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Performance analysis of linear and nonlinear techniques for automatic scaling of discretized control problems

OPERATIONS RESEARCH LETTERS 2014年第3期42卷 213-216页

作者： Sagliano, Marco Deutsch Zentrum Luft & Raumfahrt Guidance Nav & Control Dept D-28359 Bremen Germany

This paper introduces three (one linear and two nonlinear) automatic scaling techniques for NLPs with states and constraints spread over several orders of magnitude, without requiring complex off-the-shelf external tools. All of these methods have been compared to standard techniques and applied to three problems using SNOPT and IPOPT. The results confirm that the proposed techniques significantly improve the NLP conditioning, yielding more reliable and in some cases, faster NLP solutions. (C) 2014 Elsevier B.V. All rights reserved.

关键词： Automatic scaling Optimal control problem nonlinear programming problem

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An improved adaptive hp mesh refinement method in solving optimal control problems

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OPTIMAL CONTROL APPLICATIONS & METHODS 2023年第4期44卷 1828-1853页

作者： Luo, Changxin Li, Jiong Zhou, Chijun Lei, Humin Air Force Engn Univ Grad Sch Xian Peoples R China Air Force Engn Univ Air & Missile Def Coll Xian Peoples R China

In order to improve the efficiency of the adaptive hp pseudospectral method in solving the optimal control problems, an improved adaptive hp pseudospectral method is proposed in this paper. This method mainly improves the mesh refinement process of the traditional hp pseudospectral method to reduce the number of mesh iterations, so as to achieve the purpose of shortening the solving time. The focus of this method is twofold. Firstly, by judging the position of the sudden change points of control curve, the mesh is refined in advance around them. Secondly, the non-uniform segmentation iteration is carried out by using the curvature of the system state curve as the criterion. These two points together improve the solving efficiency of the proposed method. Through the convergence analysis and simulation verification, it is shown that the proposed method can effectively solve the optimal control problem, and it is also proved that the proposed method has higher solving efficiency than the traditional adaptive hp pseudospectral method.

关键词： adaptive hp method mesh refinement nonlinear programming problem optimal control pseudospectral method

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An effective simultaneous approach with variable time nodes for dynamic optimization problems

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ENGINEERING OPTIMIZATION 2017年第10期49卷 1761-1776页

作者： Xiao, Long Ying, Jiong Liu, Xinggao Ma, Liang Zhejiang Univ Coll Control Sci & Engn State Key Lab Ind Control Technol Hangzhou Zhejiang Peoples R China

An effective simultaneous approach with variable time nodes is proposed to solve the dynamic optimization problems with multiple control components, where the variable time nodes for each control component are considered as parameters directly and the interval between the neighbouring variable nodes is further refined uniformly to ensure accuracy. Consequently, the method does not treat all the nodes as parameters to ensure efficiency. The gradient formulae and the sensitivities of the states with respect to the controls and the variable time nodes are further derived to solve the nonlinear programming problem transformed from the original dynamic optimization problem. The complete framework and detailed steps of the proposed method are also given. Two classic constrained dynamic optimization problems have been tested as an illustration, and detailed comparisons of the reported literature methods are carried out. The research results show the characteristics and the effectiveness of the proposed approach.

关键词： Constrained dynamic optimization control and state parameterization nonlinear programming problem simultaneous approach

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An optimal modeling of multidimensional wave digital filtering network for free vibration analysis of symmetrically laminated composite FSDT plates

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MECHANICAL SYSTEMS AND SIGNAL PROCESSING 2015年第1期52-53卷 465-494页

作者： Tseng, Chien-Hsun Kun Shan Univ Dept Informat Engn Tainan 71013 Taiwan

The technique of multidimensional wave digital filtering (MDWDF) that builds on traveling wave formulation of lumped electrical elements, is successfully implemented on the study of dynamic responses of symmetrically laminated composite plate based on the first order shear deformation theory. The philosophy applied for the first time in this laminate mechanics relies on integration of certain principles involving modeling and simulation, circuit theory, and MD digital signal processing to provide a great variety of outstanding features. Especially benefited by the conservation of passivity gives rise to a nonlinear programming problem (NLP) for the issue of numerical stability of a MD discrete system. Adopting the augmented Lagrangian genetic algorithm, an effective optimization technique for rapidly achieving solution spaces of NLP models, numerical stability of the MDWDF network is well received at all time by the satisfaction of the Courant-Friedrichs-Levy stability criterion with the least restriction. In particular, optimum of the NLP has led to the optimality of the network in terms of effectively and accurately predicting the desired fundamental frequency, and thus to give an insight into the robustness of the network by looking at the distribution of system energies. To further explore the application of the optimum network, more numerical examples are engaged in efforts to achieve a qualitative understanding of the behavior of the laminar system. These are carried out by investigating various effects based on different stacking sequences, stiffness and span-to-thickness ratios, mode shapes and boundary conditions. Results are scrupulously validated by cross referencing with early published works, which show that the present method is in excellent agreement with other numerical and analytical methods. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： Laminated composite plate MDWDF network Courant-Friedrichs-Levy stability Free vibration analysis Augmented Lagrangian genetic algorithm nonlinear programming problem

