Related papers: Optimization-based Lyapunov function construction …
This paper considers the problem of characterizing the stability region of a large-scale networked system comprised of dissipative nonlinear subsystems, in a distributed and computationally tractable way. One standard approach to estimate…
We discuss the efficient computation of performance, reliability, and availability measures for Markov chains; these metrics, and the ones obtained by combining them, are often called performability measures. We show that this computational…
This work analyzes accelerating and decelerating wall-driven flows by quantifying the upper bound of transient energy growth using a Lyapunov-type approach. By formulating the linearized Navier-Stokes equations as a linear time-varying…
Arguing about the equilibrium distribution of continuous-time Markov chains can be vital for showing properties about the underlying systems. For example in biological systems, bistability of a chemical reaction network can hint at its…
For a discrete time Markov chain and in line with Strotz' consistent planning we develop a framework for problems of optimal stopping that are time-inconsistent due to the consideration of a non-linear function of an expected reward. We…
We investigate multivariate regular variation in the context of time-homogeneous Markov chains on general vector spaces and in random coefficient linear models. In the first part, we show that the regular variation of the stationary…
We provide a framework for empirical process theory of locally stationary processes using the functional dependence measure. Our results extend known results for stationary Markov chains and mixing sequences by another common possibility to…
In this paper, we address the problem of discovering maximal Lyapunov functions, as a means of determining the region of attraction of a dynamical system. To this end, we design a novel neural network architecture, which we prove to be a…
In the framework of the Fermi-Pasta-Ulam (FPU) model, we show a simple method to give an accurate analytical estimation of the maximal Lyapunov exponent at high energy density. The method is based on the computation of the mean value of the…
This paper studies stochastic boundedness of trajectories of a nonvanishing stochastically perturbed stable LTI system. First, two definitions on stochastic boundedness of stochastic processes are presented, then the boundedness is analyzed…
This article is concerned with stability analysis and stabilization of randomly switched nonlinear systems. These systems may be regarded as piecewise deterministic stochastic systems: the discrete switches are triggered by a stochastic…
This paper studies the problem of enforcing safety of a stochastic dynamical system over a finite time horizon. We use stochastic barrier functions as a means to quantify the probability that a system exits a given safe region of the state…
We study an approximation method of stationary characters of a two-dimensional Markov chain via the Stein method. For this purpose, innovative methods are developed to estimate the moments of the Markov chain, as well as the solution to the…
This work investigates the boundary stabilization of flows in star-shaped and tree-shaped networks of open channels governed by the Saint-Venant equations with a friction term. Due to the existence of the friction term, the steady-states…
We study the convergence analysis of continuous-time dynamical systems associated with optimization methods for strongly convex functions. Recent works have proposed systematic constructions of Lyapunov functions for such analysis, while…
Optimization plays a central role in intelligent systems and cyber-physical technologies, where speed and reliability of convergence directly impact performance. In control theory, optimization-centric methods are standard: controllers are…
We present a time change construction of affine processes with state-space $\mathbb{R}_+^m\times \mathbb{R}^n$. These processes were systematically studied in (Duffie, Filipovi\'c and Schachermayer, 2003) since they contain interesting…
Exponential stability of the nonlinear filtering equation is revisited, when the signal is a finite state Markov chain. An asymptotic upper bound for the filtering error due to incorrect initial condition is derived in the case of slowly…
We consider processes which are functions of finite-state Markov chains. It is well known that such processes are rarely Markov. However, such processes are often regular in the following sense: the distant past values of the process have…
Suppose an online platform wants to compare a treatment and control policy, e.g., two different matching algorithms in a ridesharing system, or two different inventory management algorithms in an online retail site. Standard randomized…