Modal approach to the controllability problem of distributed parameter systems (Q2879997)

In the paper, the controllability problem for linear differential equations in infinite-dimensional Hilbert space with finite-dimensional control is investigated. Basing on the results of their previous research, the author gives sufficient conditions for approximate controllability of such systems, as well as efficient method of the control design for the approximate controllability problem. This method is founded on the solving of the optimal control problem for a finite-dimensional approximation of the original system. The main purpose of the paper is to apply the results to the study of the controllability of flexible mechanical systems with small dissipation which are described by equations with modal coordinates. The condition for modal frequencies which guaranteed an existence of the solution of approximate controllability problem is obtained.