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Sen, M.De La Korean Mathematical Society 2001 대한수학회보 Vol.38 No.1
This note presents a an indirect adaptive control scheme for first-order continuous-time systems. The estimated plant model is controllable and then the adaptive scheme is free from singularities. The singularities are avoided through a modification of the estimated plant parameter vector so that its associated Sylvester matrix is guaranteed to be nonsingular. That properties is achieved by ensuring that the absolute value of its determinant does not lie below a positive threshold. A modification scheme based on the achievement of a modified diagonally dominant Sylvester matrix of the parameter estimates is also given as an alternative method. This diagonal dominance is achieved through estimates modification as a way to guarantee the controllability of the modified estimated model when a controllability measure of the ‘a priori’ estimated model fails. In both schemes, the use of a hysteresis switching function for the modification of the estimates is not required to ensure the nonsingularity of the Sylvester matrix of the estimates.
M. De la Sen 대한수학회 2003 대한수학회보 Vol.40 No.2
This note presents sufficient conditions forLyapunov's stability and instability of a class of nonlinearnonautonomous second-order ordinary differential equations. Such aclass includes as particular cases a remarkably large number ofdifferential equations with specific physical applications. Twosuccessive nonlinear transformations are applied to the originaldifferential equation in order to convert it into a moreconvenient form for stability analysis purposes. The obtainedstability / instability conditions depend closely on theparameterization of the original differential equation.
Common Fixed Points of Generalized Rational Type Cocyclic Mappings in Multiplicative Metric Spaces
Abbas, Mujahid,De la Sen, Manuel,Nazir, Talat Hindawi Limited 2015 Discrete dynamics in nature and society Vol.2015 No.-
<P>The aim of this paper is to present fixed point result of mappings satisfying a generalized rational contractive condition in the setup of multiplicative metric spaces. As an application, we obtain a common fixed point of a pair of weakly compatible mappings. Some common fixed point results of pair of rational contractive types mappings involved in cocyclic representation of a nonempty subset of a multiplicative metric space are also obtained. Some examples are presented to support the results proved herein. Our results generalize and extend various results in the existing literature.</P>
Analysis of Discrete Time Schemes for Milling Forces Control under Fractional Order Holds
Luis Rubio,Manuel de la Sen,Andrew Peter Longstaff,Alan Myers 한국정밀공학회 2013 International Journal of Precision Engineering and Vol. No.
In this paper, discrete time model reference control schemes for practical milling using different discretization of the continuous-time plant are presented. First, a basic controller scheme is addressed where a fractional order hold with pre-fixed value of the gain is used. Secondly, a multi-model scheme, which outputs different discretization in parallel with the continuous-time milling system transfer function under a fractional order hold (FROH) of correcting β ∈ [−1, 1], is dealt with. Then, an intelligent design framework is designed as a supervisory scheme with two hierarchical levels in order to find the most appropriate value for the gain β. For choosing the value of β, a tracking performance index is designed. It evaluates each pre-defined discretization of the continuous time milling transfer function and the scheme chooses the one with the smallest value of the index in order to generate the real control input to the plant. Two different methods of adjusting this value are presented and discussed. The first one selects a β-value among a fixed pre-defined set of possible values, while the second one the value of β is updated by adding or subtracting a small quantity.
FIXED POINT THEOREMS FOR CONVEX MINIMIZATION PROBLEMS IN COMPLEX VALUED CAT(0) SPACES
Godwin Amechi Okeke,Mujahid Abbas,Manuel de la Sen 경남대학교 기초과학연구소 2020 Nonlinear Functional Analysis and Applications Vol.25 No.4
In this paper, we introduce the concept of a complex valued CAT(0) space andpropose a new proximal point algorithm for certain nonlinear operators satisfying rationalexpressions in the framework of complex valued CAT(0) spaces. We prove existence of fixed point of these nonlinear mappings in such spaces. And we prove strong and -convergence of the iterative sequence generated through our proposed algorithm to the minimizer of aconvex function and the xed point of these mappings. We show that the new iterative algorithm converges faster than the modified Mann-type and Ishikawa-type proximal point algorithms.
Digital Inverse Model Control Using Generalised Holds With Extensions to the Adaptive Case
Asier Ibeas,Pedro Balaguer,Carles Pedret,Manuel de la Sen 제어·로봇·시스템학회 2010 International Journal of Control, Automation, and Vol.8 No.4
In this paper, a digital implementation of an inverse-model based control scheme is proposed using Generalised Sampling and Hold Functions. The implementation of the controller using this kind of holds allows overcoming the difficulties related to the presence of unstable zeros in the continuous-time model and the usual appearance of unstable discretisation zeros in the discrete model when a ZOH is applied. The Generalised Sampling and Hold Functions allows obtaining a discrete model of the plant with all its zeros stable which allows realizing an exact inverse model of the plant in comparison to the use of a classical ZOH which only allows, in general, an approximate inversion of the plant. The proposed approach is then extended to the adaptive case where the stability and tracking properties of the general scheme are fully proved. Simulation examples showing the scope and application of the method are also presented.