Hamiltonian Systems in Dynamic Reconstruction Problems

We consider dynamic reconstruction (DR) problems for controlled dynamical systems linear in controls and nonlinear in state variables as inaccurate current information about real motions is known. A solution of this on-line inverse problem is obtained with the help of auxiliary problems of calculus of variations (CV) for integral discrepancy functionals. Key elements of the constructions are solutions of hamiltonian systems obtained with the help of optimality conditions for the CV problems. An illustrating example is exposed. © 201817-01-00074, 18-01-00221The work is supported by Russin Foundation for Basic Research (project no. 17-01-00074 and no. 18-01-00221)