Solution of infinite horizon nonlinear optimal control problems by piecewise adomian decomposition method

    Hassan Saberi Nik Info
    Paulo Rebelo Info
    Moosarreza Shamsyeh Zahedi Info

Abstract

In this paper, a Piecewise Adomian Decomposition Method (PADM) is used to obtain the analytical approximate solution for a class of infinite horizon nonlinear optimal control problems (OCPs). The method is a new modification of the standard ADM, in which it is treated as an algorithm in a sequence of small intervals (i.e. with small time step) for finding accurate approximate solutions to the corresponding OCPs. Applying the PADM, the nonlinear two-point boundary value problem (TPBVP), derived from the application of Pontryagin's maximum principle (PMP), is transformed into a sequence of linear time-invariant TPBVP's. Through the finite iterations of algorithm, a suboptimal control law is obtained for the nonlinear optimal control problem. Comparing the methodology with some known techniques shows that the present approach is powerful and reliable. It is remarkable accuracy properties are finally demonstrated by two examples.

Keywords:

Adomian decomposition method, optimal control problems, boundary value problems, initial value problems, Pontryagin's maximum principle, Hamiltonian system

How to Cite

Nik, H. S., Rebelo, P., & Zahedi, M. S. (2013). Solution of infinite horizon nonlinear optimal control problems by piecewise adomian decomposition method. Mathematical Modelling and Analysis, 18(4), 543-560. https://doi.org/10.3846/13926292.2013.841598

Share

Published in Issue
September 1, 2013
Abstract Views
642

View article in other formats

CrossMark check

CrossMark logo

Published

2013-09-01

Issue

Section

Articles

How to Cite

Nik, H. S., Rebelo, P., & Zahedi, M. S. (2013). Solution of infinite horizon nonlinear optimal control problems by piecewise adomian decomposition method. Mathematical Modelling and Analysis, 18(4), 543-560. https://doi.org/10.3846/13926292.2013.841598

Share