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

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Abstract

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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Authors and Affiliations

  1. Advanced Control and Nonlinear Laboratory, Department of Electrical Engineering, Ferdowsi University of Mashhad, Mashhad, Iran

    Amin Jajarmi & Naser Pariz

  2. Department of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran

    Sohrab Effati & Ali Vahidian Kamyad

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  1. Amin Jajarmi
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  2. Naser Pariz
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  3. Sohrab Effati
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  4. Ali Vahidian Kamyad
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Correspondence to Amin Jajarmi.

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Jajarmi, A., Pariz, N., Effati, S. et al. Solving infinite horizon nonlinear optimal control problems using an extended modal series method. J. Zhejiang Univ. - Sci. C 12, 667–677 (2011). https://doi.org/10.1631/jzus.C1000325

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  • DOI: https://doi.org/10.1631/jzus.C1000325

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