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Numerical optimal control applied to an epidemiological model

IFAC-PapersOnLine 2018年第2期51卷 1-6页

作者： Schreppel, Christina Chudej, Kurt Wessling82234 Germany Chair of Scientific Computing University of Bayreuth Bayreuth95440 Germany

A previously published SIR-ASI optimal control model of dengue fever is described and the optimal control problem is solved in this paper by an alternative solution approach, namely by a direct transcription method. In this method, the optimal control problem is substituted by a nonlinear programming problem. The nonlinear programming problem is solved by an interior point method. In the following an a posteriori check of the necessary optimality conditions of optimal control, which has not yet been done, is performed with the discretized states, adjoints, and controls. The check shows some accordance with the numerical results, but unfortunately in this setting a seldom discrepancy is observed, which seems to be connected with the modeling of the mechanical control. © 2018

关键词： nonlinear programming Insecticides Optimal control systems Transcription Dengue fevers Direct transcription method Epidemiological modeling Mechanical control Necessary optimality condition nonlinear programming problem Numerical results Optimal controls

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On the Radau pseudospectral method: theoretical and implementation advances

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CEAS SPACE JOURNAL 2017年第3期9卷 313-331页

作者： Sagliano, Marco Theil, Stephan Bergsma, Michiel D'Onofrio, Vincenzo Whittle, Lisa Viavattene, Giulia Deutsch Zentrum Luft & Raumfahrt Robert Hooke Str 7 Bremen Germany

In the last decades the theoretical development of more and more refined direct methods, together with a new generation of CPUs, led to a significant improvement of numerical approaches for solving optimal-control problems. One of the most promising class of methods is based on pseudospectral optimal control. These methods do not only provide an efficient algorithm to solve optimalcontrol problems, but also define a theoretical framework for linking the discrete numerical solution to the analytical one in virtue of the covector mapping theorem. However, several aspects in their implementation can be refined. In this framework SPARTAN, the first European tool based on flipped-Radau pseudospectral method, has been developed. This paper illustrates the aspects implemented for SPARTAN, which can potentially be valid for any other transcription. The novelties included in this work consist specifically of a new hybridization of the Jacobian matrix computation made of four distinct parts. These contributions include a new analytical formulation for expressing Lagrange cost function for open final-time problems, and the use of dual-number theory for ensuring exact differentiation. Moreover, a self-scaling strategy for primal and dual variables, which combines the projected-Jacobian rows normalization and the covector mapping, is described. Three concrete examples show the validity of the novelties introduced, and the quality of the results obtained with the proposed methods.

关键词： Pseudospectral methods Optimal control nonlinear programming problem SPARTAN

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PARAMETER OPTIMIZATION problemS FOR MULTILAYER OPTICAL COATINGS

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CYBERNETICS AND SYSTEMS ANALYSIS 2005年第4期41卷 564-571页

作者： Stetsyuk, P. I. Mitsa, A. A. Natl Acad Sci Ukraine VM Glushkov Inst Cybernet Kiev Ukraine Uzhgorod Natl Univ Uzhgorod Ukraine

Two problems of finding optimal parameters for multilayer optical coatings are considered. They are formulated as multiextremal nonlinear programming problems with a complex objective function. Finding local extrema by first-order methods is discussed. The ways of calculating the gradient of the objective function depending on the number of layers in the optical coating are analyzed.

关键词： multilayer optical coating characteristic matrix radiation transmission factor nonlinear programming problem gradient method

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Legendre spectral collocation method for approximating the solution of shortest path problems

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SYSTEMS SCIENCE & CONTROL ENGINEERING 2015年第1期3卷 62-68页

作者： Tohidi, Emran Samadi, Omid Reza Navid Islamic Azad Univ Dept Math Zahedan Branch Zahedan Iran

In the current article, we propose an accurate spectral approximation for solving the shortest path problems with boundary and interior barriers. For this goal, the shortest path problems are modelled as variational problems (VPs). Then, the Legendre polynomials are used as a basis for approximating the solution of these problems, and by using the Chebyshev-Gauss-Lobatto collocation points together with the Legendre-Gauss quadrature rule, the VPs will be changed into nonlinear programming problems (NLPs). The resulting NLPs are solved by the NLPSolve command in MAPLE software. Three numerical examples are provided for showing the robustness of the proposed method.

