Optimal Control Theory Applications to Dynamic Reconstruction Problems

Problems on reconstruction of real motions of dynamical models are considered when statistic data on measurements of motions are given, and borders of admissible errors of the measurements are known. The dynamical models are described by ordinary differential equations depending on controlled parameters.A new approach is suggested to solve the inverse problems with the help of feedbacks in auxiliary optimal control problems. A numerical algorithm is suggested to reconstruct real motions. The basis of the algorithm is the method of characteristics of the corresponding Hamilton–Jacobi–Bellman equation. Results of simulation for a macroeconomic model are exposed and discussed.