Related papers: Discrete-Time Approximations of Fliess Operators
In this paper, we present a new discrete-time Fast Terminal Sliding Mode (FTSM) controller for mirror-based pointing systems. We first derive the decoupled model of those systems and then estimate the parameters using a nonlinear…
In this paper a spline based integral approximation is utilized to propose a sequence of approximations to the error function that converge at a significantly faster manner than the default Taylor series. The approximations can be improved…
Nonlinear (systems of) ordinary differential equations (ODEs) are common tools in the analysis of complex one-dimensional dynamic systems. In this paper we propose a smoothing approach regularized by a quasilinearized ODE-based penalty in…
This paper presents the first discrete-time distributed algorithm to track the tightest ellipsoids that outer approximates the global dynamic intersection of ellipsoids. Given an undirected network, we consider a setup where each node…
During the past three decades, the advantageous concept of the Green's function has been extended from linear systems to nonlinear ones. At that, there exist a rigorous and an approximate extensions. The rigorous extension introduces the…
We describe a procedure based on the iteration of an initial function by an appropriated operator, acting on continuous functions, in order to get a fixed point. This fixed point will be a calibrated subaction for the doubling map on the…
In this paper, we examine the problem of approximating a general linear dimensionality reduction (LDR) operator, represented as a matrix $A \in \mathbb{R}^{m \times n}$ with $m < n$, by a partial circulant matrix with rows related by…
In quantum mechanics, the Rosen-Zener model represents a two-level quantum system. Its generalization to multiple degenerate sets of states leads to larger non-autonomous linear system of ordinary differential equations (ODEs). We propose a…
In this document, we present key findings in structured matrix approximation theory, with applications to the regressive representation of dynamic financial processes. Initially, we explore a comprehensive approach involving generic…
We present an implicit relaxation scheme for the simulation of compressible flows in all Mach number regimes based on a Jin Xin relaxation approach. The main features of the proposed scheme lie in its simplicity and effectiveness. Thanks to…
In the framework of Model Predictive Control (MPC), the control input is typically computed by solving optimization problems repeatedly online. For general nonlinear systems, the online optimization problems are non-convex and…
This note details the development of a discrete-time diffusion process to approximate the midnight customer count process in a $M_\textrm{per}/\textrm{Geo}_\textrm{2timeScale}/N$ system. We prove a limit theorem that supports this diffusion…
This paper presents a study of the Koopman operator theory and its application to optimal control of a multi-robot system. The Koopman operator, while operating on a set of observation functions of the state vector of a nonlinear system,…
Approximation properties of periodic quasi-projection operators with matrix dilations are studied. Such operators are generated by a sequence of functions $\varphi_j$ and a sequence of distributions/functions $\widetilde{\varphi}_j$. Error…
We propose a general method for optimization with semi-infinite constraints that involve a linear combination of functions, focusing on the case of the exponential function. Each function is lower and upper bounded on sub-intervals by…
Symbolic models have been recently used as a sound mathematical formalism for the formal verification and control design of purely continuous and hybrid systems. In this paper we propose a sequence of symbolic models that approximates a…
Based on explicit computations, various concepts of discrete time scattering theory are reviewed, discussed, and illustrated. The dynamics are taking place on a discrete half-space. All operators are represented graphically. The expressions…
We describe an approximate rational arithmetic with round-off errors (both absolute and relative) controlled by the user. The rounding procedure is based on the continued fraction expansion of real numbers. Results of computer experiments…
In this paper, we contribute operator-splitting methods improved by the Zassenhaus product for the numerical solution of linear partial differential equations. We address iterative splitting methods, that can be improved by means of the…
Discrete-time affine processes are widely used in finance and economics and encompass count, positive, and nonnegative-valued processes. This paper develops near-unit-root asymptotic theory for this class of models. Unlike linear AR(1)…