Mixed integer programming for a special logic constrained optimal control problem

• 成果类型: Article
• 署名作者: Preda, D; Noailles, J
• 署名单位: Universite Federale Toulouse Midi-Pyrenees (ComUE); Universite de Toulouse; Institut National Polytechnique de Toulouse; Universite Toulouse III - Paul Sabatier
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-005-0584-5
• 发表日期: 2005
• 页码: 309-333
• 关键词: global optimization; algorithm

摘要

Integrating logical constraints into optimal control problems is not an easy task. In fact, optimal control problems are usually continuous while logical constraints are naturally expressed by integer (binary) variables. In this article we are interested is a particular form of an LQR optimal control problem: the energy (control L-2 norm) is to be minimized, system dynamic is linear and logical constraints on the control use are to be fulfilled. Even if the starting continuous problem is not a complicated one, difficulties arise when integrating the additional logical constraints. First, we will present two different ways of modeling the problem, both of them leading us to Mixed Integer Problems. Furthermore, algorithms (Generalized Outer Approximation, Benders Decomposition and Branch and Cut) are applied on each model and results analyzed. We also present a Benders Decomposition algorithm variant that is adapted to our problem (taking into account its particular form) and we will conclude by looking at the optimal solutions obtained in an interesting physical example: the harmonic spring.