相关论文: New Insights on One-Sided Lipschitz and Quadratica…
Numerous state-feedback and observer designs for nonlinear dynamic systems (NDS) have been developed in the past three decades. These designs assume that NDS nonlinearities satisfy one of the following function set classifications: bounded…
Control and state estimation of nonlinear systems satisfying a Lipschitz continuity condition have been important topics in nonlinear system theory for over three decades, resulting in a substantial amount of literature. The main criticism…
In this paper, we propose fixed-order set-valued (in the form of l2-norm hyperballs) observers for some classes of nonlinear bounded-error dynamical systems with unknown input signals that simultaneously find bounded hyperballs of states…
We consider the inverse problem of determining some class of nonlinear terms appearing in an elliptic equation from boundary measurements. More precisely, we study the stability issue for this class of inverse problems. Under suitable…
Extracting dynamic models from data is of enormous importance in understanding the properties of unknown systems. In this work, we employ Lipschitz neural networks, a class of neural networks with a prescribed upper bound on their Lipschitz…
A generalized dynamical robust nonlinear filtering framework is established for a class of Lipschitz differential algebraic systems, in which the nonlinearities appear both in the state and measured output equations. The system is assumed…
All Lipschitz dynamics with the weak infinitesimal contraction (WIC) property can be expressed as a Lipschitz nonlinear system in proportional negative feedback -- this statement, a ``structure theorem,'' is true in the $p=1$ and $p=\infty$…
This article provides a comprehensive understanding of optimization in deep learning, with a primary focus on the challenges of gradient vanishing and gradient exploding, which normally lead to diminished model representational ability and…
We develop an operator-theoretic framework for stability and statistical concentration in nonlinear inverse problems with block-structured parameters. Under a unified set of assumptions combining blockwise Lipschitz geometry, local…
This paper is devoted to the estimation of the Lipschitz constant of general neural network architectures using semidefinite programming. For this purpose, we interpret neural networks as time-varying dynamical systems, where the $k$-th…
Inspired by classical sensitivity results for nonlinear optimization, we derive and discuss new quantitative bounds to characterize the solution map and dual variables of a parametrized nonlinear program. In particular, we derive explicit…
In this paper, we investigate the quantum dynamics of underlying two one-dimensional quadratic Li'enard type nonlinear oscillators which are classified under the category of maximal (eight parameter) Lie point symmetry group (J. Math.…
In this paper we present a general tool to handle the presence of zero dynamics which are asymptotically but not locally exponentially stable in problems of robust nonlinear stabilization by output feedback. We show how it is possible to…
We consider the existence of a dynamically stable soliton in the one-dimensional cubic-quintic nonlinear Schr\"odinger model with strong cubic nonlinearity management for periodic and random modulations. We show that the predictions of the…
Techniques known as Nonlinear Set Membership prediction, Lipschitz Interpolation or Kinky Inference are approaches to machine learning that utilise presupposed Lipschitz properties to compute inferences over unobserved function values.…
We consider nonlinear Schrodinger equations with either local or nonlocal nonlinearities. In addition, we include periodic potentials as used, for example, in matter wave experiments in optical lattices. By considering the corresponding…
We study necessary and sufficient conditions for contraction and incremental stability of dynamical systems with respect to non-Euclidean norms. First, we introduce weak pairings as a framework to study contractivity with respect to…
The paper is concerned with open quantum systems whose Heisenberg dynamics are described by quantum stochastic differential equations driven by external boson fields. The system-field coupling operators are assumed to be quadratic…
It is demonstrated that nonlinear dynamical systems with analytic nonlinearities can be brought down to the abstract Schr\"odinger equation in Hilbert space with boson Hamiltonian. The Fourier coefficients of the expansion of solutions to…
It is well-known that the classical PID controller is by far the most widely used ones in industrial processes, despite of the remarkable progresses of the modern control theory over the past half a century. It is also true that the…