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Robust dynamic interactions are required to move robots in daily environments alongside humans. Optimisation and learning methods have been used to mimic and reproduce human movements. However, they are often not robust and their…
Functions in Hardy spaces on multiply-connected domains in the plane are given an explicit characterization in terms of a boundary condition inspired by the two-dimensional Ising model. The key underlying property is the positivity of a…
Commonly used techniques to study non-perturbative aspects of the strong interactions have a deep connection with rational approximants, and in particular with Pad\'e approximants to meromorphic functions. However, only recently this…
Stabilization of linear systems with unknown dynamics is a canonical problem in adaptive control. Since the lack of knowledge of system parameters can cause it to become destabilized, an adaptive stabilization procedure is needed prior to…
The challenge of mastering computational tasks of enormous size tends to frequently override questioning the quality of the numerical outcome in terms of accuracy. By this we do not mean the accuracy within the discrete setting, which…
In this paper, we study the complexity of the approximation of nonadmissible curves for nonlinear control-affine systems satisfying the strong H{\"o}rmander condition. Focusing on tubular approximation complexities, we provide asymptotic…
This article addresses control problems for semilinear impulsive neutral integro-differential equations with memory in a Banach space. It investigates the approximate controllability of linear and semilinear systems and proves the…
In this work we explore the fidelity of numerical approximations to the analytic spectra of hyperbolic partial differential equation systems with variable coefficients. We are particularly interested in the ability of discrete methods to…
In this work, we study the problem of learning a nonlinear dynamical system by parameterizing its dynamics using basis functions. We assume that disturbances occur at each time step with an arbitrary probability $p$, which models the…
This paper deals with the problem of robust dynamic output feedback stabilization of interval fractional-order linear time invariant (FO-LTI) systems with the fractional order $1\le\alpha<2$. In this study, a new formulation based on the…
Rate-independent systems arise in a number of applications. Usually, weak solutions to such problems with potentially very low regularity are considered, requiring mathematical techniques capable of handling nonsmooth functions. In this…
Approximate simulation, an extension of simulation relations from formal methods to continuous systems, is a powerful tool for hierarchical control of complex systems. Finding an approximate simulation relation between the full "concrete"…
In this paper, we consider a class of fractional integro-differential inclusions in Hilbert spaces. This paper deals with the approximate controllability for a class of fractional integro-differential control systems. First, we establishes…
We consider controlled martingales with bounded steps where the controller is allowed at each step to choose the distribution of the next step, and where the goal is to hit a fixed ball at the origin at time $n$. We show that the algebraic…
We establish fractional Hardy inequality on bounded domains in $\mathbb{R}^{d}$ with inverse of distance function from smooth boundary of codimension $k$, where $k=2, \dots,d$, as weight function. The case $sp=k$ is the critical case, where…
This paper studies the problems of identifiability and estimation in high-dimensional nonparametric latent structure models. We introduce an identifiability theorem that generalizes existing conditions, establishing a unified framework…
This paper establishes problem-specific sample complexity lower bounds for linear system identification problems. The sample complexity is defined in the PAC framework: it corresponds to the time it takes to identify the system parameters…
Maximum likelihood constraint inference is a powerful technique for identifying unmodeled constraints that affect the behavior of a demonstrator acting under a known objective function. However, it was originally formulated only for…
The behavior of certain weighted Hardy-type operators on rearrangement-invariant function spaces is thoroughly studied with emphasis being put on the optimality of the obtained results. First, the optimal rearrangement-invariant function…
This paper investigates the approximate controllability of linear fractional impulsive evolution equations in Hilbert spaces. The system under consideration involves the Caputo fractional derivative of order $0<\alpha\leq 1$, a closed…