Please use this identifier to cite or link to this item: http://dspace.library.iitb.ac.in/xmlui/handle/100/14111
Title: Application of a parametrization method to problem of optimal control
Authors: DESHPANDE, SA
AGASHE, SD
Keywords: Riccati Differential-Equation
Adomians Decomposition Method
Transformation
Form
Issue Date: 2011
Publisher: PERGAMON-ELSEVIER SCIENCE LTD
Citation: JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS,348(9)2390-2405
Abstract: A new approach to the problem of optimal control of linear dynamic systems is proposed that makes use of a method of input and state parametrization to transform the original problem into a problem of the Calculus of Variations. In contrast to the standard approaches for this class of problems, two salient features of the new approach are that no Lagrange multiplier functions need to be invoked and that the class of inputs can be restricted to the - relatively small - class of continuous functions, even for problems with fixed end-states. The resulting necessary conditions of optimality, i.e., the Euler Lagrange equation and the boundary conditions for the transformed problem, are proved to be equivalent to those resulting from the standard method of First Variations. In case of quadratic cost functionals, the new approach provides a simpler alternative to the well known, but equally difficult, Riccati differential equation approach and results in a simple dynamic state-feedback implementation of the optimal control. (C) 2011 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.
URI: http://dx.doi.org/10.1016/j.jfranklin.2011.06.030
http://dspace.library.iitb.ac.in/jspui/handle/100/14111
ISSN: 0016-0032
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