Related papers: Discrete dynamical systems: inverse problems and r…
This work presents a technique for learning systems, where the learning process is guided by knowledge of the physics of the system. In particular, we solve the problem of the two-point boundary optimal control problem of linear…
We consider the optimal control problem of a general nonlinear spatio-temporal system described by Partial Differential Equations (PDEs). Theory and algorithms for control of spatio-temporal systems are of rising interest among the…
A novel control design approach for general nonlinear systems is presented in this paper. The approach is based on the identification of a polynomial model of the system to control and on the on-line inversion of this model. An efficient…
We propose a novel continuous-time algorithm for inequality-constrained convex optimization inspired by proportional-integral control. Unlike the popular primal-dual gradient dynamics, our method includes a proportional term to control the…
Recent years have witnessed the rapid advancement of understanding the control mechanism of networked dynamical systems (NDSs), which are governed by components such as nodal dynamics and topology. This paper reveals that the critical…
The paper addresses an optimal control problem for a perturbed sweeping process of the rate-independent hysteresis type described by a controlled "play and stop" operator with separately controlled perturbations. This problem can be reduced…
We propose to solve inverse problems involving the temporal evolution of physics systems by leveraging recent advances from diffusion models. Our method moves the system's current state backward in time step by step by combining an…
A procedure to recover explicitly self-adjoint matrix Dirac systems on semi-axis (with both discrete and continuous components of spectrum) from rational Weyl functions is considered. Its stability is proved. GBDT version of…
In this paper, Dirac operator with some integral type nonlocal boundary conditions is studied. We show that the coefficients of the problem can be uniquely determined by a dense set of nodal points. Moreover, we give an algorithm for the…
We propose directed time series regression, a new approach to estimating parameters of time-series models for use in certainty equivalent model predictive control. The approach combines merits of least squares regression and empirical…
We study the inverse source problem for a class of viscoelastic systems from a single boundary measurement in a general spatial dimension. We give specific reconstruction formula and stability estimate for the source in terms of the…
We consider the self-adjoint Dirac operators on a finite interval with summable matrix-valued potentials and general boundary conditions. For such operators, we study the inverse problem of reconstructing the potential and the boundary…
This paper deals with fractional-order controlled systems and fractional-order controllers in the discrete domain. The mathematical description by the fractional difference equations and properties of these systems are presented. A…
Nonlinear integrable models with two spatial and one temporal variables: Kadomtsev-Petviashvili equation and two-dimensional Toda lattice are investigated on the subject of correct formulation for boundary problem that can be solved within…
In this article we deal with one-dimensional inverse problems concerning the Burgers equation and some related nonlinear systems (involving heat effects and/or variable density). In these problems, the goal is to find the size of the…
Problem of time-optimal control of linear systems with fractional dynamics is treated in the paper from the convex-analytic standpoint. A linear system of fractional differential equations involving Riemann--Liouville derivatives is…
This paper is related to an inverse problem for a class of Dirac operators with discontinuous coefficient and eigenvalue parameter contained in boundary conditions. The asymptotic formula of eigenvalues of this problem is examined. The…
Motivated by various applications, this article develops the notion of boundary control for Maxwell's equations in the frequency domain. Surface curl is shown to be the appropriate regularization in order for the optimal control problem to…
In this paper, we adopt results in nonlinear time series analysis for causal inference in dynamical settings.~Our motivation is policy analysis with panel data, particularly through the use of "synthetic control" methods. These methods…
Self-adjoint Dirac systems and subclasses of canonical systems, which generalize Dirac systems are studied. Explicit and global solutions of direct and inverse problems are obtained. A local Borg-Marchenko-type theorem, integral…