Related papers: The General Solution for Affine Control Systems on…
We complete the program for determining the full automorphism groups of all parafermion vertex operator algebras associated with simple Lie algebras and positive integral levels. We show that the full automorphism group of the parafermion…
This article describes the control behavior of any linear control systems on the group of proper motions $SE(2)$. It characterizes the controllability property and the control sets of the system.
Control systems of interest are often invariant under Lie groups of transformations. For such control systems, a geometric framework based on Lie symmetry is formulated, and from this a sufficient condition for dynamic feedback…
We obtain the list of automorphism groups for smooth plane sextic curves over an algebraically closed field K of characteristic p=0 or p>21. Moreover, we assign to each group a geometrically complete family over K describing its…
We propose a method to compute optimal control paths for autonomous vehicles deployed for the purpose of inferring a velocity field. In addition to being advected by the flow, the vehicles are able to effect a fixed relative speed with…
The problem of motion planning for affine control systems consists of designing control inputs that drive a system from a well-defined initial to final states in a desired amount of time. For control systems with drift, however,…
We develop an alternative view on the concept of connections over a vector bundle map, which consists of a horizontal lift procedure to a prolonged bundle. We further focus on prolongations to an affine bundle and introduce the concept of…
A Lie algebra structure on variation vector fields along an immersed curve in a $2$-dimensional real space form is investigated. This Lie algebra particularized to plane curves is the cornerstone in order to define a Hamiltonian structure…
We describe a method to analyze and decompose the dynamics of a control system on a Lie group subject to symmetries. The method is based on the concept of generalized Young symmetrizers of representation theory. It naturally applies to the…
We consider a class of optimal control problems on networks that generically permits a reduction to a universal set of reference problems without differential constraints that may be solved analytically. The derivation shows that input…
Let $\mathcal{X}$ be an irreducible algebraic curve defined over a finite field $\mathbb{F}_q$ of characteristic $p>2$. Assume that the $\mathbb{F}_q$-automorphism group of $\mathcal{X}$ admits as an automorphism group the direct product of…
This paper is devoted to a study of linear, differential and topological classifications for linear controlled systems governed by ordinary differential equations. The necessary and sufficient conditions for the linear and topological…
Suppose that a Lie algebra $L$ admits a finite Frobenius group of automorphisms $FH$ with cyclic kernel $F$ and complement $H$ of order 2, such that the fixed-point subalgebra of $F$ is trivial and the fixed-point subalgebra of $H$ is…
The purpose of this paper is to list the refined Humbert invariants for a given automorphism group of a curve $C/K$ of genus 2 over an algebraically closed field $K$ with characteristic $0$. This invariant is an algebraic generalization of…
In this article, we study the set of all solutions of linear differential equations using Hurwitz series. We first obtain explicit recursive expressions for solutions of such equations and study the group of differential automorphisms of…
Some simple examples from quantum physics and control theory are used to illustrate the application of the theory of Lie systems. We will show, in particular, that for certain physical models both of the corresponding classical and quantum…
We study synchronization of heterogeneous control-affine nonlinear agents interconnected through diffusive (relative-output) measurements. We separate the design into an edge-space step, specifying a stabilizing model evolution for relative…
For a curve $X$ of genus $>1$ defined over a finite field, we present a criterion which allows us to state the non existence of automorphisms of order a power of a rational prime. We show how this criterion can be used to determine the…
We classify the affine connections on compact orientable surfaces for which the pseudogroup of local isometries acts transitively. We prove that such a connection is either torsion-free and flat, the Levi-Civita connection of a Riemannian…
We study the existence of a natural `linearisation' process for generalised connections on an affine bundle. It is shown that this leads to an affine generalised connection over a prolonged bundle, which is the analogue of what is called a…