Optimal resource consumption control of perturbed systems

A method for calculating the optimal resource consumption control of perturbed dynamic systems is developed. This method includes both normal and singular solutions. According to the method proposed, the problem is subdivided into three independent tasks: (1) consideration of the effects of perturbations on the system, (2) computation of the optimal control structure, and (3) computation of the switching instants of the optimal control. The consideration of the influence of perturbations on the system and the transfer to a nonzero final state are reduced to the transformation of the initial and final states of the system. The control structure calculation is based on a specific method of quasi-optimal control formation. The control switching instants are found by using the relationship between deviations in the initial conditions of the conjugate system and deviations of the phase trajectory at the final instant. An iterative algorithm is developed, and its characteristics are considered. Results of modeling and numerical calculations are presented.