Application of the averaging method for construction of suboptimal solutions to singularly perturbed optimal control problems
The paper deals with a nonlinear singularly perturbed system. Using the idea of the averaging method, applied to the presentation of this system in the ''expanded'' time scale, the author introduces a differential inclusion whose trajectories approximate the ''slow'' parts of the trajectories of the original system. Estimations of the accuracy of this approximation are given without proofs. The approach is applied to optimal control problems for a system which is linear and asymptotically stable with respect to the ''fast'' variable.
scientific article; zbMATH DE number 3951412