Abstract
A new method of solving time-optimal control problems in real time is 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 the differential equations only over the displacement intervals of the final time point and the switching time points. The computational cost of the method is evaluated. The peculiarities of calculating the optimal control of a linear system with retarded control in real time are considered. The results of simulation and numerical calculations are presented.
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