20 citations · 36 across the 5 of their papers we have counts for
6 papers
On the structural stability of random systems
Mohamed Ali Belabbas, Artur Kirkoryan
Understanding which system structure can sustain stable dynamics is a fundamental step in the design and analysis of large scale dynamical systems. Towards this goal, we investigat…
On implicit regularization: Morse functions and applications to matrix factorization
Mohamed Ali Belabbas
In this paper, we revisit implicit regularization from the ground up using notions from dynamical systems and invariant subspaces of Morse functions. The key contributions are a ne…
Geometric Motion Planning for Affine Control Systems with Indefinite Boundary Conditions and Free Terminal Time
Shenyu Liu, Yinai Fan, Mohamed-Ali Belabbas
The problem of motion planning for affine control systems consists of designing control inputs that drive a system from a well-defined initial to final states in a desired amount o…
The Affine Geometric Heat Flow and Motion Planning for Dynamic Systems
Shenyu Liu, Yinai Fan, Mohamed Ali Belabbas
We present a new method for motion planning for control systems. The method aims to provide a natural computational framework in which a broad class of motion planning problems can…
A Homotopy Method for Motion Planning
Shenyu Liu, Mohamed Ali Belabbas
We propose a novel method for motion planning and illustrate its implementation on several canonical examples. The core novel idea underlying the method is to define a metric for w…
On sparse representations of linear operators and the approximation of matrix products
Mohamed-Ali Belabbas, Patrick J. Wolfe
Thus far, sparse representations have been exploited largely in the context of robustly estimating functions in a noisy environment from a few measurements. In this context, the ex…