Related papers: A Comparison Between Lie Group- and Lie Algebra- B…
Hypergeometric class equations are given by second order differential operators in one variable whose coefficient at the second derivative is a polynomial of degree $\leq2$, at the first derivative of degree $\leq1$ and the free term is a…
Using techniques of deformation (bi)quantization we establish a non-canonical algebra isomorphism between the deformed reduction algebra and the invariant differential operators on G/H. Further results concerning other deformations of these…
Function-correcting codes are a coding framework designed to minimize redundancy while ensuring that specific functions or computations of encoded data can be reliably recovered, even in the presence of errors. The choice of metric is…
This paper contains a fully geometric formulation of the General Equation for Non-Equilibrium Reversible-Irreversible Coupling (GENERIC). Although GENERIC, which is the sum of Hamiltonian mechanics and gradient dynamics, is a framework…
We study geometric representation theory of Lie algebroids. A new equivalence relation for integrable Lie algebroids is introduced and investigated. It is shown that two equivalent Lie algebroids have equivalent categories of infinitesimal…
We study the Ricci tensor of left-invariant pseudoriemannian metrics on Lie groups. For an appropriate class of Lie groups that contains nilpotent Lie groups, we introduce a variety with a natural $\mathrm{GL}(n,\mathbb{R})$ action, whose…
Let us consider a linear control system \Sigma on a connected Lie group G. It is known that the accessibility set A from the identity e is in general not a semigroup. In this article we associate a new algebraic object S to \Sigma which…
This article develops and proposes a geometric nonlinear proportional-integral-derivative (PID) type tracking control scheme on the Lie group of rigid body rotations, SO(3). Like PD-type attitude tracking control schemes that have been…
External and internal convertible (EIC) form-based motion control is one of the effective designs of simultaneously trajectory tracking and balance for underactuated balance robots. Under certain conditions, the EIC-based control design…
Controlling marine vehicles in challenging environments is a complex task due to the presence of nonlinear hydrodynamics and uncertain external disturbances. Despite nonlinear model predictive control (MPC) showing potential in addressing…
In this paper, we present a geometric approach for computing the controlled invariant set of a continuous-time control system. While the problem is well studied for in the ellipsoidal case, this family is quite conservative for constrained…
Function-Correcting Codes (FCCs) are a novel class of codes designed to protect function evaluations of messages against errors while minimizing redundancy. A theoretical framework for systematic FCCs to channels matched to the Lee metric…
Inverse classification is the process of perturbing an instance in a meaningful way such that it is more likely to conform to a specific class. Historical methods that address such a problem are often framed to leverage only a single…
This paper develops a new mathematical framework that enables nonparametric joint semantic and geometric representation of continuous functions using data. The joint embedding is modeled by representing the processes in a reproducing kernel…
We start from a noncompact Lie algebra isomorphic to the Dirac algebra and relate this Lie algebra in a brief review to low energy hadron physics described by the compact group SU(4). This step permits an overall physical identification of…
Hamilton-Jacobi reachability methods for safety-critical control have been well studied, but the safety guarantees derived rely on the accuracy of the numerical computation. Thus, it is crucial to understand and account for any inaccuracies…
We consider left-invariant distances $d$ on a Lie group $G$ with the property that there exists a multiplicative one-parameter group of Lie automorphisms $(0, \infty)\rightarrow\mathtt{Aut}(G)$, $\lambda\mapsto\delta_\lambda$, so that $…
A proportional iterative learning control (P-ILC) for linear models of an existing hybrid stroke rehabilitation scheme is implemented for elbow extension/flexion during a rehabilitative task. Owing to transient error growth problem of…
Fringing field has to be taken into account in the formulation of electrostatic parallel-plate actuators when the gap separating the electrodes is comparable to the geometrical dimensions of the moving plate. Even in this case, the existing…
The geometric theory of Lie systems is used to establish integrability conditions for several systems of differential equations, in particular some Riccati equations and Ermakov systems. Many different integrability criteria in the…