关键词： shortest path problems modelling Legendre polynomials Gauss-Lobatto collocation points Gauss quadrature rules nonlinear programming problem

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Model-Based Optimal Experiment Design for nonlinear Parameter Estimation Using Exact Confidence Regions

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IFAC-PapersOnLine 2017年第1期50卷 13760-13765页

作者： Gottu Mukkula, Anwesh Reddy Paulen, Radoslav Process Dynamics and Operations Group Technische Universität Dortmund Germany

Optimal experiment design is usually performed as a search over a finitely-parameterized shape that (over-) approximates the confidence region of parameters of a model. In general, there exists no such shape to exactly enclose the confidence region of a nonlinear parameter estimation problem. Due to this fact, the design-of-experiment techniques are not well established for this problem and approximate designs are conducted. In this contribution, assuming Gaussian (normally distributed) noise, we propose and study (a) two schemes to over-approximate the confidence region of parameters using an ellipsoid and an orthotope and (b) a framework for optimal experiment design. We formulate the over-approximation of the confidence region as an optimization problem. The optimal experiment design is then proposed as a bi-level optimization problem. In line with the existing optimal experiment design methodology for a linear parameter estimation problem, we also propose several design criteria that optimize some measure of the over-approximated confidence region for the nonlinear case. The proposed bi-level optimization problem is solved (i) as a nonlinear programming problem using the necessary conditions for optimality or (ii) as a nested problem with globally optimized inner-level problem. We illustrate the proposed schemes on a benchmark test case. © 2017

关键词： Parameter estimation Benchmarking Design Design of experiments Mathematical programming nonlinear analysis nonlinear programming Normal distribution Statistics Bi level optimization problems Design of experiment techniques (DoE) Least squares estimation nonlinear Parameter Estimation nonlinear programming problem Optimal controls Optimal experiment design Optimization problems

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Optimisation of the duplex D2D network: a deep learning approach

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IET NETWORKS 2020年第3期9卷 139-144页

作者： Liu, Xian Univ Arkansas Little Rock Dept Syst Engn Little Rock AR 72204 USA

For wireless networks, it is highly desirable to design a quality-of-service-promotion strategy to allocate the transmission power. In this study, the authors apply the deep learning methodology to solve such a problem in a duplex device-to-device network. The model is formulated as a constrained non-linear programming problem. The training data are generated by a standard optimisation tool. Then, an artificial neural network is designed to learn the system from the training data. Simulation results show the effectiveness of deep leaning.

关键词： learning (artificial intelligence) neural nets optimisation nonlinear programming linear programming cellular radio duplex D2D network deep learning approach wireless networks quality-of-service-promotion strategy transmission power deep learning methodology device-to-device network nonlinear programming problem training data standard optimisation tool artificial neural network deep leaning

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Design of Bridge Transport System with Equal Incremental Telescopic Motion

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TRANSACTIONS OF THE KOREAN SOCIETY OF MECHANICAL ENGINEERS A 2010年第2期34卷 227-235页

作者： Yoon, Kwang Ho Lee, Hyo Jik Lee, Jong Kwang Park, Byung Suk Kim, Kiho Korea Inst Machinery & Mat Daejeon South Korea Korea Atom Energy Res Inst Daejeon South Korea

This paper introduces the design of a bridge transport system with a telescopic tube for positioning equipment to perform remote handling tasks in a radioactive facility. It consists of an extensible and retractable telescopic tube assembly for z-direction motion, a cabling system for management of power and signal cables, and a trolley system for transverse motion and accommodating servo drives. The working environment for the bridge transport system with the telescopic tube requires strict geometrical constraints, including a short height, short telescopic tube length when retracted, and a long stroke. These constraints were met by solving a nonlinear programming problem involving the optimal dimensions. This paper introduces a cabling system for effective management of cables with changeable lengths to accommodate telescopic motions and a selection guide for servo drives that are sufficient to drive the system.

