Abdon E. Choque-Rivero

Moment perturbation of matrix polynomials

We consider a sequence of perturbed matrix orthogonal polynomials caused by some perturbation on the moments. We find an explicit relation between the perturbed polynomials and the original ones. We also analyse the perturbed second kind polynomials via its associated orthogonal polynomials and the non-perturbed second kind polynomials.

On Two extremal solutions of the admissible control problem with bounded controls

Given the Brunovsky control system of dimension m for m ≥ 2, as well as an initial position x0 and a time T greater than the time optimal control tmin, we obtain two bangbang controls with exact m switchings for every m via orthogonal polynomials on [0; T].

Dynamical inverse problem for two-velocity systems on finite trees

We consider the dynamical inverse problem for two-velocity systems on finite trees in a time-optimal setting: i. e. we assume that the dynamical Dirichlet-to-Neumann map, which we use as inverse data, is known on some finite interval (the length of this interval depends on the optical diameter of a tree). Using the controllability of a dynamical system and ideas of the Boundary Control method, we can extract the spectral data from the dynamical one, and then extend the dynamical inverse data by an explicit formula, provided we understand it in a suitable (generalized) sense. Then we can construct the Titchmarsh-Weyl function and solve the inverse problem using the leaf-peeling method.

On Korobov's admissible maximum principle

Based on the controllability function method a family of bang-bang controls satisfying Korobovs admissible maximum principle (KAMP) for the Brunovsky control system is given. By using the resultant of two polynomials the switching surface corresponding to the Pontryagin maximum principle (PMP) as well as the KAMP for control system of dimension 2 are attained. A conjecture of switching surfaces of the PMP and KAMP for the Brunovsky system of dimension 3 is presented

Factorization of the transition matrix for the general Jacobi system

The Jacobi system on a full-line lattice is considered when it contains additional weight factors. A factorization formula is derived expressing the scattering from such a generalized Jacobi system in terms of the scattering from its fragments. This is performed by writing the transition matrix for the generalized Jacobi system as an ordered matrix product of the transition matrices corresponding to its fragments. The resulting factorization formula resembles the factorization formula for the Schrodinger equation on the full line. Copyright