相关论文: Control Theory and Parametrizations of Linear Part…

In this paper, we design nonlinear state feedback controllers for discrete-time polynomial dynamical systems via the occupation measure approach. We propose the discrete-time controlled Liouville equation, and use it to formulate the…

Though switched dynamical systems have shown great utility in modeling a variety of physical phenomena, the construction of an optimal control of such systems has proven difficult since it demands some type of optimal mode scheduling. In…

We study a class of third order hyperbolic operators $P$ in $G = \{(t, x):0 \leq t \leq T, x \in U \Subset {\mathbb R}^{n}\}$ with triple characteristics at $\rho = (0, x_0, \xi), \xi \in {\mathbb R}^n \setminus \{0\}$. We consider the case…

We study bipartite unitary operators which stay invariant under the local actions of diagonal unitary and orthogonal groups. We investigate structural properties of these operators, arguing that the diagonal symmetry makes them suitable for…

Scientific machine learning for inferring dynamical systems combines data-driven modeling, physics-based modeling, and empirical knowledge. It plays an essential role in engineering design and digital twinning. In this work, we primarily…

In this paper, we study the controllability of a Schr\"odinger equation with mixed boundary conditions on disjoint subsets of the boundary: dynamic boundary condition of Wentzell type, and Dirichlet boundary condition. The main result of…

Precise formulas are derived for the expected values $<\xi>$, $<\eta>$ and variances $\delta \xi ^2$, $\delta \eta ^2$ of random variables $\xi$, $\eta$ describing the spin asymmetry of some reaction when a background process contribution…

Control properties of the Kawahara equation are considered when the equation is posed on an unbounded domain. Precisely, the paper's main results are related to an approximation theorem that ensures the exact (internal) controllability in…

The present work provides a systematic approach for the design of sampled-data observers to a wide class of 1-D, parabolic PDEs with non-local outputs. The studied class of parabolic PDEs allows the presence of globally Lipschitz nonlinear…

Considerable attention has been recently focused on quantum-mechanical systems with boundaries and/or singular potentials for which the construction of physical observables as self-adjoint (s.a.) operators is a nontrivial problem. We…

As a follow-up to a recent study in the spin-0 case [J. Bunao and E. A. Galapon, Ann. Phys. 353, 83-106 (2015)], we construct a one-particle Time of Arrival (TOA) operator conjugate to a Hamiltonian describing a free relativistic spin-1/2…

Consider a classical elliptic pseudodifferential operator $P$ on ${\Bbb R}^n$ of order $2a$ ($0<a<1)$ with even symbol. For example, $P=A(x,D)^a$ where $A(x,D)$ is a second-order strongly elliptic differential operator; the fractional…

Interconnection and Damping Assignment Passivity-Based Control (IDA-PBC) is a nonlinear control technique that assigns a port-Hamiltonian (pH) structure to a controlled system using a state-feedback law. While IDA-PBC has been extensively…

We consider a strongly elliptic differential expression of the form $b(D)^* g(x/\varepsilon) b(D)$, $\varepsilon >0$, where $g(x)$ is a matrix-valued function in ${\mathbb R}^d$ assumed to be bounded, positive definite and periodic with…

Operator learning offers a robust framework for approximating mappings between infinite-dimensional function spaces. It has also become a powerful tool for solving inverse problems in the computational sciences. This chapter surveys…

We study the statistics of Dirichlet eigenvalues of the random Schr\"odinger operator $-\epsilon^{-2}\Delta^{(\text{d})}+\xi^{(\epsilon)}(x)$, with $\Delta^{(\text{d})}$ the discrete Laplacian on $\mathbb Z^d$ and $\xi^{(\epsilon)}(x)$…

The paper is devoted to the problem of global exact controllability for a wide class of neutral and mixed time-delay systems. We consider an equivalent operator model in Hilbert space and formulate steering conditions of controllable states…

Continuity, compactness, the spectrum and ergodic properties of the differentiation operator are investigated, when it acts in the Fr\'echet space of all Dirichlet series that are uniformly convergent in all half-planes $\{s \in \mathbb{C}…

Using a Hilbert space framework inspired by the methods of orthogonal projections and Hodge decompositions, we study a general class of problems (called Z-problems) that arise in effective media theory, especially within the theory of…

In this paper, we discuss the distributed control problem governed by the following parabolic integro-differential equation (PIDE) in the abstract form \begin{eqnarray*} \frac{\partial y}{\partial t} + A y &=& \int_0^t B(t, s) y(s) ds + Gu,…