Related papers: Stabilisability and beta representations
Model robustness indicates a model's capability to generalize well on unforeseen distributional shifts, including data corruptions and adversarial attacks. Data augmentation is one of the most prevalent and effective ways to enhance…
The dynamical evolution of a recently introduced one dimensional model in \cite{biswas-sen} (henceforth referred to as model I), has been made stochastic by introducing a parameter $\beta$ such that $\beta =0$ corresponds to the Ising model…
This work is devoted to examining qualitative properties of dynamic systems, in particular, limit cycles of stochastic differential equations with both rapid switching and small diffusion. The systems are featured by multi-scale…
Given a graph $G = (V,E)$, an $(\alpha, \beta)$-ruling set is a subset $S \subseteq V$ such that the distance between any two vertices in $S$ is at least $\alpha$, and the distance between any vertex in $V$ and the closest vertex in $S$ is…
This paper proposes an optimization with penalty-based feedback design framework for safe stabilization of control affine systems. Our starting point is the availability of a control Lyapunov function (CLF) and a control barrier function…
In this paper we propose a data-driven distributionally robust Model Predictive Control framework for constrained stochastic systems with unbounded additive disturbances. Recursive feasibility is ensured by optimizing over an linearly…
For a dynamical system on n-dimensional projective space over a number field or a function field, we show that semi-stable reduction implies the minimality of the resultant. We use this to show that every such dynamical system over a number…
Traditional approaches to estimating beta in finance often involve rigid assumptions and fail to adequately capture beta dynamics, limiting their effectiveness in use cases like hedging. To address these limitations, we have developed a…
Selected results for the stability and optimal control of abstract switched systems in Banach and Hilbert space are reviewed. The dynamics are typically given in a piecewise sense by a family of nonlinearly perturbed evolutions of strongly…
We prove new characterisations of exponential stability for positive linear discrete-time systems in ordered Banach spaces, in terms of small-gain conditions. Such conditions have played an important role in the finite-dimensional systems…
This paper considers linear rational expectations models in the frequency domain. The paper characterizes existence and uniqueness of solutions to particular as well as generic systems. The set of all solutions to a given system is shown to…
In this paper, we give sufficient conditions under which linear abstract control systems for which the semigroup is analytic are stabilizable with a bounded feedback. We obtain various characterizations of that property, which extend some…
In this paper, we introduce the BMT distribution as an unimodal alternative to continuous univariate distributions supported on a bounded interval. The ideas behind the mathematical formulation of this new distribution come from computer…
In this paper we consider switched nonlinear systems under average dwell time switching signals, with an otherwise arbitrary compact index set and with additional constraints in the switchings. We present invariance principles for these…
Starting from the developed generalized point process model of $1/f$ noise (B. Kaulakys et al, Phys. Rev. E 71 (2005) 051105; cond-mat/0504025) we derive the nonlinear stochastic differential equations for the signal exhibiting 1/f^{\beta}$…
A long-standing assumption in the literature on switched linear systems is that static, homogeneous of degree one feedbacks form the most general class of controllers necessary and sufficient for stabilization. In this paper, we provide a…
This paper explores the fundamental limits of a simple system, inspired by the intermittent Kalman filtering model, where the actuation direction is drawn uniformly from the unit hypersphere. The model allows us to focus on a fundamental…
Continual learning systems are increasingly deployed in environments where retraining or reset is infeasible, yet many approaches emphasize task performance rather than the evolution of internal representations over time. In this work, we…
We analyze the performance of alternating minimization for loss functions optimized over two variables, where each variable may be restricted to lie in some potentially nonconvex constraint set. This type of setting arises naturally in…
This paper considers data rate limitations for mean square stabilization of uncertain discrete-time linear systems via finite data rate and lossy channels. For a plant having parametric uncertainties, a necessary condition and a sufficient…