Related papers: A Trajectory-Based Approach to Discrete-Time Flatn…
We use a generic notion of flatness in the enriched context to define various completions of metric spaces -- enrichments over [0,\infty] -- and preorders -- enrichments over 2. We characterize the weights of colimits commuting in…
Bifurcations are one of the most remarkable features of dynamical systems. Corral et al. [Sci. Rep. 8(11783), 2018] showed the existence of scaling laws describing the transient (finite-time) dynamics in discrete dynamical systems close to…
Because of their occasional need to return to shallow points in a search tree, existing backtracking methods can sometimes erase meaningful progress toward solving a search problem. In this paper, we present a method by which backtrack…
We discuss integrable discretizations of 3-dimensional cyclic systems, that is, orthogonal coordinate systems with one family of circular coordinate lines. In particular, the underlying circle congruences are investigated in detail, and…
We revisit the problem of computing (robust) controlled invariant sets for discrete-time linear systems. Departing from previous approaches, we consider implicit, rather than explicit, representations for controlled invariant sets.…
In this paper, we propose a new constraint, called shift-consistency, for solving matrix/tensor completion problems in the context of recommender systems. Our method provably guarantees several key mathematical properties: (1) satisfies a…
This paper is concerned with the decoupling of delayed linear forward-backward stochastic differential equations (D-FBSDEs), which is much more involved than the delay-free case due to the infinite dimension caused by the delay. A new…
Discrete-time models are very convenient to simulate a nonlinear system on a computer. In order to build the discrete-time simulation models for the nonlinear feedback systems (which is a very important class of systems in many…
Motivated by the normal form of a fast-slow ordinary differential equation exhibiting a pitchfork singularity we consider the discrete-time dynamical system that is obtained by an application of the explicit Euler method. Tracking…
We present a discrete-time formulation for the autonomous learning conjecture. The main feature of this formulation is the possibility to apply the autonomous learning scheme to systems in which the errors with respect to target functions…
Data-driven control offers a powerful alternative to traditional model-based methods, particularly when accurate system models are unavailable or prohibitively complex. While existing data-driven control methods primarily aim to construct…
We will show that there is a universal connection between the achievable closed-loop dynamics and the corresponding feedback controller that produces it. This connection shows promise to lead to new methods for robust nonlinear control in…
This paper investigates the dynamic properties of planar slider-pusher systems as a motion primitive in manipulation tasks. To that end, we construct a differential kinematic model deriving from the limit surface approach under the…
Time-discrete dynamical systems on a finite state space have been used with great success to model natural and engineered systems such as biological networks, social networks, and engineered control systems. They have the advantage of being…
Most methods for modelling dynamics posit just two time scales: a fast and a slow scale. But many applications, including many in continuum mechanics, possess a wide variety of space-time scales; often they possess a continuum of space-time…
A highly comparative, feature-based approach to time series classification is introduced that uses an extensive database of algorithms to extract thousands of interpretable features from time series. These features are derived from across…
Temporal logics over finite traces have recently seen wide application in a number of areas, from business process modelling, monitoring, and mining to planning and decision making. However, real-life dynamic systems contain a degree of…
To study discrete dynamical systems of different types --- deterministic, statistical and quantum --- we develop various approaches. We introduce the concept of a system of discrete relations on an abstract simplicial complex and develop…
Differentially flat models are frequently used to design feedforward controllers for electromechanical systems. However, control performance depends on model accuracy, which makes feedback imperative. This paper presents a control scheme…
While compactness is an essential assumption for many results in dynamical systems theory, for many applications the state space is only locally compact. Here we provide a general theory for compactifying such systems, i.e. embedding them…