Optimal Synthesis to Inverse Problems of Dynamics

Abstract

Perturbed inverse problems are under consideration for dynamical systems linear relative controls. It is assumed that sampling history and sampling error estimate are known. Auxiliary optimal control problems are introduced to minimize a regularized integral discrepancy functional. The trajectories of the system are constructed with the help of Optimal Synthesis in the domain of admissible motions. It is proven that realizations of Optimal Synthesis generating trajectories of the system and minimizing the discrepancy functional in the domain are solutions of the perturbed inverse problem of dynamics.