Application of variational iteration method for Hamilton-Jacobi-Bellman equations. (English) Zbl 1270.49004
Summary: In this paper, we use the variational iteration method (VIM) for optimal control problems. First, optimal control problems are transferred to Hamilton-Jacobi-Bellman (HJB) equation as a nonlinear first order hyperbolic partial differential equation. Then, the basic VIM is applied to construct a nonlinear optimal feedback control law. By this method, the control and state variables can be approximated as a function of time. Also, the numerical value of the performance index is obtained readily. In view of the convergence of the method, some illustrative examples are presented to show the efficiency and reliability of the presented method.
MSC:
| 49J20 | Existence theories for optimal control problems involving partial differential equations |
Keywords:
optimal control problems; Hamilton-Jacobi-Bellman (HJB) Equations; variational iteration method (VIM); Banach’s fixed point theoremReferences:
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