Related papers: Discrete dynamical systems: inverse problems and r…
In this paper, we consider the approximate controllability of partial differential equations with time derivatives of non-integer order via boundary control. We first show the unique existence of the solution under smooth boundary…
We apply methods of the so-called `inverse problem of the calculus of variations' to the stabilization of an equilibrium of a class of two-dimensional controlled mechanical systems. The class is general enough to include, among others, the…
We show the equivalence of inverse problems for different dynamical systems and corresponding canonical systems. For canonical system with general Hamiltonian we outline the strategy of studying the dynamic inverse problem and procedure of…
We study the inverse problems for the second order hyperbolic equations of general form with time-dependent coefficients assuming that the boundary data are given on a part of the boundary. The main result of this paper is the determination…
We establish a link between stability estimates for a hyperbolic inverse problem via the Boundary Control method and the blowup of a constant appearing in the contexts of optimal unique continuation and cost of approximate controllability.
In this paper inverse problems for Dirac operator with nonlocal conditions are considered. Uniqueness theorems of inverse problems from the Weyl-type function and spectra are provided, which are generalizations of the well-known Weyl…
The boundary control (BC-) method is an approach to inverse problems based upon their deep relations to control and system theory. We show that the classical integral equations of inverse problem theory (Gelfand-Levitan, Krein and Marchenko…
Solving inverse problems by dynamical variant of the BC-method is basically reduced to inverting the connecting operator $C^T$ of the dynamical system, for which the problem is stated. Realizing the method numerically, one needs to invert…
This article develops variational integrators for a class of underactuated mechanical systems using the theory of discrete mechanics. Further, a discrete optimal control problem is formulated for the considered class of systems and…
Control problems frequently arise in scientific and industrial applications, where the objective is to steer a dynamical system from an initial state to a desired target state. Recent advances in deep learning and automatic differentiation…
The paper is devoted to the study of a new class of optimal control problems for nonsmooth dynamical systems governed by nonconvex discontinuous differential inclusions of the sweeping type with involving variable time into optimization. We…
We consider the dynamical system with boundary control for the vector Schr\"odinger equation on the interval with a non-self-adjoint matrix potential. For this system, we study the inverse problem of recovering the matrix potential from the…
We discuss a class of linear control problems in a Hilbert space setting, which covers diverse systems such as hyperbolic and parabolic equations with boundary control and boundary observation even including memory terms. We introduce…
We consider the dynamic problems for the discrete systems with discrete time associated with finite and semi-infinite Jacobi matrices. The result of the paper is a procedure of association of special Hilbert spaces of functions, namely de…
We develop a method to control discrete-time systems with constant but initially unknown parameters from linear temporal logic (LTL) specifications. We introduce the notions of (non-deterministic) parametric and adaptive transition systems…
We discuss a class of linear control problems in a Hilbert space setting. This class encompasses such diverse systems as port-Hamiltonian systems, Maxwell's equations with boundary control or the acoustic equations with boundary control and…
In this article we investigate the connection between regularization theory for inverse problems and dynamic programming theory. This is done by developing two new regularization methods, based on dynamic programming techniques. The aim of…
We provide a necessary and sufficient condition for a rough control driving a differential equation to be reconstructable, to some order, from observing the resulting controlled evolution. Physical examples and applications in stochastic…
We consider a dynamic inverse problem for a dynamical system which describes the propagation of waves in a Krein string. The problem is reduced to an integral equation and an important special case is considered when the string density is…
A novel method to solve inverse problems for the wave equation is introduced. The method is a combination of the boundary control method and an iterative time reversal scheme, leading to adaptive imaging of coefficient functions of the wave…