6 papers
Structural Visibility in Dynamical Systems on Hypergraphs: A Pattern Formation Perspective
Moise R. Mouyebe, Anthony M. Bloch
Hypergraphs encode rich multiway interactions, but not all structural information is equally accessible through the dynamics. By analyzing pattern-forming instabilities in reaction…
The Monge--Kantorovich problem, the Schur--Horn theorem, and the diffeomorphism group of the annulus
Anthony M. Bloch, Tudor S. Ratiu
First, we analyze the discrete Monge--Kantorovich problem, linking it with the minimization problem of linear functionals over adjoint orbits. Second, we consider its generalizatio…
Coupling Induced Stabilization of Network Dynamical Systems and Switching
Moise R. Mouyebe, Anthony M. Bloch
This paper investigates the stability and stabilization of diffusively coupled network dynamical systems. We leverage Lyapunov methods to analyze the role of coupling in stabilizin…
On the Local Controllability of a Class of Quadratic Systems
Moise R. Mouyebe, Anthony M. Bloch
The local controllability of a rich class of affine nonlinear control systems with nonhomogeneous quadratic drift and constant control vector fields is analyzed. The interest in th…
Symmetric Discrete Optimal Control and Deep Learning
Anthony M. Bloch, Peter E. Crouch, Tudor S. Ratiu
We analyze discrete optimal control problems and their connection with back propagation and deep learning. We consider in particular the symmetric representation of the discrete ri…
Dissipation Induced Instabilities
Anthony Bloch, P. S. Krishnaprasad, Jerrold E. Marsden +1
The main goal of this paper is to prove that if the energy-momentum (or energy-Casimir) method predicts formal instability of a relative equilibrium in a Hamiltonian system with sy…