In this study, we propose a landing guidance control method for the Moon using two control methods. The landing of a spacecraft on the Moon is divided into two phases: the powered descending phase and the vertical des...
详细信息
In this study, we propose a landing guidance control method for the Moon using two control methods. The landing of a spacecraft on the Moon is divided into two phases: the powered descending phase and the vertical descending phase. The powered descending phase aims to optimize the entire trajectory to satisfy the termination constraint, instead of allowing for a relatively long control period. This phase performs feedback control using trajectory updates via nonlinear optimization. The vertical-descending phase aims to achieve accurate control over a short control period. This phase applies nonlinear model predictive control for fast optimization on finite time intervals. First, the landing of a spacecraft on the Moon is modeled as a two- body problem of the Moon and spacecraft, and equations of motion are derived. Subsequently, we formulated an optimization problem for each phase and developed the proposed landing guidance method by combining the two control methods. Furthermore, numerical simulations based on the derived equations of motion were performed to confirm the effectiveness of the proposed method and to compare its performance with another optimization method, the successive convexification (SCvx) algorithm.
In order to achieve robot trajectory tracking in fixed-time, a novel fixed-time zeroing neural network model is designed. Initially, the inverse kinematic model of robot trajectory tracking is translated into a time-v...
详细信息
In order to achieve robot trajectory tracking in fixed-time, a novel fixed-time zeroing neural network model is designed. Initially, the inverse kinematic model of robot trajectory tracking is translated into a time-varying quadratic programs problem. Subsequently, a novel fixed-time zeroing neural network is proposed for solving the time-varying quadratic programs problem. Furthermore, the fixed-time stability of this model is rigorously established, and an upper bound of convergence time, irrespective of the initial point, is estimated. Finally, numerical simulation results underscore the efficacy of the proposed methodologies. A novel fixed-time zeroing neural network model is designed to robot trajectory tracking by solving the time-varying quadratic programs problem. While, its fixed-time stability is proven and the upper bound of convergence time independent of initial point is estimated. image
Mobile edge computing, a prospective wireless communication framework, can contribute to offload a large number of tasks to unmanned aerial vehicle (UAV) mobile edge servers. Besides, the demand for server computation...
详细信息
The nonlinear optimization problem with possible infeasible constraints was studied early by Burke (J Math Anal Appl, 139:19-351, 1989) and was revisited by Dai and Zhang (CSIAM Trans Appl Math, 2:551-584, 2021;Math P...
详细信息
The nonlinear optimization problem with possible infeasible constraints was studied early by Burke (J Math Anal Appl, 139:19-351, 1989) and was revisited by Dai and Zhang (CSIAM Trans Appl Math, 2:551-584, 2021;Math Program, 200:633-667, 2023) in a broad perspective. This paper considers nonlinear optimization with least & ell;1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ell _1$$\end{document}-norm measure of constraint violations and introduces the concepts of the D-stationary point, the DL-stationary point, and the DZ-stationary point with the help of exact penalty function. If the stationary point is feasible, they correspond to the Fritz-John stationary point, the KKT stationary point, and the singular stationary point, respectively. In order to show the usefulness of these specific stationary points, we propose an exact penalty sequential quadratic programming (SQP) method with inner and outer iterations and analyze its global and local convergence. The proposed method admits convergence to a D-stationary point and rapid infeasibility detection without driving the penalty parameter to zero, which demonstrates the commentary given in Byrd et al (SIAM J Optim, 20:2281-2299, 2010) and can be thought to be a supplement of the theory of nonlinear optimization on rapid detection of infeasibility. Some illustrative examples and preliminary numerical results demonstrate that the proposed method is robust and efficient in solving infeasible nonlinear problems and a degenerate problem without LICQ in the literature.
We discuss the (first- and second-order) optimality conditions for nonlinear programming under the relaxed constant rank constraint qualification (RCRCQ). Although the optimality conditions are well established in the...
详细信息
We discuss the (first- and second-order) optimality conditions for nonlinear programming under the relaxed constant rank constraint qualification (RCRCQ). Although the optimality conditions are well established in the literature, the proofs presented here are based solely on the well-known inverse function theorem. This is the only prerequisite from real analysis used to establish two auxiliary results needed to prove the optimality conditions. To be precise, we provide a simple and alternative proof that RCRCQ is a constraint qualification that implies strong second-order optimality conditions.
In the smooth constrained optimization setting, this work introduces the Domain Complementary Approximate Karush-Kuhn-Tucker (DCAKKT) condition, inspired by a sequential optimality condition recently devised for non-s...
