相关论文: Domain-of-Attraction Estimation for Uncertain Non-…

In this paper, we prove some a priori estimates for a system of partial differential equations arising in the nonstationary flow of a nonhomogeneous incompressible asymmetric fluid in a bounded domain with smooth boundary. The unknowns of…

We present a numerical algorithm for finding real non-negative solutions to polynomial equations. Our methods are based on the expectation maximization and iterative proportional fitting algorithms, which are used in statistics to find…

A novel approach to the problem of partial state estimation of nonlinear systems is proposed. The main idea is to translate the state estimation problem into one of estimation of constant, unknown parameters related to the systems initial…

We propose a technique for the design and analysis of adaptation algorithms in dynamical systems. The technique applies both to systems with conventional Lyapunov-stable target dynamics and to ones of which the desired dynamics around the…

Appropriate estimation of Region of Attraction for a nonlinear dynamical system plays a key role in system analysis and control design. Sum-of-Squares optimization is a powerful tool enabling Region of Attraction estimation for polynomial…

Projection-based model reduction has become a popular approach to reduce the cost associated with integrating large-scale dynamical systems so they can be used in many-query settings such as optimization and uncertainty quantification. For…

Physical systems experience nonlinear disturbances which have the potential to disrupt desired behavior. For a particular disturbance, whether or not the system recovers from the disturbance to a desired stable equilibrium point depends on…

The topic of statistical inference for dynamical systems has been studied extensively across several fields. In this survey we focus on the problem of parameter estimation for non-linear dynamical systems. Our objective is to place results…

Analyzing nonlinear systems with attracting robust invariant sets (RISs) requires estimating their domains of attraction (DOAs). Despite extensive research, accurately characterizing DOAs for general nonlinear systems remains challenging…

While convergence of polynomial chaos approximation for linear equations is relatively well understood, a lot less is known for non-linear equations. The paper investigates this convergence for a particular equation with quadratic…

In many applications it is important to understand the sensitivity of eigenvalues of a matrix polynomial to perturbations of the polynomial. The sensitivity commonly is described by condition numbers or pseudospectra. However, the…

In this paper, we study the nonlinear inverse problem of estimating the spectrum of a system matrix, that drives a finite-dimensional affine dynamical system, from partial observations of a single trajectory data. In the noiseless case, we…

This study covers an analytical approach to calculate positively invariant sets of dynamical systems. Using Lyapunov techniques and quantifier elimination methods, an automatic procedure for determining bounds in the state space as an…

We consider the problem of computing the maximal invariant set of discrete-time black-box nonlinear systems without analytic dynamical models. Under the assumption that the system is asymptotically stable, the maximal invariant set…

In nonlinear dynamics, basins of attraction link a given set of initial conditions to its corresponding final states. This notion appears in a broad range of applications where several outcomes are possible, which is a common situation in…

Validating and controlling safety-critical systems in uncertain environments necessitates probabilistic reachable sets of future state evolutions. The existing methods of computing probabilistic reachable sets normally assume that…

The motivation of this work stems from the numerical approximation of bounded functions by polynomials satisfying the same bounds. The present contribution makes use of the recent algebraic characterization found in [B. Despr\'es, Numer.…

This article describes a multivariate polynomial regression method where the uncertainty of the input parameters are approximated with Gaussian distributions, derived from the central limit theorem for large weighted sums, directly from the…

The task of approximating a function of d variables from its evaluations at a given number of points is ubiquitous in numerical analysis and engineering applications. When d is large, this task is challenged by the so-called curse of…

In this paper we propose an approach to evaluate the domain of attraction of asymptotically stable periodic solutions obtained via averaging principle (second Bogolubov's theorem or Mel'nikov's method). We discuss also how this result is…