Related papers: Quotients of affine connection control systems
This paper introduces the notion of an excellent quotient, which is stronger than a universal geometric quotient. The main result is that for an action of a connected solvable group $G$ on an affine scheme Spec$(R)$ there exists a…
Hybrid systems, and especially piecewise affine (PWA) systems, are often used to model gene regulatory networks. In this paper we elaborate on previous work about control problems for this class of models, using also some recent results…
Correlation matrices are used in many domains of neurosciences such as fMRI, EEG, MEG. However, statistical analyses often rely on embeddings into a Euclidean space or into Symmetric Positive Definite matrices which do not provide intrinsic…
The quotient operation, which is dual to the composition, is crucial in specification theories as it allows the synthesis of missing specifications and thus enables incremental design. In this paper, we consider a specification theory based…
Substructural type systems, such as affine (and linear) type systems, are type systems which impose restrictions on copying (and discarding) of variables, and they have found many applications in computer science, including quantum…
This work delves into the {\it quotient of an affine semigroup by a positive integer}, exploring its intricate properties and broader implications. We unveil an {\it associated tree} that serves as a valuable tool for further analysis.…
This paper deals with fractional-order controlled systems and fractional-order controllers in the discrete domain. The mathematical description by the fractional difference equations and properties of these systems are presented. A…
The affine coherent states quantization is a promising integral quantization of Hamiltonian systems when the phase space includes at least one conjugate pair of variables which takes values from a half-plane. Such a situation is common for…
This paper presents a coordinate-free formulation of virtual holonomic constraints for underactuated Lagrangian control systems on Riemannian manifolds. It is shown that when a virtual constraint enjoys a regularity property, the…
This paper considers control systems defined on Lie algebroids. After deriving basic controllability tests for general control systems, we specialize our discussion to the class of mechanical control systems on Lie algebroids. This class of…
In this paper we give a self-contained treatment of finite group quotients of admissible (formal) schemes and adic spaces that are locally topologically finite type over a locally strongly noetherian adic space.
The purpose of this paper is to use the framework of Lie algebroids to study optimal control problems for affine connection control systems on Lie groups. In this context, the equations for critical trajectories of the problem are…
In this paper we use an affine connection formulation to study an optimal control problem for a class of nonholonomic, under-actuated mechanical systems. In particular, we aim at minimizing the norm-squared of the control input to move the…
The goal of this paper is to provide conditions under which a quantum stochastic differential equation (QSDE) preserves the commutation and anticommutation relations of the SU(n) algebra, and thus describes the evolution of an open n-level…
Qubits on solid state devices could potentially provide the rapid control necessary for developing scalable quantum information processors. Materials innovation and design breakthroughs have increased functionality and coherence of qubits…
A finite dimensional operator that commutes with some symmetry group admits quotient operators, which are determined by the choice of associated representation. Taking the quotient isolates the part of the spectrum supporting the chosen…
There is an abstract notion of connection in any tangent category. In this paper, we show that when applied to the tangent category of affine schemes, this recreates the classical notion of a connection on a module (and similarly, in the…
Complete controllability of degenerate quantum system using quantum accessor modeled as a qubit chain with nearest neighborhood coupling is investigated. Sufficient conditions on the length of accessor and the way of coupling between…
We consider the structure of classes of curves on a projective simply connected surface for which fundamental groups of the complements admit free quotients having rank greater than one with irreducible components belonging to a selected…
Even though organic conductors have complicated crystalline structure with low symmetry and large unit cell, band structure calculations predict multiband quasi-two dimensional electronic structure yielding very simple Fermi surface in most…