相关论文: Sharp estimates for biorthogonal families to expon…

Unconditional guaranteed lower and upper eigenvalue bounds are mandatory for the understanding of the Schr\"odinger eigenvalue spectrum and its spectral gaps. While upper eigenvalue bounds are naturally induced by conforming…

This paper is concerned with orthonormal systems in real intervals, given with zero Dirichlet boundary conditions. More specifically, our interest is in systems with a skew-symmetric differentiation matrix (this excludes orthonormal…

In this paper, we study approximate and exact controllability of the linear difference equation $x(t) = \sum\_{j=1}^N A\_j x(t - \Lambda\_j) + B u(t)$ in $L^2$, with $x(t) \in \mathbb C^d$ and $u(t) \in \mathbb C^m$, using as a basic tool a…

The optimal time for the controllability of linear hyperbolic systems in one dimensional space with one-side controls has been obtained recently for time-independent coefficients in our previous works. In this paper, we consider linear…

We present a predictive feedback control method for a class of quasilinear hyperbolic systems with one boundary control input. Assuming exact model knowledge, convergence to the origin, or tracking at the uncontrolled boundary, are achieved…

We address the problem of output reference tracking for unknown non-linear multi-input, multi-output systems described by functional differential equations. This class of systems includes those with a strict relative degree, and…

In this paper we introduce a method to find the minimal control time for the null controllability of 1D first-order linear hyperbolic systems by one-sided boundary controls when the coefficients are regular enough.

We consider a class of nonautonomous parabolic first-order coupled systems in the Lebesgue space $L^p({\mathbb R}^d;{\mathbb R}^m)$, $(d,m \ge 1)$ with $p\in [1,+\infty)$. Sufficient conditions for the associated evolution operator ${\bf…

This paper concerns the null controllability for a class of stochastic degenerate parabolic equations. We first establish a global Carleman estimate for a linear forward stochastic degenerate equation with multiplicative noise. Using this…

In this thesis, we provide an initial investigation into bounds for topological entropy of switched linear systems. Entropy measures, roughly, the information needed to describe the behavior of a system with finite precision on finite time…

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 propose a certainty-equivalence scheme for adaptive control of scalar linear systems subject to additive, i.i.d. Gaussian disturbances and bounded control input constraints, without requiring prior knowledge of the bounds of the system…

We study the performance of the certainty equivalent controller on Linear Quadratic (LQ) control problems with unknown transition dynamics. We show that for both the fully and partially observed settings, the sub-optimality gap between the…

Open effective field theories provide a systematic framework for describing physical systems interacting with an environment whose microscopic details are unknown, unobservable, or uncalculable. A basic step in constructing any effective…

The large-time asymptotics of the solutions to a class of degenerate parabolic cross-diffusion systems is analyzed. The equations model the interaction of an arbitrary number of population species in a bounded domain with no-flux boundary…

We detail in this article the necessity of a change of paradigm for the delay-robust control of systems composed of two linear first order hyperbolic equations. One must go back to the classical trade-off between convergence rate and…

The evidence lower bound (ELBO) is one of the most central objectives for probabilistic unsupervised learning. For the ELBOs of several generative models and model classes, we here prove convergence to entropy sums. As one result, we…

We consider an infinite strip $\Omega_L=(0,2\pi L)^{d-1}\times\mathbb{R}$, $d\geq 2$, $L>0$, and study the control problem of the heat equation on $\Omega_L$ with Dirichlet or Neumann boundary conditions, and control set…

In this paper, a class of nonlinear driftless control-affine systems satisfying the bracket generating condition is considered. A gradient-free optimization algorithm is developed for the minimization of a cost function along the…

In this paper, we are interested in the minimal null control time of one-dimensional first-order linear hyperbolic systems by one-sided boundary controls. Our main result is an explicit characterization of the smallest and largest values…