详细信息
In the smooth constrained optimization setting, this work introduces the Domain Complementary Approximate Karush-Kuhn-Tucker (DCAKKT) condition, inspired by a sequential optimality condition recently devised for non-smooth constrained optimization problems. It is shown that the augmented Lagrangian method can generate limit points satisfying DCAKKT, and it is proved that such a condition is not related to previously established sequential optimality conditions. An essential characteristic of the DCAKKT is to capture the asymptotic potential increasing of the Lagrange multipliers using a single parameter. Besides that, DCAKKT points satisfy the Strong Approximate Gradient Projection (SAGP) condition. Due to the intrinsic features of DCAKKT, which combine strength and generality, this novel and genuine sequential optimality condition may shed some light upon the practical performance of algorithms that are yet to be devised.
Transmission network expansion planning is a critical and complex problem related to the operation and development of electrical power systems. It is typically formulated as a mixed-integer nonlinear programming (MINL...
详细信息
Transmission network expansion planning is a critical and complex problem related to the operation and development of electrical power systems. It is typically formulated as a mixed-integer nonlinear programming (MINLP) problem with combinatorial characteristics. Various mathematical models have been proposed to better approximate real-world system behavior, but even the most relaxed formulations remain computationally challenging. This paper introduces a search space reduction strategy to reduce the gap between the optimal solution of the MINLP model and its relaxed counterpart by strategically considering surrogate constraints. This approach enhances computational efficiency, significantly reducing processing time when using an optimization solver. By applying this method, we successfully determined the previously unknown optimal solution for the Brazilian north-northeast system.
DC microgrids are becoming more common in modern systems, so computation methodologies such as the power flow, the optimal power flow, and the state estimation require being adapted to this new reality. This paper dea...
详细信息
DC microgrids are becoming more common in modern systems, so computation methodologies such as the power flow, the optimal power flow, and the state estimation require being adapted to this new reality. This paper deals with the latter problem, which consists of reconstructing the state variables given voltage and power measurements. Although the model of DC grids is undoubtedly less complicated than its counterpart AC, it is still a nonlinear/non-convex optimization problem. Our approach is based on the idea of solving the problem in a matrix space. Although it may be counter-intuitive to transform from R-n to R-nxn, a matrix space exhibits better geometric properties that allow an elegant formulation and, in some cases, an efficient form to solve the optimization problem. We compare two methodologies: semidefinite programming and manifold optimization. The former relaxes the problem to a convex set, whereas the latter maintains the geometry of the original problem. A specialized gradient method is proposed to solve the problem in the matrix manifold. Extensive numerical experiments are conducted to showcase the key characteristics of both methodologies. Our study aims to shed light on the potential benefits of employing matrix space techniques in addressing operation problems in DC microgrids and power system computations in general.
Phasor measurement units (PMUs) are deployed at power grid nodes around the transmission grid, determining precise power system monitoring conditions. In real life, it is not realistic to place a PMU at every power gr...
详细信息
Phasor measurement units (PMUs) are deployed at power grid nodes around the transmission grid, determining precise power system monitoring conditions. In real life, it is not realistic to place a PMU at every power grid node;thus, the lowest PMU number is optimally selected for the full observation of the entire network. In this study, the PMU placement model is reconsidered, taking into account single- and multi-capacity placement models rather than the well-studied PMU placement model with an unrestricted number of channels. A restricted number of channels per monitoring device is used, instead of supposing that a PMU is able to observe all incident buses through the transmission connectivity lines. The optimization models are declared closely to the power dominating set and minimum edge cover problem in graph theory. These discrete optimization problems are directly related with the minimum set covering problem. Initially, the allocation model is declared as a constrained mixed-integer linear program implemented by mathematical and stochastic algorithms. Then, the 0/1 integer linear problem is reformulated into a non-convex constraint program to find optimality. The mathematical models are solved either in binary form or in the continuous domain using specialized optimization libraries, and are all implemented in YALMIP software in conjunction with MATLAB. Mixed-integer linear solvers, nonlinear programming solvers, and heuristic algorithms are utilized in the aforementioned software packages to locate the global solution for each instance solved in this application, which considers the transformation of the existing power grids to smart grids.
The loss of octane in the gasoline refining process can cause huge economic losses. However, the analysis and optimisation of octane loss is a high-dimensional nonlinear programming problem. In this work, we propose a...
详细信息
The loss of octane in the gasoline refining process can cause huge economic losses. However, the analysis and optimisation of octane loss is a high-dimensional nonlinear programming problem. In this work, we propose a compound variable selection scheme. Based on the results of independent variables by outlier and high correlation filtering, the representative operations are selected by random forest and grey correlation analysis, and the octane loss is then predicted by the BP neural network and XGBoost. To optimise the octane loss, an operation optimisation scheme based on fast gradient modification (FGM) is proposed. Experiments show that the composite variable selection scheme proposed in this paper can effectively screen independent and representative variables and has high prediction accuracy for octane loss. The proposed optimisation method also has sufficient feasibility and meets the needs of real scenes.
暂无评论