相关论文: Methods for determination and approximation of dom…
A systematic approach to maximise estimates on the region of attraction in the exponential stabilisation of geometrically exact (nonlinear) beam models via boundary feedback is presented. Starting from recently established stability results…
In this letter, we study the case of autonomous agents which are required to move to some new position based solely on the distance measured from predetermined reference points, or anchors. A novel approach, referred to as…
Most of nonlinear robust control methods just consider the affine nonlinear nominal model. When the nominal model is assumed to be affine nonlinear, available information about existing non-affine nonlinearities is ignored. For non-affine…
A numerical analysis for the fully discrete approximation of an operator Lyapunov equation related to linear SPDEs (stochastic partial differential equations) driven by multiplicative noise is considered. The discretization of the Lyapunov…
This paper considers discontinuous dynamical systems, i.e., systems whose associated vector field is a discontinuous function of the state. Discontinuous dynamical systems arise in a large number of applications, including optimal control,…
This paper presents new results that allow one to address the discrete-time general nonlinear robust control problem. The uncertain system is described by a general nonlinear function set characterized by the nominal model and the…
A novel method for stability and instability study of autonomous dynamical systems using the flow and divergence of the vector field is proposed. A relation between the method of Lyapunov functions and the proposed method is established.…
We introduce an autonomous system with closed-loop damping for first-order convex optimization. While, to this day, optimal rates of convergence are almost exclusively achieved by non-autonomous methods via open-loop damping (e.g.,…
Approximating regions of attraction in nonlinear systems require extensive computational and analytical efforts. In this paper, nonlinear vector fields are recasted as sum of vectors where each individual vector is used to construct an…
We develop a theory of accelerated first-order optimization from the viewpoint of differential equations and Lyapunov functions. Building upon the previous work of many researchers, we consider differential equations which model the…
A general numerical method using sum of squares programming is proposed to address the problem of estimating the region of attraction (ROA) of an asymptotically stable equilibrium point of a nonlinear polynomial system. The method is based…
Stochastic dynamical systems are fundamental in state estimation, system identification and control. System models are often provided in continuous time, while a major part of the applied theory is developed for discrete-time systems.…
This paper is concerned with the asymptotic stability analysis of a one dimensional wave equation with Dirichlet boundary conditions subject to a nonlinear distributed damping with an L p functional framework, p $\in$ [2, $\infty$]. Some…
We investigate discret conditions for stability and asymptotic stability by Lyapunov and the point of equilibrium of autonomous system of differential equations.
We consider optimal interpolation of functions analytic in simply connected domains in the complex plane. By choosing a specific structure for the approximant, we show that the resulting first order optimality conditions can be interpreted…
In this manuscript, we study the properties of a family of second-order differential equations with damping, its discretizations and their connections with accelerated optimization algorithms for $m$-strongly convex and $L$-smooth…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
Let us assume that $f$ is a continuous function defined on the unit ball of $\mathbb R^d$, of the form $f(x) = g (A x)$, where $A$ is a $k \times d$ matrix and $g$ is a function of $k$ variables for $k \ll d$. We are given a budget $m \in…
This paper considers a wide class of smooth continuous dynamic nonlinear systems (control objects) with a measurable vector of state. The problem is to find a special function (Lyapunov function), which in the framework of the second…
We present a unified convergence analysis for first order convex optimization methods using the concept of strong Lyapunov conditions. Combining this with suitable time scaling factors, we are able to handle both convex and strong convex…