相关论文: Carleman Linearization of Nonlinear Systems and It…

Universal approximation theorems establish the expressive capacity of neural network architectures. For dynamical systems, existing results are limited to finite time horizons or systems with a globally stable equilibrium, leaving…

This is a survey, which is a continuation of the previous survey of the author about applications of Carleman estimates to Inverse Problems, J. Inverse and Ill-Posed Problems, 21, 477-560, 2013. It is shown here that Tikhonov functionals…

We exploit the key idea that nonlinear system identification is equivalent to linear identification of the socalled Koopman operator. Instead of considering nonlinear system identification in the state space, we obtain a novel linear…

This paper studies approximate solutions of a linear fractional vector optimization problem without requiring boundedness of the constraint set. We establish necessary and sufficient conditions for approximating weakly efficient points of…

This paper deals with diagnosability of discrete-time nonlinear systems with unknown inputs and quantized outputs. We propose a novel notion of diagnosability that we term approximate diagnosability, corresponding to the possibility of…

The analysis of complex nonlinear systems is often carried out using simpler piecewise linear representations of them. A principled and practical technique is proposed to linearize and evaluate arbitrary continuous nonlinear functions using…

In the first part of this paper we introduced an algorithm that uses reachable set approximation to approximate the minimum time function of linear control problems. To illustrate the error estimates and to demonstrate differences to other…

This paper addresses the question whether there are numerical schemes for constant-coefficient advection problems that can yield convergent solutions for an infinite time horizon. The motivation is that such methods may serve as building…

This paper deals with the finite-time stabilization of a class of nonlinear infinite-dimensional systems. First, we consider a bounded matched perturbation in its linear form. It is shown that by using a set-valued function, both the…

We present a new formulation based on the classical Dirichlet-Neumann formulation for interface coupling problems in linearized elasticity. By using Taylor series expansions, we derive a new set of interface conditions that allow our…

This paper proposes an approach, Spectral Dynamics Embedding Control (SDEC), to optimal control for nonlinear stochastic systems. This method reveals an infinite-dimensional feature representation induced by the system's nonlinear…

Infinitesimal contraction analysis provides exponential convergence rates between arbitrary pairs of trajectories of a system by studying the system's linearization. An essentially equivalent viewpoint arises through stability analysis of a…

Decentralized optimization is a powerful paradigm that finds applications in engineering and learning design. This work studies decentralized composite optimization problems with non-smooth regularization terms. Most existing gradient-based…

We study linear function approximation in a finite basis under finite-precision arithmetic. In a highly non-orthogonal basis, certain directions are only weakly represented, so that rounding errors can significantly distort the effectively…

The first part of this paper is devoted to introducing an approach to compute the approximate minimum time function of control problems which is based on reachable set approximation and uses arithmetic operations for convex compact sets. In…

In this paper, we consider the infinite horizon optimal control problem for nonlinear systems. Under the conditions of controllability of the linearized system around the origin, and nonlinear controllability of the system to a terminal set…

We present recent results on the existence of a continuous time limit for Ensemble Kalman Filter algorithms. In the setting of continuous signal and observation processes, we apply the original Ensemble Kalman Filter algorithm proposed by…

We explore a linear inhomogeneous elasticity equation with random Lam\'e parameters. The latter are parameterized by a countably infinite number of terms in separated expansions. The main aim of this work is to estimate expected values…

Assessment of the degree of boundedness/stability of multidimensional nonlinear systems with time-dependent and nonperiodic coefficients is an important problem in various applied areas which has no adequate resolution yet. Most of the…

This work investigates the finite-horizon optimal covariance steering problem for discrete-time linear systems subject to both additive and multiplicative uncertainties as well as state and input chance constraints. In particular, a…