Related papers: Geometric analysis of differential-algebraic equat…
There exist many examples of systems which have some symmetries, and which one may monitor with symmetry preserving controls. Since symmetries are preserved along the evolution, full controllability is not possible, and controllability has…
This paper is concerned with a linear-quadratic (LQ, for short) optimal control problem for backward stochastic differential equations (BSDEs, for short), where the coefficients of the backward control system and the weighting matrices in…
Given a graph $\Gamma$, one may conside the set $X$ of its vertices as a metric space by assuming that all edges have length one. We consider two versions of homology theory of $\Gamma$ and their $K$-theory counterparts -- the $K$-theory of…
We initiate the study of counting Markov Equivalence Classes (MEC) under logical constraints. MECs are equivalence classes of Directed Acyclic Graphs (DAGs) that encode the same conditional independence structure among the random variables…
This paper considers the problem of canonical-correlation analysis (CCA) (Hotelling, 1936) and, more broadly, the generalized eigenvector problem for a pair of symmetric matrices. These are two fundamental problems in data analysis and…
We study optimal control problems that are governed by semilinear elliptic partial differential equations that involve non-Lipschitzian nonlinearities. It is shown that, for a certain class of such PDEs, the solution map is Fr\'{e}chet…
The purpose of this paper is to describe explicitly the solution for linear control systems on Lie groups. In case of linear control systems with inner derivations, the solution is given basically by the product of the exponential of the…
We consider a coupled system composed of a linear differential-algebraic equation (DAE) and a linear large-scale system of ordinary differential equations where the latter stands for the dynamics of numerous identical particles. Replacing…
A class of state models, called Kronecker-Weierstrass models (or, simply, KW-models), is introduced, and the state representation problem for linear differential systems is studied in the context of these models. It is shown, in particular,…
We propose and analyze a new discretization technique for a linear-quadratic optimal control problem involving the fractional powers of a symmetric and uniformly elliptic second oder operator; control constraints are considered. Since these…
Previously, the controllability problem of a linear time-invariant dynamical system was mapped to the maximum matching (MM) problem on the bipartite representation of the underlying directed graph, and the sizes of MMs on random bipartite…
We study numerically the ODE/IM correspondence for untwisted affine Lie algebras associated with simple Lie algebras including exceptional type. We consider the linear problem obtained from the massless limit of that of the modified affine…
This work investigates an elliptic optimal control problem defined on uncertain domains and discretized by a fictitious domain finite element method and cut elements. Key ingredients of the study are to manage cases considering the usually…
An eigenvalue based framework is developed for the H-infinity norm analysis and its norm minimization of coupled systems with time-delays, which are naturally described by delay differential algebraic equations (DDAEs). For these equations…
We design an algorithm for control of a linear switched system by means of Geometric Algebra. More precisely, we develop a switching path searching algorithm for a two-dimensional linear dynamical switched system with non-singular matrix…
This article describes a new, efficient way of finding control and state trajectories in optimal control problems by reformulation as a system of differential-algebraic equations (DAEs). The optimal control and state vectors can be obtained…
This paper considers control systems defined on Lie algebroids. After deriving basic controllability tests for general control systems, we specialize our discussion to the class of mechanical control systems on Lie algebroids. This class of…
This paper provides a unified framework connecting dynamical systems with tools from topological data analysis and geometric topology and inspires new interactions among dynamical systems, topology, and nonlinear analysis. To this end, we…
The article examines a linear-quadratic Neumann control problem that is governed by a non-coercive elliptic equation. Due to the non-self-adjoint nature of the linear control-to-state operator, it is necessary to independently study both…
Counterfactual explanations (CEs) aim to enhance the interpretability of machine learning models by illustrating how alterations in input features would affect the resulting predictions. Common CE approaches require an additional model and…