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A COMBINED ADAPTIVE CONTROL PARAMETRIZATION AND HOMOTOPY CONTINUATION TECHNIQUE FOR THE NUMERICAL SOLUTION OF BANG–BANG OPTIMAL CONTROL PROBLEMS

Part of: Existence theories Numerical methods in calculus of variations and optimal control Nonlinear algebraic or transcendental equations

Published online by Cambridge University Press:  09 October 2014

M. A. MEHRPOUYA ,
M. SHAMSI  and
M. RAZZAGHI
M. A. MEHRPOUYA
Affiliation:
Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, No. 424, Hafez Avenue, Tehran, Iran email m.a.mehrpouya@aut.ac.ir, m_shamsi@aut.ac.ir
M. SHAMSI*
Affiliation:
Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, No. 424, Hafez Avenue, Tehran, Iran email m.a.mehrpouya@aut.ac.ir, m_shamsi@aut.ac.ir
M. RAZZAGHI
Affiliation:
Department of Mathematics and Statistics, Mississippi State University, Mississippi State, MS 39762, USA email razzaghi@math.msstate.edu
*
✉m_shamsi@aut.ac.ir
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Abstract

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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.

Keywords

bang–bang optimal controlswitching pointnumerical methodscontrol parametrization methodhomotopy continuation technique

MSC classification

Secondary: 49J30: Optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.) 65H20: Global methods, including homotopy approaches 49M37: Methods of nonlinear programming type
Type
Research Article
Information
The ANZIAM Journal , Volume 56 , Issue 1 , July 2014 , pp. 48 - 65
Copyright
Copyright © 2014 Australian Mathematical Society 

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