Optimum design of discrete-time differentiators via semi-infinite programming approach

Ho, Charlotte Yuk-Fan and Ling, Bingo Wing-Kuen and Liu, Yan-Qun and Tam, Peter Kwong-Shun and Teo, Kok-Lay (2008) Optimum design of discrete-time differentiators via semi-infinite programming approach. IEEE Transactions on Instrumentation and Measurement, 57 (10). pp. 2226-2230. ISSN 0018-9456

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Full text URL: http://dx.doi.org/10.1109/TIM.2008.922090

Abstract

In this paper, a general optimum full band high order discrete-time differentiator design problem is formulated as a peak constrained least square optimization problem.
That is, the objective of the optimization problem is to minimize the total weighted square error of the magnitude response subject to the peak constraint of the weighted
error function. This problem formulation provides a great flexibility for the tradeoff between the ripple energy and the ripple magnitude of the discrete-time differentiator.
The optimization problem is actually a semi-infinite programming problem. Our recently developed dual parametrization algorithm is applied for solving the problem. The main advantage of employing the dual parameterization algorithm for solving the problem is the guarantee of the convergence of the algorithm and the obtained solution being the global optimal solution that satisfies the corresponding continuous constraints. Moreover, the computational cost of the algorithm is lower than that of algorithms implementing the semi-definite programming approach.

Item Type:Article
Additional Information:In this paper, a general optimum full band high order discrete-time differentiator design problem is formulated as a peak constrained least square optimization problem. That is, the objective of the optimization problem is to minimize the total weighted square error of the magnitude response subject to the peak constraint of the weighted error function. This problem formulation provides a great flexibility for the tradeoff between the ripple energy and the ripple magnitude of the discrete-time differentiator. The optimization problem is actually a semi-infinite programming problem. Our recently developed dual parametrization algorithm is applied for solving the problem. The main advantage of employing the dual parameterization algorithm for solving the problem is the guarantee of the convergence of the algorithm and the obtained solution being the global optimal solution that satisfies the corresponding continuous constraints. Moreover, the computational cost of the algorithm is lower than that of algorithms implementing the semi-definite programming approach.
Keywords:Discrete-time differentiators, Semi-infinite programming, Dual parameterization algorithm, Peak constrained least square approach, Eigen approach, Remez approach, Semi-definite programming approach
Subjects:H Engineering > H660 Control Systems
H Engineering > H661 Instrumentation Control
H Engineering > H310 Dynamics
Divisions:College of Science > School of Engineering
ID Code:2692
Deposited By: Bev Jones
Deposited On:13 Jun 2010 13:33
Last Modified:13 Mar 2013 08:39

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