Method of Successive Approximations for Optimal Control under Uncertainty of Initial Data: An Interval Approach

This article discusses the development of an interval algorithm based on the method of successive approximations for solving optimal control problems under uncertainty of initial data. To achieve this goal, interval analysis methods are applied, allowing for the consideration of variations in system parameters. A numerical implementation of the algorithm is provided, along with a description of a computational experiment using a model example. The results demonstrate that the proposed method can construct confidence intervals for the solutions to the optimal control problem, making it useful for practical applications in situations with uncertainty in initial parameters.