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Car-like robot motion planning based on grey relational pattern analysis

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JOURNAL OF THE CHINESE INSTITUTE OF ENGINEERS 2003年第1期26卷 1-12页

作者： Yeh, MF Lu, HC Tatung Univ Dept Elect Engn Taipei 104 Taiwan Lunghwa Univ Sci & Technol Dept Elect Engn Taoyuan 333 Taiwan

This paper proposes a simple exploring approach for a car-like robot to determine a near-optimal path between prescribed initial and goal positions, based on the nonlinear programming problem and grey relational pattern analysis. No matter whether the considered workspace is known or not in advance, the proposed approach can make the car-like robot explore and move in a workspace containing multiple convex obstacles. Unlike other exploring approaches, the proposed find-path procedure must consist of at least one trial. Each trial contains two main stages, one is termed the forward search stage and the other is named the backward search stage. After all possible trials have occurred, an additional stage, called the decision-making stage, is then introduced to determine the near-optimal and collision-free path, which is guaranteed to reach the goal. In addition, the presented method is applicable for on-line planning applications and, furthermore, can solve the so-called local minimum problems. Simulation results for a workspace with multiple convex obstacles demonstrate the searching performance of our approach and its potential as an on-line path planner in a known or an unknown workspace.

关键词： car-like robot motion planning grey relational pattern analysis nonlinear programming problem convex obstacle

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A framework of shape optimisation based on the isogeometric boundary element method toward designing thin-silicon photovoltaic devices

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ENGINEERING WITH COMPUTERS 2019年第2期35卷 423-449页

作者： Takahashi, Toru Yamamoto, Tatsuro Shimba, Yuta Isakari, Hiroshi Matsumoto, Toshiro Nagoya Univ Grad Sch Engn Dept Mech Syst Engn Furo Cho Nagoya Aichi 4648603 Japan Nagoya Univ Grad Sch Engn Dept Micronano Syst Engn Furo Cho Nagoya Aichi 4648603 Japan

We propose a gradient-based optimisation framework to design the shape of the interfaces in periodic layered structures, which can model photovoltaic devices, optical gratings, etc., according to a desired electromagnetic property. To this end, we first develop an isogeometric boundary element method (IGBEM) to analyse singly periodic boundary value problems for 2D Helmholtz equation in layered media. By nature, the IGBEM is not only numerically accurate but also suitable for the shape optimisation in comparison with the conventional boundary- and domain-type solvers. Next, we derive the shape derivative (or shape sensitivity) of the objective function in terms of the magnetic field strength or energy absorption rate on the basis of the adjoint variable method. The shape derivative can be computed by solving the primal and adjoint problems with the IGBEM. Subsequently, we map our shape optimisation problems to nonlinear programming problems in order to exploit a general-purpose software for the latter problems. After verifying our optimisation framework rigorously by comparing with the exact solutions, we demonstrate a shape optimisation of the silicon-metal interface in a model of thin-silicon photovoltaic devices: it is crucial to determine the interface so that the energy of the incident light can be confined in the silicon layer as much as possible when the thickness of the layer is unconventionally small;one micrometre in our model. The optimal shape achieved 8.6 times higher absorption rate than the reference (flat) shape. This simulation shows that the proposed framework is capable of making a fundamental contribution to analysing and designing photovoltaic devices as well as photonic and plasmonic devices that consist of singly periodic layers.

关键词： Boundary element method Isogeometric analysis Periodic structure Shape optimisation Adjoint variable method nonlinear programming problem Quasi-Newton method Photovoltaic device Surface plasmon Plasmonics

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Network expansion planning with microgrid aggregators under uncertainty

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IET GENERATION TRANSMISSION & DISTRIBUTION 2018年第9期12卷 2105-2114页

作者： Sardou, Iman Goroohi Azad-Farsani, Ehsan Univ Jiroft Dept Elect Engn Jiroft Iran Golpayegan Univ Technol Dept Elect Engn Golpayegan Iran

In this paper, a bi-objective robust model is proposed for network expansion planning (NEP) considering the integration of the microgrid aggregators. The objectives include minimization of both the expansion cost and transmission lines loading index. Forced outages of system components are taken into account as the system uncertainties. A hybrid method as the combination of gravitational search algorithm (GSA) and primal-dual interior point (PDIP) method is employed to solve the nonlinear programming (NLP) problem of the NEP. In the proposed hybrid method, the operation sub-problems are solved by the PDIP method under the worst-case single component contingencies, while the expansion plan is defined as scenario independent variables obtained by the GSA algorithm. To detect the worst-case single component contingencies with the severest effects on the system security, a subsidiary optimization problem is solved for each load level of the system. A realistic network of Qom as a part of Tehran Regional Electric Company, Iran, as well as IEEE 118-bus test system are analysed to evaluate the efficiency of the proposed method. A key conclusion is that the stochastic model may not provide sufficient security level, and a robust model is required to ensure the system security against the severe contingencies.

