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Journal of Zhejiang University SCIENCE C 2011 Vol.12 No.8 P.667-677


Solving infinite horizon nonlinear optimal control problems using an extended modal series method

Author(s):  Amin Jajarmi, Naser Pariz, Sohrab Effati, Ali Vahidian Kamyad

Affiliation(s):  Advanced Control and Nonlinear Laboratory, Department of Electrical Engineering, Ferdowsi University of Mashhad, Mashhad, Iran, Department of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran

Corresponding email(s):   jajarmi@stu-mail.um.ac.ir

Key Words:  Infinite horizon nonlinear optimal control problem, Pontryagin’, s maximum principle, Two-point boundary value problem, Extended modal series method

Amin Jajarmi, Naser Pariz, Sohrab Effati, Ali Vahidian Kamyad. Solving infinite horizon nonlinear optimal control problems using an extended modal series method[J]. Journal of Zhejiang University Science C, 2011, 12(8): 667-677.

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%A Amin Jajarmi
%A Naser Pariz
%A Sohrab Effati
%A Ali Vahidian Kamyad
%J Journal of Zhejiang University SCIENCE C
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%N 8
%P 667-677
%@ 1869-1951
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%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.C1000325

T1 - Solving infinite horizon nonlinear optimal control problems using an extended modal series method
A1 - Amin Jajarmi
A1 - Naser Pariz
A1 - Sohrab Effati
A1 - Ali Vahidian Kamyad
J0 - Journal of Zhejiang University Science C
VL - 12
IS - 8
SP - 667
EP - 677
%@ 1869-1951
Y1 - 2011
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.C1000325

This paper presents a new approach for solving a class of infinite horizon nonlinear optimal control problems (OCPs). In this approach, a nonlinear two-point boundary value problem (TPBVP), derived from pontryagin’;s maximum principle, is transformed into a sequence of linear time-invariant TPBVPs. Solving the latter problems in a recursive manner provides the optimal control law and the optimal trajectory in the form of uniformly convergent series. Hence, to obtain the optimal solution, only the techniques for solving linear ordinary differential equations are employed. An efficient algorithm is also presented, which has low computational complexity and a fast convergence rate. Just a few iterations are required to find an accurate enough suboptimal trajectory-control pair for the nonlinear OCP. The results not only demonstrate the efficiency, simplicity, and high accuracy of the suggested approach, but also indicate its effectiveness in practical use.

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