On an application of the Boundary control method to classical moment problems.

We establish relationships between the classical moments problems which are problems of a construction of a measure supported on a real line, on a half-line or on an interval from prescribed set of moments with the Boundary control approach to a dynamic inverse problem for a dynamical system with discrete time associated with Jacobi matrices. We show that the solution of corresponding truncated moment problems is equivalent to solving some generalized spectral problems.

Active Control of a Very Large Floating Beam Structure

In this paper, a novel boundary control method is investigated to suppress the vertical vibration of a very large floating structure (VLFS) with regular waves. The VLFS can be described as a distributed parameter system with partial differential equation (PDE). The proposed boundary controllers are developed based on Lyapunov's direct method to act on the upstream and downstream ends of the VLFS, respectively. Along with the suitable choice of control parameters, the proposed controllers could stabilize the vertical vibration of the VLFS subjected to regular waves. This study verifies the effectiveness of the proposed control methods to the VLFS. Then, the effects of wave amplitude and bending rigidity on the hydroelastic response of the VLFS are investigated.