关键词： distributed power generation power distribution planning substations search problems nonlinear programming power system security network expansion planning microgrid aggregators NEP problem power system planner substations effective biobjective robust model expansion cost transmission lines loading index system components system uncertainties hybrid method gravitational search algorithm GSA primal-dual interior point method nonlinear programming problem NLP operation subproblems PDIP method worst-case single component contingencies scenario independent variables first stage decision variables subsidiary optimisation problem Qom Tehran Regional Electric Company IEEE 118-bus test system Iran stochastic model security level economical solution

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A robust pseudospectral method for numerical solution of nonlinear optimal control problems

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INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS 2021年第6期98卷 1146-1165页

作者： Mehrpouya, Mohammad Ali Peng, Haijun Tafresh Univ Dept Math Tafresh *** Iran Dalian Univ Technol State Key Lab Struct Anal Ind Equipment Dept Engn Mech Dalian Peoples R China

In the present paper, a robust pseudospectral method for efficient numerical solution of nonlinear optimal control problems is presented. In the proposed method, at first, based on the Pontryagin's minimum principle, the first-order necessary conditions of optimality which are led to the Hamiltonian boundary value problem are derived. Then, utilizing a pseudospectral method for discretization, the nonlinear optimal control problem is converted to a system of nonlinear algebraic equations. However, the need to have a good initial guess may lead to a challenging problem for solving the obtained system of nonlinear equations. So, an optimization approach is introduced to simplify the need of a good initial guess. Numerical findings of some benchmark examples are presented at the end and computational features of the proposed method are reported.

关键词： Optimal control Hamiltonian boundary value problem Pontryagin's minimum principle pseudospectral methods nonlinear programming problem

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Parameter optimization using the L_∞ exact penalty function and strictly convex quadratic programming problems

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APPLIED MATHEMATICS AND COMPUTATION 2008年第2期198卷 833-848页

作者： Fabien, Brian C. Univ Washington Dept Mech Engn Seattle WA 98195 USA

This paper presents an algorithm for the numerical solution of constrained parameter optimization problems. The solution strategy is based on a sequential quadratic programming (SQP) technique that uses the L-infinity exact penalty function. Unlike similar SQP algorithms the method proposed here solves only strictly convex quadratic programs to obtain the search directions. The global convergence properties of the algorithm are enhanced by the use of a nonmonotone line search and second-order corrections to avoid the Maratos effect. The paper also presents an ANSI C implementation of the algorithm. The effectiveness of the proposed method is demonstrated by solving numerous parameter optimization and optimal control problems that have appeared in the literature. (C) 2007 Elsevier Inc. All rights reserved.

关键词： nonlinear programming problem sequential quadratic programming convex quadratic programming computer code

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Constrained NLP via gradient flow penalty continuation: Towards self-tuning robust penalty schemes

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COMPUTERS & CHEMICAL ENGINEERING 2017年 101卷 243-258页

作者： Scott, Felipe Conejeros, Raul Vassiliadis, Vassilios S. Univ Andes Fac Ingn & Ciencias Aplicadas Green Technol Res Grp Mons Alvaro del Portillo 12455 Santiago 7620001 Chile Pontificia Univ Catolica Valparaiso Sch Biochem Engn Av Brasil 2085 Valparaiso Chile Univ Cambridge Dept Chem Engn & Biotechnol Cambridge CB2 3RA England

This work presents a new numerical solution approach to nonlinear constrained optimization problems based on a gradient flow reformulation. The proposed solution schemes use self-tuning penalty parameters where the updating of the penalty parameter is directly embedded in the system of ODEs used in the reformulation, and its growth rate is linked to the violation of the constraints and variable bounds. The convergence properties of these schemes are analyzed, and it is shown that they converge to a local minimum asymptotically. Numerical experiments using a set of test problems, ranging from a few to several hundred variables, show that the proposed schemes are robust and converge to feasible points and local minima. Moreover, results suggest that the GF formulations were able to find the optimal solution to problems where conventional NLP solvers fail, and in less integration steps and time compared to a previously reported GF formulation. (C) 2017 Elsevier Ltd. All rights reserved.

关键词： Gradient flow nonlinear programming problem Convergence analysis

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