Related papers: Singularly Perturbed Averaging with Application to…
Concatenating matrices is a common technique for uncovering shared structures in data through singular value decomposition (SVD) and low-rank approximations. The fundamental question arises: How does the singular value spectrum of the…
Ill-posed inverse problems are ubiquitous in applications. Under- standing of algorithms for their solution has been greatly enhanced by a deep understanding of the linear inverse problem. In the applied communities ensemble-based filtering…
The averaging method is a classical powerful tool in perturbation theory of dynamical systems. There are two major obstacles to applying the averaging method, resonances and separatrices. In this paper we obtain realistic asymptotic…
Simple feedback loops, inspired from extremum-seeking, are proposed to lock a probe-frequency to the transition frequency of a single quantum system following quantum Monte-Carlo trajectories. Two specific quantum systems are addressed, a…
The increasing integration of power electronic devices is driving the development of more advanced tools and methods for the modeling, analysis, and control of modern power systems to cope with the different time-scale oscillations. In this…
Distributed optimization for resource allocation problems is investigated and a sub-optimal continuous-time algorithm is proposed. Our algorithm has lower order dynamics than others to reduce burdens of computation and communication, and is…
We propose a novel targeted exploration strategy designed specifically for uncertain linear time-invariant systems with energy-bounded disturbances, i.e., without any assumptions on the distribution of the disturbances. We use classical…
Convergence of Extremum Seeking (ES) algorithms has been established in the limit of small gains. Using averaging theory and contraction analysis, we propose a framework for computing explicit bounds on the departure of the ES scheme from…
We study an adaptive source seeking problem, in which a mobile robot must identify the strongest emitter(s) of a signal in an environment with background emissions. Background signals may be highly heterogeneous and can mislead algorithms…
Iterative algorithms aimed at solving some problems are discussed. For certain problems, such as finding a common point in the intersection of a finite number of convex sets, there often exist iterative algorithms that impose very little…
We investigate statistical properties of a likelihood approach to nonparametric estimation of a singular distribution using deep generative models. More specifically, a deep generative model is used to model high-dimensional data that are…
This paper considers simulation-based optimization of the performance of a regime-switching stochastic system over a finite set of feasible configurations. Inspired by the stochastic fictitious play learning rules in game theory, we propose…
We introduce a micro-macro parareal algorithm for the time-parallel integration of multiscale-in-time systems. The algorithm first computes a cheap, but inaccurate, solution using a coarse propagator (simulating an approximate slow…
This paper presents a geometric control framework on the Lie group SO(3) for 3D source-seeking by robots with first-order attitude dynamics and constant translational speed. By working directly on SO(3), the approach avoids Euler-angle…
We consider bounded extremum seeking controls for time-varying linear systems with uncertain coefficient matrices and measurement uncertainty. Using a new change of variables, Lyapunov functions, and a comparison principle, we provide…
We consider binary infinite order stochastic chains perturbed by a random noise. This means that at each time step, the value assumed by the chain can be randomly and independently flipped with a small fixed probability. We show that the…
The scaling behaviour of the diffraction intensity near the origin is investigated for (partially) ordered systems, with an emphasis on illustrative, rigorous results. This is an established method to detect and quantify the fluctuation…
In this work we introduce the notion of an angular spectrum for a linear discrete time nonautonomous dynamical system. The angular spectrum comprises all accumulation points of longtime averages formed by maximal principal angles between…
We analyze stability and robustness properties of an extremum seeking scheme that employs oscillatory dither signals with sufficiently large amplitudes and frequencies. Our study takes both input and output disturbances into account. We…
We consider perturbation-based extremum seeking, which recovers an approximate gradient of an analytically unknown objective function through measurements. Using classical needle variation analysis, we are able to explicitly quantify the…