A method of optimal real-time computation of a linear system with retarded control

A new method of solving time-optimal control problems in real time has been developed. The method is based on the following: 1) approximating the attainability sets with a family of hyperplanes; 2) subdividing the whole computational process into the computations performed beforehand and those that are carried out while the control takes place; 3) integrating differential equations only over the displacement intervals of the control completion moment and the switching moments. The labor-intensive characteristic of the method is evaluated. Characteristics of calculating the optimal control of a linear system with retarded control in real time are considered. The results of modeling and numerical estimations are presented.