Related papers: Characterising Robust Instances of Ultimate Positi…
We investigate practical algorithms to find or disprove the existence of small subsets of a dataset which, when removed, reverse the sign of a coefficient in an ordinary least squares regression involving that dataset. We empirically study…
We consider dynamical systems arising from substitutions over a finite alphabet. We prove that such a system is linearly repetitive if and only if it is minimal. Based on this characterization we extend various results from primitive…
The efficacy of robust optimization spans a variety of settings with uncertainties bounded in predetermined sets. In many applications, uncertainties are affected by decisions and cannot be modeled with current frameworks. This paper takes…
This paper studies a class of random nonlinear systems with time-varying delay, in which the $r$-order moment ($r\geq1$) of the random disturbance is finite. Firstly, some general conditions are proposed to guarantee the existence and…
Distributionally robust optimization is used to tackle decision making problems under uncertainty where the distribution of the uncertain data is ambiguous. Many ambiguity sets have been proposed for continuous uncertainty that build on…
We investigate continuous regularization methods for linear inverse problems of static and dynamic type. These methods are based on dynamic programming approaches for linear quadratic optimal control problems. We prove regularization…
Non-linear dynamical systems represent a compact, flexible, and robust tool for reactive motion generation. The effectiveness of dynamical systems relies on their ability to accurately represent stable motions. Several approaches have been…
Probabilistic solvers for ordinary differential equations (ODEs) provide efficient quantification of numerical uncertainty associated with simulation of dynamical systems. Their convergence rates have been established by a growing body of…
It is well known that, contrary to the autonomous case, the stability/instability of solutions of nonautonomous linear ordinary differential equations $x' = A(t) x$ is in no relation to the sign of the real parts of the eigenvalues of…
This work presents a sum-of-squares (SOS) based framework to perform data-driven stabilization and robust control tasks on discrete-time linear systems where the full-state observations are corrupted by L-infinity bounded input,…
This paper proposes several definitions of robust stability for logic dynamical systems (LDSs) with uncertain switching, including robust/uniform robust set stability and asymptotical (or infinitely convergent)/finite-time set stability…
Datasets typically contain inaccuracies due to human error and societal biases, and these inaccuracies can affect the outcomes of models trained on such datasets. We present a technique for certifying whether linear regression models are…
Autonomous systems often operate in multi-agent settings and need to make concurrent, strategic decisions, typically in uncertain environments. Verification and control problems for these systems can be tackled with concurrent stochastic…
It is known that input-output approaches based on scaled small-gain theorems with constant $D$-scalings and integral linear constraints are non-conservative for the analysis of some classes of linear positive systems interconnected with…
We consider two algorithms which can be used for proving positivity of sequences that are defined by a linear recurrence equation with polynomial coefficients (P-finite sequences). Both algorithms have in common that while they do succeed…
Recourse provides individuals who received undesirable labels (e.g., denied a loan) from algorithmic decision-making systems with a minimum-cost improvement suggestion to achieve the desired outcome. However, in practice, models often get…
Classical conditions for ensuring the robust stability of a linear system in feedback with a sector-bounded nonlinearity include small gain, circle, passivity, and conicity theorems. In this work, we present a similar stability condition,…
In the paper we study the subject of positivity of systems with sequential fractional difference. We give formulas for the unique solutions of systems in linear and semi-linear cases. The positivity of systems is considered.
A fundamental challenge in learning an unknown dynamical system is to reduce model uncertainty by making measurements while maintaining safety. We formulate a mathematical definition of what it means to safely learn a dynamical system by…
In this paper, we consider the problem of stabilizing discrete-time linear systems by computing a nearby stable matrix to an unstable one. To do so, we provide a new characterization for the set of stable matrices. We show that a matrix $A$…