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Optimization method for solving bang-bang and singular control problems

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Abstract

In this paper we study optimal control problems with the control variable appearing linearly. A novel method for optimization with respect to the switching times of controls containing both bang-bang and singular arcs is presented. This method transforms the control problem into a finite-dimensional optimization problem by reformulating the control problem as a multi-stage optimization problem. The optimal control problem is partitioned as several stages, with each stage corresponding to a particular control arc. A control vector parameterization approach is applied to convert the control problem to a static nonlinear programming (NLP) problem. The control profiles and stage lengths act as decision variables. Based on the Pontryagin maximal principle, a multi-stage adjoint system is constructed to calculate the gradients required by the NLP solvers. Two examples are studied to demonstrate the effectiveness of this strategy.

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Authors and Affiliations

  1. College of Information and Control Engineering, China University of Petroleum, Dongying Shandong, 257061, China

    Shurong Li, Ruiyan Zhao & Qiang Zhang

Authors
  1. Shurong Li
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  2. Ruiyan Zhao
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  3. Qiang Zhang
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Corresponding author

Correspondence to Shurong Li.

Additional information

This work was supported by the Natural Science Foundation of China (No. 60974039) and the National Science and Technology Major Project (No. 2008ZX05011).

Shurong LI received his B.S. degree from Shandong University in 1987. He later obtained M.S. and Ph.D. degrees from the Institute of Systems Science at Chinese Academy of Sciences in 1990 and 1993, respectively. He finished his postdoctoral research at Tsinghua University in 1995. Currently, he is a professor of the China University of Petroleum (East China). His recent research interests include optimal control and optimization, nonlinear control, intelligent control.

Ruiyan ZHAO is a Ph.D. candidate at the College of Information and Control Engineering, China University of Petroleum (East China). His major research interests include optimal control theory and the related applications in reservoir recovery.

Qiang ZHANG is a Ph.D. candidate at the College of Information and Control Engineering, China University of Petroleum (East China). His major research interests include optimal control theory and the related applications in reservoir recovery and chemical engineering.

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Li, S., Zhao, R. & Zhang, Q. Optimization method for solving bang-bang and singular control problems. J. Control Theory Appl. 10, 559–564 (2012). https://doi.org/10.1007/s11768-012-0276-7

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  • DOI: https://doi.org/10.1007/s11768-012-0276-7

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