A combined adaptive control parametrization and homotopy continuation technique for the numerical solution of bang–bang optimal control problems

Authors

  • M. A. Mehrpouya Amirkabir University of Technology
  • M. Shamsi Amirkabir Univercity of Technology
  • M. Razzaghi Mississippi State University

DOI:

https://doi.org/10.21914/anziamj.v56i0.7200

Keywords:

bang–bang optimal control, switching point, numerical methods, control parametrization method, homotopy continuation technique

Abstract

We present an efficient computational procedure for the solution of bang–bang optimal control problems. The method is based on a well-known adaptive control parametrization method, which is one of the direct methods for numerical solution of optimal control problems. First, the adaptive control parametrization method is reviewed and then its advantages and disadvantages are illustrated. In order to resolve the need for a priori knowledge about the structure of optimal control and for resolving the sensitivity to an initial guess, a homotopy continuation technique is combined with the adaptive control parametrization method. The present combined method does not require any assumptions on the control structure and the number of switching points. In addition, the switching points are captured accurately; also, efficiency of the method is reported through illustrative examples. doi:10.1017/S1446181114000261

Author Biographies

M. A. Mehrpouya, Amirkabir University of Technology

Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology

M. Shamsi, Amirkabir Univercity of Technology

Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology

M. Razzaghi, Mississippi State University

Department of Mathematics and Statistics, Mississippi State University, Mississippi State, USA.

Published

2014-11-02

Issue

Section

Articles for Printed Issues