Related papers: On the almost sure central limit theorem for ARX p…
We provide complementary results for a family of models with dependence on their previous $k$-sum. Using a martingale-based approach, we establish a functional central limit theorem and analyze the limiting behavior of the center of mass.…
This paper is concerned with the robust tracking control of linear uncertain systems, whose unknown system parameters and disturbances are bounded within ellipsoidal sets. We propose an adaptive robust control that can actively learn the…
Almost-global orientation trajectory tracking for a rigid body with external actuation has been well studied in the literature, and in the geometric setting as well. The tracking control law relies on the fact that a rigid body is a simple…
The article considers systems of interacting particles on networks with adaptively coupled dynamics. Such processes appear frequently in natural processes and applications. Relying on the notion of graph convergence, we prove that for large…
We develop a method for the model reference adaptive control (MRAC) of LTI systems via Extremum Seeking (ES). Our proof of global asymptotic tracking enables design of the adaptive controller to satisfy averaging requirements, and…
For systems with uncertain linear models, bounded additive disturbances and state and control constraints, a robust model predictive control algorithm incorporating online model adaptation is proposed. Sets of model parameters are…
We prove annealed central limit theorems for finite pattern counts in the measurement record of discrete-time quantum trajectories generated by repeated measurements in a disordered environment. Under summable mixing assumptions on the…
Funnel control achieves output tracking with guaranteed tracking performance for unknown systems and arbitrary reference signals. In particular, the tracking error is guaranteed to satisfy time-varying error bounds for all times (it evolves…
We define the local empirical process, based on $n$ i.i.d. random vectors in dimension $d$, in the neighborhood of the boundary of a fixed set. Under natural conditions on the shrinking neighborhood, we show that, for these local empirical…
A novel method of an adaptive linear quadratic (LQ) regulation of uncertain continuous linear time-invariant systems is proposed. Such an approach is based on the direct self-tuning regulators design framework and the exponentially stable…
Over the last 30 years, extensive work has been devoted to developing central limit theory for partial sums of subordinated long memory linear time series. A much less studied problem, motivated by questions that are ubiquitous in extreme…
For a generalized Hodge Laplace equation, we prove the quasi-optimal convergence rate of an adaptive mixed finite element method. This adaptive method can control the error in the natural mixed variational norm when the space of harmonic…
In this paper we study the Markov-modulated M/M/$\infty$ queue, with a focus on the correlation structure of the number of jobs in the system. The main results describe the system's asymptotic behavior under a particular scaling of the…
Model predictive control (MPC) for tracking is a recently introduced approach, which extends standard MPC formulations by incorporating an artificial reference as an additional optimization variable, in order to track external and…
The Adaptive Multilevel Splitting algorithm is a very powerful and versatile iterative method to estimate the probability of rare events, based on an interacting particle systems. In an other article, in a so-called idealized setting, the…
We consider the best arm identification problem, where the goal is to identify the arm with the highest mean reward from a set of $K$ arms under a limited sampling budget. This problem models many practical scenarios such as A/B testing. We…
This paper deals with some reachability issues for piecewise linear switched systems with time-dependent coefficients and multiplicative noise. Namely, it aims at characterizing data that are almost reachable at some fixed time T > 0…
We prove an almost sure central limit theorem on the Poisson space, which is perfectly tailored for stabilizing functionals emerging in stochastic geometry. As a consequence, we provide almost sure central limit theorems for $(i)$ the total…
The work [8] established memory loss in the time-dependent (non-random) case of uniformly expanding maps of the interval. Here we find conditions under which we have convergence to the normal distribution of the appropriately scaled…
In this article we quantify almost sure martingale convergence theorems in terms of the tradeoff between asymptotic almost sure rates of convergence (error tolerance) and the respective modulus of convergence. For this purpose we generalize…