complex optimization problems from FELA. The algorithm also introduces several new features to the existing methods, including: (i) a novel method for determining a reasonable updating step length; (ii) the avoidance of solving an additional “phase one problem” for finding an initial feasible point; and (iii) the proposition of an empirical criterion for detecting infeasibility problems. The effectiveness of the proposed approach has been demonstrated through several classic examples derived from geotechnical engineering. The initial two examples show the superior convergence speed of the novel approach compared to existing methods. Additionally, the third example highlights the efficacy of the feasibility detection criterion for problems involving both prescribed and unknown external forces.

Economical Design Comparison of Large-Span Composite Floor Systems with I Beams and Corrugated Web Beams

A comparative study of composite floor systems with I-beams and corrugated web beams is performed based on non-linear programming (NLP) algorithm. The optimization is conducted to find the most economical design with minimum steel consumption considering variables associated with the cross-sectional dimensions and multiple constraints from standards, specifications and engineering practices. Various parameters of live loads ranging from 2 to 10 kN/m2 and spans ranging from 20 to 100 m are considered. The optimization results reveal that composite floors with corrugated web beams have reasonable and economical cross-sections with less steel consumption, owing to the high performance of the corrugated web in shear resistance and stability. Further comparative studies show that composite floors with corrugated web beams are economically competitive for spans larger than 30 m with a steel saving of 20–60%, and composite floors with welded I-beams can be applicable for spans less than 30 m considering the simpler configuration and construction. In addition, a spatially structured cable-supported steel–concrete composite floor system is proposed and recommended for super-large-span floor structures considering the cost-effectiveness of the analyzed floor systems reduces as the span further increases.

Analysis The Policies Balancing Conservation and Community Interests in Maasai Mara

This paper aims to examine what policies are appropriate to balance conservation and community interests in the Maasai Mara. Grey Relational Analysis (GRA) is used to examine the relationship between indicators divided into two categories: wildlife species interests and economic industrial interests. A qualitative analysis is performed to establish a one-to-one linear correlation between the indicators. Multiple objective nonlinear programming and genetic algorithm are then applied to determine an objective function that quantizes the interests. Maximize the number of wildlife species and local community income by simulation. After the analysis of that simulation, an Fuzzy Comprehensive Evaluation (FCE) model combined with the Analytic Hierarchy Process (AHP) are employed to analyze the impact of different policies for different regions by studying the relationships between factors affecting the wildlife reserve, such as migration patterns of wildlife and the impact of human activities. This approach helps to determine the best policy decision based on the scores and pros and cons of each policy.

Fast and Robust Computation of Optimal Rotor Designs Using Blade Element Momentum Theory

Recent years have seen a renewed interest in rotary-wing aircraft, due to the emergence of urban air mobility. In the conceptual design of such aircraft, fast estimation of rotor performance is important. A challenge is that rotor performance models require a detailed description of the blade geometry, which is not always available at this stage. We have developed a new, robust method for rapidly computing optimal rotor designs, which is derived from blade element momentum theory. In this paper, we derive the rotor design method and prove its convergence for all reasonable model inputs. We verify the design method by comparing the optimal rotor designs it computes to those found by a nonlinear programming algorithm. Thousands of numerical experiments yield relative errors of less than 13 and 5% in terms of the chord and twist profiles, respectively, and less than 0.3% in terms of efficiency, thrust, torque, and power coefficients. In addition, the design method computes optimal designs 170 times faster compared to the nonlinear programming algorithm. Based on these findings, we expect this new rotor design method to be useful in the conceptual design of rotary-wing aircraft.

Optimization of spline parameters in approximation of multivalued functions

Objectives. Methods for spline approximation of a sequence of points in a plane are increasingly used in various disciplines. A spline is defined as a single-valued function consisting of a known number of repeating elements, of which the most widely used are polynomials. When designing the routes of linear structures, it is necessary to consider a problem with an unknown number of elements. An algorithm implemented for solving this problem when designing a longitudinal profile was published earlier. Here, since the spline elements comprise circular arcs conjugated by line segments, the spline is a single-valued function. However, when designing a route plan, the spline is generally a multivalued function. Therefore, the previously developed algorithm is unsuitable for solving this problem, even if the same spline elements are used. The aim of this work is to generalize the obtained results to the case of approximation of multivalued functions while considering various features involved in designing the routes of linear structures. The first stage of this work consisted in determining the number of elements of the approximating spline using dynamic programming. In the present paper, the next stage of solving this problem is carried out.Methods. The spline parameters were optimized using a new mathematical model in the form of a modified Lagrange function and a special nonlinear programming algorithm. In this case, it is possible to analytically calculate the derivatives of the objective function with respect to the spline parameters in the absence of its analytical expression. Results. A mathematical model and algorithm were developed to optimize the parameters of a spline as a multivalued function consisting of circular arcs conjugated by line segments. The initial approximation is the spline obtained at the first stage.Conclusions. The previously proposed two-stage spline approximation scheme for an unknown number of spline elements is also suitable for approximating multivalued functions given by a sequence of points in a plane, in particular, for designing a plan of routes for linear structures.

An efficient control allocation algorithm for over-actuated AUVs trajectory tracking with fault-tolerant control

Fault-tolerant control of actuator faults in over-actuated autonomous underwater vehicles (AUVs) during trajectory tracking has involved problems. First, the fault-tolerant control method of controlling typical rudder faults, including lost, jammed, and/or deformed rudders, is introduced to reconstruct the control input, and a complete scheme of self-diagnosis and fault-tolerant control is proposed based on a sliding mode observer (SMO). Secondly, an efficient nonlinear saturation constraint sequential quadratic programming (SC-SQP) algorithm is proposed to solve the control allocation problem of multi-constraint quadratic programming, in particular with the motion in the initial or kinetic cycle transition stages. Considering the time-varying and unknown disturbances that occur in oceans, the control moments are compensated by the SMO to resist the perturbation of the hydrodynamic coefficient. Finally, the simulations show that the SC-SQP algorithm is efficient and can be used to solve the typical rudder faults with perturbation of the hydrodynamic coefficient during the fault-tolerant trajectory tracking control for over-actuated AUVs.

Neutrosophic Treatment of Duality Linear Models and the Binary Simplex Algorithm

One of the most important theories in linear programming is the dualistic theory and its basic idea is that for every linear model has dual linear model, so that solving the original linear model gives a solution to the dual model. Therefore, when we solving the linear programming model, we actually obtain solutions for two linear models. In this research, we present a study of the models. The neutrosophic dual and the binary simplex algorithm, which works to find the optimal solution for the original and dual models at the same time. The importance of this algorithm is evident in that it is relied upon in several operations research topics, such as integer programming algorithms, some nonlinear programming algorithms, and sensitivity analysis in linear programming...