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Given a countable discrete amenable group, we study conditions under which a set map into a Banach space (or more generally, a complete semi-normed space) can be realized as the ergodic sum of a vector under a group representation, such…
We propose a learning-based robust predictive control algorithm that compensates for significant uncertainty in the dynamics for a class of discrete-time systems that are nominally linear with an additive nonlinear component. Such systems…
Nonlinear systems with model uncertainty are often described by stochastic differential equations. Some techniques from random dynamical systems are discussed. They are relevant to better understanding of solution processes of stochastic…
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…
In the present paper, we consider random invariant densities and the mean ergodic theorem for Markov operator cocycles which are applicable to quenched type random dynamical systems. We give necessary and sufficient conditions for the…
Despite their deterministic nature, dynamical systems often exhibit seemingly random behaviour. Consequently, a dynamical system is usually represented by a probabilistic model of which the unknown parameters must be estimated using…
A class of quasi-variational-hemivariational inequalities in reflexive Banach spaces is studied. The inequalities contain a convex potential, a locally Lipschitz superpotential, and an implicit obstacle set of constraints. Results on the…
This paper considers discontinuous dynamical systems, i.e., systems whose associated vector field is a discontinuous function of the state. Discontinuous dynamical systems arise in a large number of applications, including optimal control,…
This paper is concerned with robust performance criteria for linear continuous time invariant stochastic systems driven by statistically uncertain random processes. The uncertainty is understood as the deviation of imprecisely known…
This note introduces a new notion of random dynamical system with inputs and outputs, and sketches a small-gain theorem for monotone systems which generalizes a similar theorem known for deterministic systems.
The reduction of dynamical systems has a rich history, with many important applications related to stability, control and verification. Reduction of nonlinear systems is typically performed in an exact manner - as is the case with…
We derive high-probability finite-sample uniform rates of consistency for $k$-NN regression that are optimal up to logarithmic factors under mild assumptions. We moreover show that $k$-NN regression adapts to an unknown lower intrinsic…
This work deals with the stability analysis of nonlinear sampled-data systems under nonuniform sampling. It establishes novel relationships between the stability property of the exact discrete-time model for a given sequence of (aperiodic)…
For smooth random dynamical systems we consider the quenched linear and higher-order response of equivariant physical measures to perturbations of the random dynamics. We show that the spectral perturbation theory of Gou\"ezel, Keller, and…
We obtain an uniform tail estimates for natural normed sums of independent random variables (r.v.) with regular varying tails of distributions. We give also many examples on order to show the exactness of offered estimates and discuss some…
We investigate various relaxations of additivity for set maps into Banach spaces in the context of representations of amenable groups. Specifically, we establish conditions under which asymptotically additive and almost additive set maps…
A weakly admissible mesh (WAM) on a continuum real-valued domain is a sequence of discrete grids such that the discrete maximum norm of polynomials on the grid is comparable to the supremum norm of polynomials on the domain. The asymptotic…
This paper considers three dichotomy concepts (exponential dichotomy, uniform exponential dichotomy and strong exponential dichotomy) in the general context of non-invertible evolution operators in Banach spaces. Connections between these…
In this paper we survey known results of characterizations of reflexive Banach spaces, which are based on convergence of usual and generalized arithmetic mean (or Ces\`aro sum), weakly compact subsets, affine sets in a Banach space or its…
In order to bring contraction analysis into the very fruitful and topical fields of stochastic and Bayesian systems, we extend here the theory describes in \cite{Lohmiller98} to random differential equations. We propose new definitions of…