In this thesis we study stability from several viewpoints. After covering the practical importance, the rich history and the ever-growing list of manifestations of stability, we study the following. (i) (Statistical identification of stable dynamical syste ...
Motivated by policy gradient methods in the context of reinforcement learning, we derive the first large deviation rate function for the iterates generated by stochastic gradient descent for possibly non-convex objectives satisfying a Polyak-Łojasiewicz co ...
Suppose that the origin is globally asymptotically stable under a set of continuous vector fields on Euclidean space and suppose that all those vector fields come equipped with - possibly different - convex Lyapunov functions. We show that this implies the ...
Most zeroth-order optimization algorithms mimic a first-order algorithm but replace the gradient of the objective function with some noisy gradient estimator that can be computed from a small number of function evaluations. This estimator is constructed ra ...
Society for Industrial & Applied Mathematics (SIAM)2024
We characterize when a compact, invariant, asymptotically stable attractor on a locally compact Hausdorff space is a strong deformation retract of its domain of attraction. ...
Institute of Electrical and Electronics Engineers Inc.2024
We propose a principled method for projecting an arbitrary square matrix to the non- convex set of asymptotically stable matrices. Leveraging ideas from large deviations theory, we show that this projection is optimal in an information-theoretic sense and ...
Two dynamical systems are topologically equivalent when their phase-portraits can be morphed into each other by a homeomorphic coordinate transformation on the state space. The induced equivalence classes capture qualitative properties such as stability or ...
Dynamical systems are topologically equivalent when their orbits can be mapped onto each other via a homeomorphic change of coordinates. We will show that in general, closed-loop systems resulting from Linear Quadratic Optimal Control problems are all topo ...
