Related papers: Time-stepping and Krylov methods for large-scale i…
We provide general methods for explicitly constructing strict Lyapunov functions for fully nonlinear slowly time-varying systems. Our results apply to cases where the given dynamics and corresponding frozen dynamics are not necessarily…
Discrete numerical methods with finite time-steps represent a practical technique to solve initial-value problems involving nonlinear differential equations. These methods seem particularly useful to the study of chaos since no analytical…
We devote our studies to the subject of weakly nonintegrable dynamics of systems with a macroscopic number of degrees of freedom. Our main points of interest are the relations between the timescales of thermalization and the timescales of…
Linear dynamical systems are canonical models for learning-based control of plants with uncertain dynamics. The setting consists of a stochastic differential equation that captures the state evolution of the plant understudy, while the true…
Large continuous-time Markov chains with exponentially small transition rates arise in modeling complex systems in physics, chemistry and biology. We propose a constructive graph-algorithmic approach to determine the sequence of critical…
Multi-adaptive Galerkin methods are extensions of the standard continuous and discontinuous Galerkin methods for the numerical solution of initial value problems for ordinary or partial differential equations. In particular, the…
This paper introduces a new class of algorithms for solving large-scale linear inverse problems based on new flexible and inexact Golub-Kahan factorizations. The proposed methods iteratively compute regularized solutions by approximating a…
We develop a linear systems theory that coincides with the existing theories for continuous and discrete dynamical systems, but that also extends to linear systems defined on nonuniform time domains. The approach here is based on…
We describe an approach for exploiting structure in Markov Decision Processes with continuous state variables. At each step of the dynamic programming, the state space is dynamically partitioned into regions where the value function is the…
Recently, there has been great interest in connections between continuous-time dynamical systems and optimization methods, notably in the context of accelerated methods for smooth and unconstrained problems. In this paper we extend this…
Motivated by recent applications of the Lyapunov's method in artificial neural networks, which could be considered as dynamical systems for which the convergence of the system trajectories to equilibrium states is a necessity. We re-look at…
The numerical integration of stiff equations is a challenging problem that needs to be approached by specialized numerical methods. Exponential integrators form a popular class of such methods since they are provably robust to stiffness and…
An algorithm for a family of self-starting high-order implicit time integration schemes with controllable numerical dissipation is proposed for both linear and nonlinear transient problems. This work builds on the previous works of the…
Many scientific applications require the evaluation of the action of the matrix function over a vector and the most common methods for this task are those based on the Krylov subspace. Since the orthogonalization cost and memory requirement…
Robust Model Predictive Control (MPC) for nonlinear systems is a problem that poses significant challenges as highlighted by the diversity of approaches proposed in the last decades. Often compromises with respect to computational load,…
Nonlinear dynamical systems are ubiquitous in nature and they are hard to forecast. Not only they may be sensitive to small perturbations in their initial conditions, but they are often composed of processes acting at multiple scales.…
Practical implementations of Gaussian smoothing algorithms have received a great deal of attention in the last 60 years. However, almost all work focuses on estimating complete time series (''fixed-interval smoothing'', $\mathcal{O}(K)$…
Robust Markov Decision Processes (MDPs) are receiving much attention in learning a robust policy which is less sensitive to environment changes. There are an increasing number of works analyzing sample-efficiency of robust MDPs. However,…
Learning stable dynamics from observed time-series data is an essential problem in robotics, physical modeling, and systems biology. Many of these dynamics are represented as an inputs-output system to communicate with the external…
We suggest and compare different methods for the numerical solution of Lyapunov like equations with application to control of Markovian jump linear systems. First, we consider fixed point iterations and associated Krylov subspace…