Solving optimal control problems by variational approach based on the Adomian´s Decomposition Method

In this work the Adomian´s Decomposition Method (ADM) is used to solve optimal control problems. The Lagrange multiplier method is adopted to derive the necessary conditions of optimality as a set of first-order differential equations. Then, by doing some algebraic manipulations, these equations are converted to a one ordinary differential equation, which can be easily solved, iteratively, using Adomian´s Decomposition Method to deduce the optimal control law. The proposed design approach is illustrated by several examples.