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In the present work, a simple algorithm for stabilizing an unknown linear time-invariant system is proposed, assuming only that this system is stabilizable. The suggested algorithm is based on first performing a partial identification of…
Algorithms for signal recovery in compressed sensing (CS) are often improved by stabilization techniques, such as damping, or the less widely known so-called fractional approach, which is based on the expectation propagation (EP) framework.…
We introduce a class of first-order methods for smooth constrained optimization that are based on an analogy to non-smooth dynamical systems. Two distinctive features of our approach are that (i) projections or optimizations over the entire…
Although it is relatively easy to apply, the gradient method often displays a disappointingly slow rate of convergence. Its convergence is specially based on the structure of the matrix of the algebraic linear system, and on the choice of…
We present a new solution for fundamental problems in nonlinear dynamical systems: finding, verifying, and stabilizing cycles. The solution we propose consists of a new control method based on mixing previous states of the system (or the…
Learning-based control of linear systems received a lot of attentions recently. In popular settings, the true dynamical models are unknown to the decision-maker and need to be interactively learned by applying control inputs to the systems.…
It is a known fact that not all controllable systems can be asymptotically stabilized by a continuous static feedback. Several approaches have been developed throughout the last decades, including time-varying, dynamical and even…
Non-linear dynamical systems represent a compact, flexible, and robust tool for reactive motion generation. The effectiveness of dynamical systems relies on their ability to accurately represent stable motions. Several approaches have been…
A method of stabilizing 2-cycles in discrete dynamic systems by Delayed Feedback Control is developed by using classic Harmonic Analysis.
In this article we introduce new possibilities of bounding the stability constants that play a vital role in the reduced basis method. By bounding stability constants over a neighborhood we make it possible to guarantee stability at more…
This paper focuses on the mathematical approaches to the analysis of stability that is a crucial step in the design of dynamical systems. Three methods are presented, namely, absolutely integrable impulse response, Fourier integral, and…
As the main contribution, this document provides a consistent discretization of a class of fixed-time stable systems, namely predefined-time stable systems. In the unperturbed case, the proposed approach allows obtaining not only a…
This paper deals with the convergence time analysis of a class of fixed-time stable systems with the aim to provide a new non-conservative upper bound for its settling time. Our contribution is fourfold. First, we revisit the well-known…
This paper presents a new control, namely additive-state-decomposition dynamic inversion stabilized control, that is used to stabilize a class of multi-input multi-output (MIMO) systems subject to nonparametric time-varying uncertainties…
This tutorial paper provides an introduction to recently developed tools for machine learning, especially learning dynamical systems (system identification), with stability and robustness constraints. The main ideas are drawn from…
In this paper we consider discrete gradient methods for approximating the solution and preserving a first integral (also called a constant of motion) of autonomous ordinary differential equations. We prove under mild conditions for a large…
In this article we develop and analyze novel iterative regularization techniques for the solution of systems of nonlinear ill--posed operator equations. The basic idea consists in considering separately each equation of this system and…
In this paper, we propose a new numerical strategy for the stabilization of evolution systems. The method is based on the methodology given by Ammari, Nicaise andPignotti in ''Stabilization by switching time-delay, Asymptot. Anal., 83…
We propose a novel framework for learning stabilizable nonlinear dynamical systems for continuous control tasks in robotics. The key idea is to develop a new control-theoretic regularizer for dynamics fitting rooted in the notion of…
In this document, we deal with the stabilization problem of slow-fast systems (or singularly perturbed Ordinary Differential Equations) at a non-hyperbolic point. The class of systems studied here have the following properties: 1) they have…