Solution of optimal control problems under piecewise constant, piecewise linear, and piecewise given on a class of functions control actions

Optimal control problems for objects described by ordinary differential equations system on the classes of piecewise constant, piecewise linear, and piecewise given control functions are considered. Both the piecewise constant values of the coefficients participating in the expression of controls as well as the boundaries of constancy intervals of these values are optimized. Analytic formulas for the gradient of the functional on the optimized parameters are obtained. These formulas allow using efficient first order optimization methods to solve the problems numerically. Results of numerical experiments are given.