关键词： Bridge Transport System Telescopic Tube PRIDE nonlinear programming problem BDSM

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Efficient Partial Condensing Algorithms for nonlinear Model Predictive Control with Partial Sensitivity Update

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IFAC-PapersOnLine 2018年第20期51卷 406-411页

作者： Chen, Yutao Frison, Gianluca van Duijkeren, Niels Bruschetta, Mattia Beghi, Alessandro Diehl, Moritz Department of Information Engineering University of Padova Italy University of Freiburg Germany Department of Mechanical Engineering LeuvenKU United Kingdom

In nonlinear Model Predictive Control(NMPC), an optimal control problem (OCP) is solved repeatedly at every sampling instant. To satisfy the real-time restriction, modern methods tend to convert the OCP into structured nonlinear programming problems (NLP), which are approximately solved on-line. Real-Time Iteration is one of the promising NMPC algorithms that solves the NLP using a single Sequential Quadratic programming (SQP) iteration. To solve Quadratic programming (QP) problems efficiently, recently proposed partial condensing techniques reformulate large and sparse QP problems into smaller but still sparse ones. In this paper, we propose two tailored partial condensing algorithms by combining partial sensitivity updating schemes, that are recently proposed to update part of the sensitivities of dynamics. We show that such a combination can significantly reduce the computational time for partial condensing and for the full RTI step. © 2018

关键词： Model predictive control Iterative methods nonlinear systems Optimal control systems Predictive control systems Quadratic programming Real time control Structured programming Computational time nonlinear model predictive control nonlinear programming problem Numerical optimizations Optimal control problem Real time implementations Sampling instants Sequential quadratic programming

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The Multiplier Method of Hestenes and Powell Applied to Convex programming

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1973年第6期12卷 555-562页

作者： Rockafellar, R. T. Univ Washington Dept Math Seattle WA 98195 USA

For nonlinear programming problems with equality constraints, Hestenes and Powell have independently proposed a dual method of solution in which squares of the constraint functions are added as penalties to the Lagrangian, and a certain simple rule is used for updating the Lagrange multipliers after each cycle. Powell has essentially shown that the rate of convergence is linear if one starts with a sufficiently high penalty factor and sufficiently near to a local solution satisfying the usual second-order sufficient conditions for optimality. This paper furnishes the corresponding method for inequality-constrained problems. Global convergence to an optimal solution is established in the convex case for an arbitrary penalty factor and without the requirement that an exact minimum be calculated at each cycle. Furthermore, the Lagrange multipliers are shown to converge, even though the optimal multipliers may not be unique.

关键词： Optimization Theory Penalty Factor nonlinear programming problem Mathematical programming problem Convex Case

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Numerical solution of an optimal control problem in cancer treatment: Combined radio and anti-angiogenic therapy

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IFAC-PapersOnLine 2015年第1期28卷 665-666页

作者： Chudej, Kurt Wagner, Lisa Pesch, Hans Josef Lehrstuhl für Ingenieurmathematik Universität Bayreuth Bayreuth95440 Germany Numerische Mathematik und Wissenschaftliches Rechnen Universität Darmstadt Germany

Several therapies and also combined therapies for cancer treatment exist mathematical models of which have partly been also optimized by means of optimal control methods. Here we focus on an optimal control problem describing a combined radiotherapy and an anti-angiogenic treatment. The underlying model is taken from literature where, however, despite rigorous analytical investigations a complete numerical solution is missing. In order to fill this gap, a direct solution approach has been developed for which both state and control functions of the optimal control problem are discretized. The resulting nonlinear programming problem is solved via the modelling language AMPL and the interior point solution method IPOPT. In an a posteriori step we try to check the main necessary conditions of optimal control theory in order to verify the candidate optimality of the continuous problem via the approximate discrete optimal solution. The most interested feature of this model from the viewpoint of optimal control theory is the fact that singular control subarcs exist for a two-dimensional control vector. However, the arising numerical difficulties caused by chattering controls prevented us so far from a complete candidate optimal solution. © 2015, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

关键词： Control theory Diseases Modeling languages nonlinear programming Optimal control systems Radiotherapy Analytical investigations Anti angiogenic treatment Direct solution approaches Discrete optimal solution nonlinear programming problem Optimal controls Singular control Tumor treatment

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