Related papers: Model reduction for fully nonlinear stochastic sys…
Many nonlinear dynamical systems can be written as Lure systems, which are described by a linear time-invariant system interconnected with a diagonal static sector-bounded nonlinearity. Sufficient conditions are derived for the global…
Stochastic contraction analysis is a recently developed tool for studying the global stability properties of nonlinear stochastic systems, based on a differential analysis of convergence in an appropriate metric. To date, stochastic…
This paper investigates the robust stabilisation of a class of fractional-order non-linear systems via fixed-order dynamic output feedback controller in terms of linear matrix inequalities (LMIs). The systematic stabilisation algorithm…
This paper considers the reduction of the Langevin equation arising from bio-molecular models. To facilitate the construction and implementation of the reduced models, the problem is formulated as a reduced-order modeling problem. The…
When solving linear stochastic differential equations numerically, usually a high order spatial discretisation is used. Balanced truncation (BT) and singular perturbation approximation (SPA) are well-known projection techniques in the…
Given a family of systems, identifying stabilizing switching signals in terms of infinite walks constructed by concatenating cycles on the underlying directed graph of a switched system that satisfy certain conditions, is a well-known…
Suitable reduced order models (ROMs) are computationally efficient tools in characterizing key dynamical and statistical features of nature. In this paper, a systematic multiscale stochastic ROM framework is developed for complex systems…
Modelling real world systems involving humans such as biological processes for disease treatment or human behavior for robotic rehabilitation is a challenging problem because labeled training data is sparse and expensive, while high…
In this paper we deal with infinite-dimensional nonlinear forward complete dynamical systems which are subject to external disturbances. We first extend the well-known Datko lemma to the framework of the considered class of systems. Thanks…
Hyperexponential stability is investigated for dynamical systems with the use of both, explicit and implicit, Lyapunov function methods. A nonlinear hyperexponential control is designed for stabilizing linear systems. The tuning procedure…
In this note we identify a class of underactuated mechanical systems whose desired constant equilibrium position can be globally stabilised with the ubiquitous PID controller. The class is characterised via some easily verifiable conditions…
Coarse-graining or model reduction is a term describing a range of approaches used to extend the time-scale of molecular simulations by reducing the number of degrees of freedom. In the context of molecular simulation, standard…
This paper introduces a new algorithm for numerically computing equilibrium (i.e. stationary) distributions for Markov chains and Markov jump processes with either a very large finite state space or a countably infinite state space. The…
In this paper we propose a new Koopman operator approach to the decomposition of nonlinear dynamical systems using Koopman Gramians. We introduce the notion of an input-Koopman operator, and show how input-Koopman operators can be used to…
In this paper we study the problem of model reduction of linear network systems. We aim at computing a reduced order stable approximation of the network with the same topology and optimal w.r.t. H2 norm error approximation. Our approach is…
Stochastic gradient methods with momentum are widely used in applications and at the core of optimization subroutines in many popular machine learning libraries. However, their sample complexities have not been obtained for problems beyond…
In uncertainty quantification, critical parameters of mathematical models are substituted by random variables. We consider dynamical systems composed of ordinary differential equations. The unknown solution is expanded into an orthogonal…
Graphical continuous Lyapunov models offer a new perspective on modeling causally interpretable dependence structure in multivariate data by treating each independent observation as a one-time cross-sectional snapshot of a temporal process.…
This paper proposes a non-intrusive, data-driven reduced-order modeling framework for stochastic optimal control problems governed by partial differential equations. The control problem is formulated with a quadratic cost functional and…
For overparameterized optimization tasks, such as those found in modern machine learning, global minima are generally not unique. In order to understand generalization in these settings, it is vital to study to which minimum an optimization…