Related papers: Controllability and Observability Imply Exponentia…
We analyze a time-coarsening strategy for model predictive control (MPC) that we call diffusing-horizon MPC. This strategy seeks to overcome the computational challenges associated with optimal control problems that span multiple…
We study spatial decay properties of sensitivities in a nonlinear optimal control problem with a graph-structured interaction topology. For a problem with nonlinear decoupled dynamics and quadratic cost, we show that a perturbation of the…
Exponential dichotomies play a central role in stability theory for dynamical systems. They allow to split the state space into two subspaces, where all trajectories in one subspace decay whereas all trajectories in the other subspace grow,…
This paper presents the main characteristics of the evolutionary optimization code named EOS, Evolutionary Optimization at Sapienza, and its successful application to challenging, real-world space trajectory optimization problems. EOS is a…
Given an energy-dissipating port-Hamiltonian system, we characterise the exponential decay of the energy via the model ingredients under mild conditions on the Hamiltonian density $\mathcal{H}$. In passing, we obtain generalisations for…
We introduce a numerically stable reformulation of controllability scoring based on a scaled controllability Gramian, which remains reliably computable even for unstable systems. The resulting optimization problems define dynamics-aware…
This paper is concerned with the leader-following output consensus problem in the framework of distributed nonlinear observers. In stead of certain hypotheses on the leader system, a group of geometric conditions is put forward to develop a…
Finite-dimensional state-space representations of unsteady aerodynamics implicitly assume a system with fading memory. However, the impulse response of the two-dimensional inviscid (Euler) equations is characterized by an asymptotic…
We consider the problem of modulation and estimation of a random parameter $U$ to be conveyed across a discrete memoryless channel. Upper and lower bounds are derived for the best achievable exponential decay rate of a general moment of the…
We consider a transport equation by a gradient vector field with a small viscous perturbation --$\epsilon\Delta_g$. We study uniform observability (resp. controllability) properties in the (singular) vanishing viscosity limit…
Deep learning experiments by Cohen et al. [2021] using deterministic Gradient Descent (GD) revealed an Edge of Stability (EoS) phase when learning rate (LR) and sharpness (i.e., the largest eigenvalue of Hessian) no longer behave as in…
Recent findings (e.g., arXiv:2103.00065) demonstrate that modern neural networks trained by full-batch gradient descent typically enter a regime called Edge of Stability (EOS). In this regime, the sharpness, i.e., the maximum Hessian…
A well-known boundary observability inequality for the elasticity system establishes that the energy of the system can be estimated from the solution on a sufficiently large part of the boundary for a sufficiently large time. This…
Stochastic gradient descent (SGD) is the workhorse of large-scale learning, yet classical analyses rely on assumptions that can be either too strong (bounded variance) or too coarse (uniform noise). The expected smoothness (ES) condition…
For general second order evolution equations, we prove an optimal condition on the degree of unboundedness of the damping, that rules out finite-time extinction. We show that control estimates give energy decay rates that explicitly depend…
This work is concerned with the distributed controllability of the one-dimensional wave equation over non-cylindrical domains. The controllability in that case has been obtained in [Castro-Cindea-Munch, Controllability of the linear…
This paper examines the local exponential stability (LES) of trajectories for nonlinear systems on Riemannian manifolds. We present necessary and sufficient conditions for LES of a trajectory on a Riemannian manifold by analyzing the…
Recently, domain-uniform stabilizability and detectability has been the central assumption %in order robustness results on the to ensure robustness in the sense of exponential decay of spatially localized perturbations in optimally…
Recent research has observed that in machine learning optimization, gradient descent (GD) often operates at the edge of stability (EoS) [Cohen, et al., 2021], where the stepsizes are set to be large, resulting in non-monotonic losses…
Gradient descent and stochastic gradient descent are central to modern machine learning, yet their behavior under large step sizes remains theoretically unclear. Recent work suggests that acceleration often arises near the edge of…