Numerical Methods Based on Gaussian Quadrature and Continuous Runge-Kutta Integration for Optimal Control Problems

机译：基于高斯正交和连续Runge-Kutta积分的最优控制问题数值方法

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This paper provides a numerical approach for solving optimal control problems governed by ordinary differential equations. Continuous extension of an explicit, fixed step-size Runge-Kutta scheme is used in order to approximate state variables; moreover, the objective function is discretized by means of Gaussian quadrature rules. The resulting scheme represents a nonlinear programming problem, which can be solved by optimization algorithms. With the aim to test the proposed method, it is applied to different problems.

机译：本文提供了一种数值方法来解决由常微分方程控制的最优控制问题。为了近似状态变量，使用了显式，固定步长的Runge-Kutta方案的连续扩展。此外，目标函数通过高斯正交规则离散化。所得方案表示一个非线性规划问题，可以通过优化算法来解决。为了测试所提出的方法，将其应用于不同的问题。

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来源
《International Conference on Computational Science and Its Applications(ICCSA 2004) pt.2; 20040514-20040517; Assisi; IT》|2004年|P.971-978|共8页
会议地点 Assisi(IT);Assisi(IT)
作者
Fasma Diele; Carmela Marangi; Stefania Ragni;
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作者单位

Istituto per le Applicazioni del Calcolo M. Picone, CNR, Via Amendola 122, 70126 Bari, Italy;

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会议组织
原文格式 PDF
正文语种 eng
中图分类理论、方法;
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1. Gaussian quadrature as a numerical integration method for estimating area under the curve. [J] . Amisaki T Biological & pharmaceutical bulletin . 2001,第1期

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2. GPOPS - Ⅱ: A MATLAB Software for Solving Multiple-Phase Optimal Control Problems Using hp-Adaptive Gaussian Quadrature Collocation Methods and Sparse Nonlinear Programming [J] . MICHAEL A. PATTERSON, ANIL V. RAO ACM transactions on mathematical software . 2015,第1期

机译：GPOPS-Ⅱ：使用hp自适应高斯正交配置方法和稀疏非线性规划解决多相最优控制问题的MATLAB软件
3. Costate approximation in optimal control using integral Gaussian quadrature orthogonal collocation methods [J] . Francolin Camila C., Benson David A., Hager William W., Optimal Control Applications and Methods . 2015,第4期

机译：使用积分高斯正交正交配置法的最优控制中的共态逼近。
4. Numerical Methods Based on Gaussian Quadrature and Continuous Runge-Kutta Integration for Optimal Control Problems [C] . Fasma Diele, Carmela Marangi, Stefania Ragni International Conference on Computational Science and its Applications . 2004

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5. Theory and implementation of numerical methods based on Runge-Kutta integration for solving optimal control problems [D] . Schwartz, Adam Lowell 1996

机译：基于Runge-Kutta积分求解最优控制问题的数值方法的理论与实现
6. A fast quadrature-based numerical method for the continuous spectrum biphasic poroviscoelastic model of articular cartilage [O] . Michael Stuebner, Mansoor A. Haider -1

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7. Direct Optimization Using Gaussian Quadrature and Continuous Runge-Kutta Methods: Application to an Innovation Diffusion Model [O] . Fasma Diele, Carmela Marangi, Stefania Ragni 2004

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8. An Improved Method of Error Control for Runge-Kutta Numerical Integration [R] . Walters, R. K., Engebos, B. F. 1968

机译：一种改进的Runge-Kutta数值积分误差控制方法

Numerical Methods Based on Gaussian Quadrature and Continuous Runge-Kutta Integration for Optimal Control Problems

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