A novel compact piecewise-linear representation: Research Articles

Authors:
Chengtao Wen;Shuning Wang;Hao Zhang;Muhammadnaid Junaid Khan
Affiliations:
Institute of Systems Engineering, Department of Automation, Tsinghua University, Beijing, 100084, PR China;Institute of Systems Engineering, Department of Automation, Tsinghua University, Beijing, 100084, PR China;Institute of Systems Engineering, Department of Automation, Tsinghua University, Beijing, 100084, PR China;Institute of Systems Engineering, Department of Automation, Tsinghua University, Beijing, 100084, PR China
Venue:
International Journal of Circuit Theory and Applications
Year:
2005

Citing 0
Cited 3

Brief paper: Identification of dynamic systems using Piecewise-Affine basis function models

Automatica (Journal of IFAC)
A max-piecewise-linear neural network for function approximation

Neurocomputing
Analytical expression of explicit MPC solution via lattice piecewise-affine function

Automatica (Journal of IFAC)

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Abstract

A new compact MAX representation for 2-D continuous piecewise-linear (PWL) functions is developed in this paper. The representation is promising since it can be easily generalized into higher dimensions. We also establish the explicit functional form of basis function and demonstrate that the proposed basis function is the elementary ‘building block’ from which a fully general 2-D PWL function can be constructed. In addition, we reveal the relationship of basis function with minimal degenerate intersection and Hinging Hyperplane, which shows that the MAX model can unify Chua's canonical expression, Li's representation, lattice PWL function and Bremann's Hinging Finding Algorithm into one common theoretical framework. Copyright © 2005 John Wiley & Sons, Ltd.Project jointly supported by National Natural Science Foundation of China(60374061) and 973 program of China (2002CB312200).