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In this paper, the Picard’s iteration method is proposed to obtain an approximate analytical solution for linear and nonlinear optimal control problems with quadratic objective functional. It consists in deriving the necessary optimality conditions using the minimum principle of Pontryagin, which result in a two-point-boundary-value-problem (TPBVP). By applying the Picard’s iteration method to the resulting TPBVP, the optimal control law and the optimal trajectory are obtained in the form of a truncated series. The efficiency of the proposed technique for handling optimal control problems is illustrated by four numerical examples, and comparison with other methods is made.

We are studying an optimal control problem with free initial condition. The initial state of the optimized system is not known exactly, information on initial state is exhausted by inclusions x0 2 X0. Accessible controls for optimization of continuous dynamic system are discrete controls defined on quantized axes. The method presented is based on the concepts and operations of the adaptive method (9) of linear programming. The results are illustrated by a fourth order problem, efficiency estimates of proposed methods are given.