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

  • Amin Jajarmi
  • Naser Pariz
  • Sohrab Effati
  • Ali Vahidian Kamyad


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.

Key words

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

CLC number



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Copyright information

© Journal of Zhejiang University Science Editorial Office and Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Amin Jajarmi
    • 1
  • Naser Pariz
    • 1
  • Sohrab Effati
    • 2
  • Ali Vahidian Kamyad
    • 2
  1. 1.Advanced Control and Nonlinear Laboratory, Department of Electrical EngineeringFerdowsi University of MashhadMashhadIran
  2. 2.Department of Applied Mathematics, Faculty of Mathematical SciencesFerdowsi University of MashhadMashhadIran

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