Related papers: Input-Output Pseudospectral Bounds for Transient A…
Following a stimulus, the neural response typically strongly varies in time and across neurons before settling to a steady-state. While classical population coding theory disregards the temporal dimension, recent works have argued that…
End-to-end optimization has achieved state-of-the-art performance on many specific problems, but there is no straight-forward way to combine pretrained models for new problems. Here, we explore improving modularity by learning a post-hoc…
This paper proposes a distributed strategy regulated on a subset of individual buses in a power network described by the swing equations to achieve transient frequency control while preserving asymptotic stability. Transient frequency…
Using the superstatistics method, we propose an extension of the random matrix theory to cover systems with mixed regular-chaotic dynamics. Unlike most of the other works in this direction, the ensembles of the proposed approach are basis…
Online identification of post-contingency transient stability is essential in power system control, as it facilitates the grid operator to decide and coordinate system failure correction control actions. Utilizing machine learning methods…
Even if a linear system of ordinary differential equations has a globally attracting equilibrium at the origin, small disturbances from the equilibrium may lead to large transient excursions before the system stabilizes. This…
Understanding and predicting mobility dynamics in transportation networks is critical for infrastructure planning, resilience analysis, and traffic management. Traditional graph-based models typically assume memoryless movement, limiting…
We prove an approximate spectral theorem for non-self-adjoint operators and investigate its applications to second order differential operators in the semi-classical limit. This leads to the construction of a twisted FBI transform. We also…
The advent of deep learning and recurrent neural networks revolutionized the field of time-series processing. Therefore, recent research on spectrum prediction has focused on the use of these tools. However, spectrum prediction, which…
Analysis of mathematical models in ecology and epidemiology often focuses on asymptotic dynamics, such as stable equilibria and periodic orbits. However, many systems exhibit long transient behaviors where certain aspects of the dynamics…
In spite of their huge success, transformer models remain difficult to scale in depth. In this work, we develop a unified signal propagation theory and provide formulae that govern the moments of the forward and backward signal through the…
We introduce system norms which assess transient behavior of stable Linear Time-Invariant (LTI) systems. This allows us to address undesired responses to initial conditions, finite resource consumption signals, or persistent perturbations.…
This work presents a new sufficient condition for synthesizing nonlinear controllers that yield bounded closed-loop tracking error transients despite the presence of unmatched uncertainties that are concurrently being learned online. The…
Platooning has been exploited as a method for vehicles to minimize energy consumption. In this article, we present a constraint-driven optimal control framework that yields emergent platooning behavior for connected and automated vehicles…
This work considers artificial feed-forward neural networks as parametric approximators in optimal control of discrete-time systems. Two different approaches are introduced to take polytopic input constraints into account. The first…
Deep reinforcement learning approaches are becoming appealing for the design of nonlinear controllers for voltage control problems, but the lack of stability guarantees hinders their deployment in real-world scenarios. This paper constructs…
The pseudospectra (or spectral instability) of non-selfadjoint operators is a topic of current interest in applied mathematics. In fact, for non-selfadjoint operators the resolvent could be very large outside the spectrum, making the…
Low-rank pseudoinverses are widely used to approximate matrix inverses in scalable machine learning, optimization, and scientific computing. However, real-world matrices are often observed with noise, arising from sampling, sketching, and…
In this paper, we address the stability of transport systems and wave propagation on networks with time-varying parameters. We do so by reformulating these systems as non-autonomous difference equations and by providing a suitable…
We propose an analytical technique to study large fluctuations and switching from internal noise in complex networks. Using order-disorder kinetics as a generic example, we construct and analyze the most probable, or optimal path of…