Notes on Numerical Methods for Solving Optimal Control Problems

カテゴリ: 論文誌(論文単位)

グループ名: 【D】産業応用部門（英文）

発行日: 2016/03/01

タイトル(英語): Notes on Numerical Methods for Solving Optimal Control Problems

著者名: Francesco Biral (Dep. Industrial Engineering, University of Trento), Enrico Bertolazzi (Dep. Industrial Engineering, University of Trento), Paolo Bosetti (Dep. Industrial Engineering, University of Trento)

著者名(英語): Francesco Biral (Dep. Industrial Engineering, University of Trento), Enrico Bertolazzi (Dep. Industrial Engineering, University of Trento), Paolo Bosetti (Dep. Industrial Engineering, University of Trento)

キーワード: optimal control，direct methods，indirect methods

要約(英語): Recent advances in theory, algorithms, and computational power make it possible to solve complex, optimal control problems both for off-line and on-line industrial applications. This paper starts by reviewing the technical details of the solution methods pertaining to three general categories: dynamic programming, indirect methods, and direct methods. With the aid of a demonstration example, the advantages and disadvantages of each method are discussed, along with a brief review of available software. The main result that emerges is the indirect method being numerically competitive with the performance of direct ones based on non-linear programming solvers and interior point algorithms. The second part of the paper introduces an indirect method based on the Pontryagin Minimum Principle (PMP). It also presents a detailed procedure and software tools (named PINS) to formulate the problem, automatically generate the C++ code, and eventually obtain a numerical solution for several optimal control problems of practical relevance. The application of PMP relates to the analytical derivation of necessary conditions for optimality. This aspect―often regarded in the literature as a drawback―is here exploited to build a robust yet efficient numerical method that formally eliminates the controls from the resulting Boundary Value Problem, thus gaining robustness and a high convergence rate. The elimination of the control is obtained either via their explicit formulation function of state and Lagrange multipliers―when possible―or via an iterative numerical solution. The paper closes presenting a minimum time manoeuvre of a car using a fairly complex vehicle model which also includes tyre saturation.

本誌: IEEJ Journal of Industry Applications Vol.5 No.2 （2016） Special Issue on Motion Control and its Related Technologies

本誌掲載ページ: 154-166 p

原稿種別: 論文／英語

電子版へのリンク: https://www.jstage.jst.go.jp/article/ieejjia/5/2/5_154/_article/-char/ja/