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Front. Inform. Technol. Electron. Eng.  2011, Vol. 12 Issue (8): 667-677    DOI: 10.1631/jzus.C1000325
    
Solving infinite horizon nonlinear optimal control problems using an extended modal series method
Amin Jajarmi*,1, Naser Pariz1, Sohrab Effati2, Ali Vahidian Kamyad2
1 Advanced Control and Nonlinear Laboratory, Department of Electrical Engineering, Ferdowsi University of Mashhad, Mashhad, Iran 2 Department of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran
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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.

Key words： Infinite horizon nonlinear optimal control problem      Pontryagin’s maximum principle      Two-point boundary value problem      Extended modal series method     
Received: 19 September 2010      Published: 03 August 2011
CLC:  TP13  
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Amin Jajarmi
Naser Pariz
Sohrab Effati
Ali Vahidian Kamyad
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Amin Jajarmi, Naser Pariz, Sohrab Effati, Ali Vahidian Kamyad. Solving infinite horizon nonlinear optimal control problems using an extended modal series method. Front. Inform. Technol. Electron. Eng., 2011, 12(8): 667-677.

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http://www.zjujournals.com/xueshu/fitee/10.1631/jzus.C1000325     OR     http://www.zjujournals.com/xueshu/fitee/Y2011/V12/I8/667


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

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.

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