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

M. A. Mehrpouya, M. Shamsi, M. Razzaghi

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

Keywords


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



DOI: http://dx.doi.org/10.21914/anziamj.v56i0.7200



Remember, for most actions you have to record/upload into this online system
and then inform the editor/author via clicking on an email icon or Completion button.
ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.