Related papers: Characterising Robust Instances of Ultimate Positi…
Many learning algorithms are formulated in terms of finding model parameters which minimize a data-fitting loss function plus a regularizer. When the regularizer involves the l0 pseudo-norm, the resulting regularization path consists of a…
A strictly increasing sequence (n_k) of positive integers is said to be a Hilbertian Jamison sequence if for any bounded operator T on a separable Hilbert space such that the supremum over k of the norms ||T^{n_k}|| is finite, the set of…
End-to-end engineering design pipelines, in which designs are evaluated using concurrently defined optimal controllers, are becoming increasingly common in practice. To discover designs that perform well even under the misspecification of…
This paper considers the problem of testing whether there exists a non-negative solution to a possibly under-determined system of linear equations with known coefficients. This hypothesis testing problem arises naturally in a number of…
We study the problem of determining self-sustained oscillations in discrete-time linear time-invariant relay feedback systems. Concretely, we are interested in predicting when such a system admits unimodal oscillations, i.e., when the…
Robust output regulation for linear time-varying systems has remained an open problem for decades. To address this, we propose the trajectory-matching system immersion framework, by reformulating the regulator equation into a more…
We consider the notion of resilience for cyber-physical systems, that is, the ability of the system to withstand adverse events while maintaining acceptable functionality. We use finite temporal logic to express the requirements on the…
Identifying a linear system model from data has wide applications in control theory. The existing work on finite sample analysis for linear system identification typically uses data from a single system trajectory under i.i.d random inputs,…
We consider a class of inverse problems where it is possible to aggregate the results of multiple experiments. This class includes problems where the forward model is the solution operator to linear ODEs or PDEs. The tremendous size of such…
We study finite and countably infinite systems of stochastic differential equations, in which the drift and diffusion coefficients of each component (particle) are determined by its rank in the vector of all components of the solution. We…
We consider solving linear optimization (LO) problems with uncertain objective coefficients. For such problems, we often employ robust optimization (RO) approaches by introducing an uncertainty set for the unknown coefficients. Typical RO…
This paper investigates the robustness of the Lur'e problem under positivity constraints, drawing on results from the positive Aizerman conjecture and robustness properties of Metzler matrices. Specifically, we consider a control system of…
We study the computational complexity of the Escape Problem for discrete-time linear dynamical systems over compact semialgebraic sets, or equivalently the Termination Problem for affine loops with compact semialgebraic guard sets. Consider…
Ordinary differential equations (ODEs) provide a powerful framework for modeling dynamic systems arising in a wide range of scientific domains. However, most existing ODE methods focus on a single system, and do not adequately address the…
Robust optimization is a framework for modeling optimization problems involving data uncertainty and during the last decades has been an area of active research. If we focus on linear programming (LP) problems with i) uncertain data, ii)…
Robustness guarantees are important properties to be looked for during control design. They ensure stability of closed-loop systems in face of uncertainties, unmodeled effects and bounded disturbances. While the theory on robust stability…
While the asymptotic stability of positive linear systems in the presence of bounded time delays has been thoroughly investigated, the theory for nonlinear positive systems is considerably less well-developed. This paper presents a set of…
Closed-loop positivity of feedback interconnections of positive monotone nonlinear systems is investigated. It is shown that an instantaneous gain condition on the open-loop systems which implies feedback well-posedness also guarantees…
This work studies the design problem of feedback stabilizers for discrete-time systems with input delays. A backstepping procedure is proposed for disturbance-free discrete-time systems. The feedback law designed by using backstepping…
Ensuring safety through set invariance has proven to be a valuable method in various robotics and control applications. This paper introduces a comprehensive framework for the safe probabilistic invariance verification of both discrete- and…