Extended multi-interval Legendre-Gauss-Radau pseudospectral method for mixed-integer optimal control problem in engineering

Abstract

Many engineering optimisation problems can be summarised as mixed-integer optimal control problems (MIOCPs) owing to the needs for mixed-integer dynamic control decisions. However, the convergence theory of Legendre-Gauss-Radau (LGR) approximation fails to apply to such non-smooth and discontinuous optimal control problems. Therefore, this paper develops an extended multi-interval LGR pseudospectral method (EMLGR), which has the following features: (i) the mixed-integer controls at the end of each interval and the interval intersections are added as two new controls to avoid the unrestrained control and shorten the switching time of integer control, and (ii) a smart adaptive collocation monitor (SACM) is provided to optimise the polynomial order and interval structure for further reducing computational complexity and improving approximation precision. The detailed solution procedure of EMLGR is given in this study, and experimental studies including five challenging practical engineering MIOCPs are taken to verify the superiorities of the proposed EMLGR in efficiency, accuracy and stability.

Keywords:

• Optimal control
• mixed-integer
• Legendre-Gauss-Radau pseudospectral
• smart adaptive collocation monitor

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is supported by the National Natural Science Foundation of China [Grant Number 61573378]; and the Beijing University of Posts and Telecommunications (BUPT) Excellent Ph.D. Students Foundation [Grant Number CX2019113].

Notes on contributors

Zhe Liu

Zhe Liu is a PhD candidate at School of Artificial Intelligence, Beijing University of Posts and Telecommunications. His research interest includes optimal control, intelligent optimization algorithms, etc.

Shurong Li

Shurong Li is a Professor at School of Artificial Intelligence, Beijing University of Posts and Telecommunications. He obtained his PhD in Basic Mathematics from Institute of Systems Science, Chinese Academy of Sciences in 1993. His research interest covers optimal control, nonlinear control, intelligent control, robust control and their applications.

Kai Zhao

Kai Zhao is a PhD candidate at College of Information and Control Engineering, China University of Petroleum (East China). His research interest includes optimal control, system identification, etc.