A highly computational efficient method to solve nonlinear optimal control problems

作者：Jajarmi A^*; Pariz N; Kamyad A Vahidian; Effati S

来源：Scientia Iranica, 2012, 19(3): 759-766.

DOI：10.1016/j.scient.2011.08.029

• Nonlinear optimal control problem
• Pontryagin's maximum principle
• Two-point boundary value problem
• Optimal homotopy perturbation method
• Suboptimal control

In this paper, a new analytical technique, called the Optimal Homotopy Perturbation Method (OHPM), is suggested to solve a class of nonlinear Optimal Control Problems (OCP's). Applying the OHPM to a nonlinear OCP, the nonlinear Two-Point Boundary Value Problem (TPBVP), derived from the Pontryagin's maximum principle, is transformed into a sequence of linear time-invariant TPBVP's. Solving the latter problems in a recursive manner provides the optimal trajectory and the optimal control law, in the form of rapid convergent series. Furthermore, the convergence of obtained series is controlled through a number of auxiliary functions involving a number of constants, which are optimally determined. In this study, an efficient algorithm is also presented, which has low computational complexity and fast convergence rate. Just a few iterations are required to find a 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.

• 出版日期2012-6