Open-loop optimal controller design using variational iteration method

This article presents a design approach of a finite-time open-loop optimal controller using Pontryagin’s minimum principle. The resulting equations constitute a two-point boundary-value problem, which is generally impossible to solve analytically and, furthermore the numerical solution is difficult to obtain due to the coupled nature of the solutions. In this paper, the variational iteration method is adopted to easily solve Hamilton equations by use of iteration formulas derived from the correction functionals corresponding to Hamilton equations. The proposed approach allows to derive the numerical solution of the optimal control problem but an analytical or approximate expression of the optimal control law can often be obtained as a function of the time variable, depending on the nature of the control problem, which is simple to implement. The different possible forms of control law that can be attained following the proposed design approach are illustrated by four application examples.

► Dynamic optimization using Pontryagin’s minimum principle.
► Solve Hamilton equations together with minimization of Hamiltonian.
► Variational iterative calculation to obtain control law.
► Demonstration of convergence.
► Four examples with various solutions: analytical, close to analytical, numerical.