• Bulletin of the Korean Mathematical Society
• /
• v.50 no.6
• /
• pp.1781-1797
• /
• 2013

Let x : $M{\rightarrow}\mathbb{R}^n$ be an n - 1-dimensional hypersurface in $\mathbb{R}^n$, L be the Laguerre Blaschke tensor, B be the Laguerre second fundamental form and $D=L+{\lambda}B$ be the Laguerre para-Blaschke tensor of the immersion x, where ${\lambda}$ is a constant. The aim of this article is to study Laguerre Blaschke isoparametric hypersurfaces and Laguerre para-Blaschke isoparametric hypersurfaces in $\mathbb{R}^n$ with three distinct Laguerre principal curvatures one of which is simple. We obtain some classification results of such isoparametric hypersurfaces.

• Bulletin of the Korean Mathematical Society
• /
• v.53 no.3
• /
• pp.875-884
• /
• 2016

Let x : $^{Mn-1}{\rightarrow}{\mathbb{R}}^n$ ($n{\geq}4$) be an umbilical free hyper-surface with non-zero principal curvatures. Then x is associated with a Laguerre metric g, a Laguerre tensor L, a Laguerre form C, and a Laguerre second fundamental form B, which are invariants of x under Laguerre transformation group. We denote the Laguerre scalar curvature by R and the trace-free Laguerre tensor by ${\tilde{L}}:=L-{\frac{1}{n-1}}tr(L)g$. In this paper, we prove a local classification result under the assumption of parallel Laguerre form and an inequality of the type $${\parallel}{\tilde{L}}{\parallel}{\leq}cR$$ where $c={\frac{1}{(n-3){\sqrt{(n-2)(n-1)}}}$ is appropriate real constant, depending on the dimension.

• 제어로봇시스템학회:학술대회논문집
• /
• 2005.06a
• /
• pp.1189-1191
• /
• 2005

This paper introduces the least-squares order-recursive lattice (LSORL) Laguerre smoother that has order-recursive smoothing structure based on the Laguerre signal representation. The LSORL Laguerre smoother gives excellent performance for a channel equalization problem with smaller order of tap-weights than its counterpart algorithm based on the transversal filter structure. Simulation results show that the LSORL Laguerre smoother gives better performance than the LSORL transversal smoother.

• Advances in robotics research
• /
• v.2 no.1
• /
• pp.99-112
• /
• 2018

The main contribution of this work is the design of a field programmable gate array (FPGA) based ARX-Laguerre proportional-integral observation (PIO) system for fault detection and identification (FDI) in a multi-input, multi-output (MIMO) nonlinear uncertain dynamical robot manipulators. An ARX-Laguerre method was used in this study to dynamic modeling the robot manipulator in the presence of uncertainty and disturbance. To address the challenges of robustness, fault detection, isolation, and estimation the proposed FPGA-based PI observer was applied to the ARX-Laguerre robot model. The effectiveness and accuracy of FPGA based ARX-Laguerre PIO was tested by first three degrees of the freedom PUMA robot manipulator, yielding 6.3%, 10.73%, and 4.23%, average performance improvement for three types of faults (e.g., actuator fault, sensor faults, and composite fault), respectively.

• Korean Journal of Mathematics
• /
• v.16 no.1
• /
• pp.51-55
• /
• 2008

Let f be an analytic function with a simple zero in the reals or the complex numbers. An extraneous fixed-point of an iteration function is a fixed-point different from a zero of f. We prove that all extraneous fixed-points of Laguerre-like iteration functions and general Laguerre-like functions are repulsive.

• Journal of the Korean Mathematical Society
• /
• v.48 no.5
• /
• pp.913-926
• /
• 2011

The family of q-Laguerre polynomials $\{L_n^{(\alpha)}({\cdot};q)\}_{n=0}^{\infty}$ is usually defined for 0 < q < 1 and ${\alpha}$ > -1. We extend this family to a new one in which arbitrary complex values of the parameter ${\alpha}$ are allowed. These so-called generalized q-Laguerre polynomials fulfil the same three term recurrence relation as the original ones, but when the parameter ${\alpha}$ is a negative integer, no orthogonality property can be deduced from Favard's theorem. In this work we introduce non-standard inner products involving q-derivatives with respect to which the generalized q-Laguerre polynomials $\{L_n^{(-N)}({\cdot};q)\}_{n=0}^{\infty}$, for positive integers N, become orthogonal.

• Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
• /
• v.29 no.2
• /
• pp.40-46
• /
• 2015

This paper presents a method of controlling a three-phase VSI (Voltage Source Inverter) using MPC (Model Predictive Control) designed using Laguerre functions. It also provides a model of the three-phase VSI and its resistive-inductive load and then an overview of MPC design using Laguerre functions. The biggest challenge in using MPC is the high number of computations involved, which makes online implementation difficult. On the other hand, the LMPC (Laguerre Model Predictive Control) reduces the number of computations made and so online implementation becomes possible where traditional MPC would be unteneble. The simulation results from MATLAB are also provided.

• Journal of Power Electronics
• /
• v.16 no.2
• /
• pp.598-609
• /
• 2016

The good control performance of permanent magnet linear synchronous motor (LSM) drive systems is difficult to achieve using linear controllers because of uncertainty effects, such as fictitious forces. A backstepping control system using adaptive modified recurrent Laguerre orthogonal polynomial neural network uncertainty observer (OPNNUO) is proposed to increase the robustness of LSM drive systems. First, a field-oriented mechanism is applied to formulate a dynamic equation for an LSM drive system. Second, a backstepping approach is proposed to control the motion of the LSM drive system. With the proposed backstepping control system, the mover position of the LSM drive achieves good transient control performance and robustness. As the LSM drive system is prone to nonlinear and time-varying uncertainties, an adaptive modified recurrent Laguerre OPNNUO is proposed to estimate lumped uncertainties and thereby enhance the robustness of the LSM drive system. The on-line parameter training methodology of the modified recurrent Laguerre OPNN is based on the Lyapunov stability theorem. Furthermore, two optimal learning rates of the modified recurrent Laguerre OPNN are derived to accelerate parameter convergence. Finally, the effectiveness of the proposed control system is verified by experimental results.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
• /
• v.18 no.9
• /
• pp.1023-1029
• /
• 2007

In this paper, we propose the method to solve the BLT equations using Laguerre polynomials in time domain. The solution of BLT equations is obtained by recursive, differential and integral properties of Laguerre polynomials. The verification of the proposed method is tested by applying it to the two-wired transmission line with resistors and capacitors, which is illuminated by the electromagnetic plane wave pulse. And the result is compared with the corresponding transient responses obtained from inverse fast Fourier transform(IFFT) of the frequency domain solutions of BLT equations.

• Communications of the Korean Mathematical Society
• /
• v.23 no.2
• /
• pp.201-209
• /
• 2008

In this paper we introduce two products of tempered distributions with positive support. These products are based in the Laguerre representation of distributions. We calculate some products as, $[{\delta}]x^{\lambda}_+={\delta}[x^{\lambda}_+]=0\;and\;[x^{\lambda}_+]x^{\mu}_+=x^{{\lambda}+{\mu}}_+$ for appropriate ${\lambda}$ and ${\mu}$.