Numerical Solution of Optimal Control Problems of Nonlinear Dynamical Systems

A numerical method for solving the optimal control problems for objects that are described by the system of nonlinear ordinary differential equations in the class of piecewise constant, piecewise linear and piecewise-defined controls, is proposed. In problems piecewise constant values of the coefficients of the formulas of control are optimized, and, what is more important, the boundaries of the constancy intervals of these values are optimized. The analytical formulas of the functional gradient by the parameters, which are optimized, are obtained. The functional gradient formulas, obtained for the initial continuous and appropriate discretized problems of optimal control in the class of piecewise constant controls, were compared. Numerical results are presented on the example of solving model problems.