Related papers: Dominance margins for feedback systems
Stochastic feedback systems give rise to a variety of notions of stability. The conditions for the stability of the median, mean, and variance stability conditions differ. These conditions can be stated explicitly for scalar discrete-time…
Stability theory plays a crucial role in feedback control. However, adaptive control theory requires advanced and specialized stability notions that are not frequently used in standard feedback control theory. The present document is a set…
Foundation models excel in stable environments, yet often fail where reliability matters most: medicine, finance, and policy. This Fidelity Paradox is not just a data problem; it is structural. In domains where rules change over time, extra…
Models of coupled binary elements capture memory effects in complex dissipative materials, such as transient responses or sequential computing, when their interactions are chosen appropriately. However, for random interactions, self-loops -…
This article is concerned with stability analysis and stabilization of randomly switched systems under a class of switching signals. The switching signal is modeled as a jump stochastic (not necessarily Markovian) process independent of the…
This Ph.D. thesis is divided in two parts. The first one concerns the equilibrium properties of glassy systems. Some aspects of the phenomenology of glasses and of theories attempting to describe them are reviewed in chapter 1. A study of…
The functional demands of robotic systems often require completing various tasks or behaviors under the effect of disturbances or uncertain environments. Of increasing interest is the autonomy for dynamic robots, such as multirotors, motor…
Borrowing the concept of organizing center from singularity theory, the paper proposes a methodology to realize nonlinear behaviors such as switches, relaxation oscillators, or bursters from core circuits that reveal the fundamental role of…
The concept of random dynamical system is a comparatively recent development combining ideas and methods from the well developed areas of probability theory and dynamical systems. Due to our inaccurate knowledge of the particular physical…
The problem of stabilization of a system of coupled PDEs of the forth-order by means of boundary control is investigated. The considered setup arises from the classical Euler-Bernoulli beam model, and constitutes a generalization of…
Robustness is a fundamental property of machine learning classifiers required to achieve safety and reliability. In the field of adversarial robustness of image classifiers, robustness is commonly defined as the stability of a model to all…
We consider the distributed control of a network of heterogeneous agents with double integrator dynamics to maintain a rigid formation in 1D Euclidean space. The control signal at a vehicle is allowed to use relative position and velocity…
Self-organization through noisy interactions is ubiquitous across physics, mathematics, and machine learning, yet how long-range structure emerges from local noisy dynamics remains poorly understood. Here, we investigate three paradigmatic…
A number of simplified dynamical problems is studied in an attempt to clarify some of the mechanisms leading to turbulence and the existing proposals to control this transition. A simplified set of boundary layer equations displays a…
Contraction theory is a mathematical framework for studying the convergence, robustness, and modularity properties of dynamical systems and algorithms. In this opinion paper, we provide five main opinions on the virtues of contraction…
Recent developments in data-driven control have revived interest in the behavioral approach to systems theory, where systems are defined as sets of trajectories rather than being described by a specific model or representation. However,…
This paper presents a new theory, known as robust dynamic pro- gramming, for a class of continuous-time dynamical systems. Different from traditional dynamic programming (DP) methods, this new theory serves as a fundamental tool to analyze…
Rigidity is an emergent property of materials - it is not a feature of individual components that comprise the structure, but instead arises from interactions between many constituent parts. Recently, it has been recognized that…
Fluctuations and noise may alter the behavior of dynamical systems considerably. For example, oscillations may be sustained by demographic fluctuations in biological systems where a stable fixed point is found in the absence of noise. We…
This paper introduces a novel framework for estimation theory by introducing a second-order diagnostic for estimator design. While classical analysis focuses on the bias-variance trade-off, we present a more foundational constraint. This…