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Infinitesimal contraction analysis provides exponential convergence rates between arbitrary pairs of trajectories of a system by studying the system's linearization. An essentially equivalent viewpoint arises through stability analysis of a…
We consider the problem of planning a collision-free path of a robot in the presence of risk zones. The robot is allowed to travel in these zones but is penalized in a super-linear fashion for consecutive accumulative time spent there. We…
This note introduces a sufficient Linear Matrix Inequality (LMI) condition for the ultimate boundedness of a class of continuous-time dynamical systems with conic uncertain/nonlinear terms.
Girard's Light linear logic (LLL) characterized polynomial time in the proof-as-program paradigm with a bound on cut elimination. This logic relied on a stratification principle and a "one-door" principle which were generalized later…
In real world applications, uncertain parameters are the rule rather than the exception. We present a reachability algorithm for linear systems with uncertain parameters and inputs using set propagation of polynomial zonotopes. In contrast…
We consider the problem of system identification of partially observed linear time-invariant (LTI) systems. Given input-output data, we provide non-asymptotic guarantees for identifying the system parameters under general heavy-tailed noise…
We derive finite time error bounds for estimating general linear time-invariant (LTI) systems from a single observed trajectory using the method of least squares. We provide the first analysis of the general case when eigenvalues of the LTI…
Lattices are a popular field of study in mathematical research, but also in more practical areas like cryptology or multiple-input/multiple-output (MIMO) transmission. In mathematical theory, most often lattices over real numbers are…
Linear time-periodic (LTP) dynamical systems frequently appear in the modeling of phenomena related to fluid dynamics, electronic circuits, and structural mechanics via linearization centered around known periodic orbits of nonlinear…
Cuspidal robots are robots with at least two inverse kinematic solutions that can be connected by a singularity-free path. Deciding the cuspidality of generic 3R robots has been studied in the past, but extending the study to…
We survey the problem of deciding the stability or stabilizability of uncertain linear systems whose region of uncertainty is a polytope. This natural setting has applications in many fields of applied science, from Control Theory to…
We develop a new tool, namely polynomial and linear algebraic methods, for studying systems of word equations. We illustrate its usefulness by giving essentially simpler proofs of several hard problems. At the same time we prove extensions…
This work is devoted to the study of the relationships between graph theory and the qualitative analysis of ordinary differential equations, with a special focus on two-dimensional systems. In particular, we reinterpret classical results…
The problem of high-dimensional path-dependent optimal stopping (OS) is important to multiple academic communities and applications. Modern OS tasks often have a large number of decision epochs, and complicated non-Markovian dynamics,…
Assessment of the degree of boundedness/stability of multidimensional nonlinear systems with time-dependent and nonperiodic coefficients is an important problem in various applied areas which has no adequate resolution yet. Most of the…
In this paper, we consider the problem of computing robust controlled invariants for discrete-time monotone dynamical systems. We consider different classes of monotone systems depending on whether the sets of states, control inputs and…
This paper is devoted to the complexity analysis of a particular property, called "algebraic robustness" owned by all known symbolic methods of parametric polynomial equation solving (geometric elimination). It is shown that any parametric…
We show that the problem to decide whether two (convex) polytopes, given by their vertex-facet incidences, are combinatorially isomorphic is graph isomorphism complete, even for simple or simplicial polytopes. On the other hand, we give a…
We use the algebraic structure of cyclic codes and some properties of the discrete Fourier transform to give a reformulation of several classical bounds for the distance of cyclic codes, by extending techniques of linear algebra. We propose…
This paper takes a computational learning theory approach to a problem of linear systems identification. It is assumed that input signals have only a finite number k of frequency components, and systems to be identified have dimension no…