22 citations · 109 across the 52 of their papers we have counts for
32 papers · 1 filter
Structural stability of systems and cycle covers in random graphs
Mohamed Ali Belabbas
Structural system theory studies which network topologies can sustain a prescribed system property such as controllability or stability. When the topology is itself random, the rel…
Interpretable Gradient Descent for Kalman Gain
M. A. Belabbas, A. Olshevsky
We derive a decomposition for the gradient of the innovation loss with respect to the filter gain in a linear time-invariant system, decomposing as a product of an observability Gr…
On the invariance of super-linearization under polynomial automorphisms
Anmol Harshana, Mohamed-Ali Belabbas
We prove that the super-linearizability of polynomial systems is preserved by all currently known classes of polynomial automorphisms of . We then establish connections betwe…
Constructing Stochastic Matrices for Weighted Averaging in Gossip Networks
Erkan Bayram, Mohamed-Ali Belabbas
The convergence of the gossip process has been extensively studied; however, algorithms that generate a set of stochastic matrices, the infinite product of which converges to a ran…
On Infinite-horizon Minimum Energy Control
Mohamed-Ali Belabbas, Xudong Chen
We address the infinite-horizon minimum energy control problem for linear time-invariant finite-dimensional systems . We show that the problem admits a solution if and only…
Time-delay Induced Stochastic Optimization and Extremum Seeking
Naum Dimitrieski, Michael Reyer, Mohamed-Ali Belabbas +1
In this paper a novel stochastic optimization and extremum seeking algorithm is presented, one which is based on time-delayed random perturbations and step size adaptation. For the…
Dynamic Global Feedback Stabilization: why do the twist?
Mohamed-Ali Belabbas, Jehyung Ko
We investigate global dynamic feedback stabilization from a topological viewpoint. In particular, we consider the general case of dynamic feedback systems, whereby the total space…
Graphons and the -property
Mohamed-Ali Belabbas, Xudong Chen
A graphon satisfies the -property if graphs sampled from it contain a Hamiltonian decomposition almost surely, which in turn implies that the corresponding network topologies ar…
Vector-Valued Gossip over -Holonomic Networks
Erkan Bayram, Mohamed-Ali Belabbas, Tamer Başar
We study the weighted average consensus problem for a gossip network of agents with vector-valued states. For a given matrix-weighted graph, the gossip process is described by a se…
A Sufficient Condition for the Super-linearization of Polynomial Systems
Mohamed-Ali Belabbas, Xudong Chen
We provide in this paper a sufficient condition for a polynomial dynamical system to be super-linearizable, i.e., to be such that all its trajectories are lin…
Canonical forms for polynomial systems with balanced super-linearizations
M. -A. Belabbas
A system is Koopman super-linearizable if it admits a finite-dimensional embedding as a linear system. Super-linearization is used to leverage methods from linear systems theory to…
Visible and hidden observables in super-linearization
Mohamed-Ali Belabbas
We call a system super-linearizable if it admits finite-dimensional embedding as a linear system -- known as a finite-dimensional Koopman embedding; said otherwise, if its dynamics…
Geometric Characterization of the -property for Step-graphons
Mohamed Ali Belabbas, Xudong Chen
In a recent paper arXiv:2109.08340, we have exhibited a set of conditions that are necessary for the -property to hold for the class of step-graphons. In this paper, we prove th…
The H-property of Line Graphons
Mohamed-Ali Belabbas, Xudong Chen, Tamer Basar
We explore in this paper sufficient conditions for the -property to hold, with a particular focus on the so-called line graphons. A graphon is a symmetric, measurable function f…
On gradient flows initialized near maxima
Mohamed-Ali Belabbas
Let be a closed Riemannian manifold, and let be a smooth function on . We show the following holds generically for the function : for each maximu…
On the H-property for step-graphons and edge polytopes
Mohamed-Ali Belabbas, Xudong Chen, Tamer Basar
Graphons can be used as stochastic models to sample graphs on nodes for arbitrarily large. A graphon is said to have the -property if admits a decomp…
On Structural Rank and Resilience of Sparsity Patterns
Mohamed Ali Belabbas, Xudong Chen, Daniel Zelazo
A sparsity pattern in , for , is a vector subspace of matrices admitting a basis consisting of canonical basis vectors in $\mathbb{R}^{n \times m}…
Gossip over Holonomic Graphs
Xudong Chen, Mohamed-Ali Belabbas, Ji Liu
A gossip process is an iterative process in a multi-agent system where only two neighboring agents communicate at each iteration and update their states. The neighboring condition…
Geometric Heat Flow Method for Legged Locomotion Planning
Yinai Fan, Shenyu Liu, Mohamed-Ali Belabbas
We propose in this paper a motion planning method for legged robot locomotion based on Geometric Heat Flow framework. The motion planning task is challenging due to the hybrid natu…
On Integer Balancing of Digraphs
Mohamed-Ali Belabbas, Xudong Chen
A weighted digraph is balanced if the sums of the weights of the incoming and of the outgoing edges are equal at each vertex. We show that if these sums are integers, then the edge…
Triangulated Laman Graphs, Local Stochastic Matrices, and Limits of Their Products
Mohamed Ali Belabbas, Xudong Chen
We derive conditions on the products of stochastic matrices guaranteeing the existence of a unique limit invariant distribution. Belying our approach is the hereby defined notion o…
Gradient Approximation and Multi-Variable Derivative-Free Optimization based on Non-Commutative Maps
Jan Feiling, Mohamed-Ali Belabbas, Christian Ebenbauer
In this work, multi-variable derivative-free optimization algorithms for unconstrained optimization problems are developed. A novel procedure for approximating the gradient of mult…
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…