PAPER TITLE (FONT SIZE 12; UPPERCASE)
A. B. Silva1, C. John2, R. S. Lee3 and S. Sharma4
1
Department of Mechatronics, Faculty of Engineering, South Asian Institute of Technology and Medicine (SAITM),
Sri Lanka. Email: silva@saitm.edu.lk
2
Harvard School of Engineering, Harvard University, USA, Email: john123@ seas.harvard.edu
3
Departments of Chemistry, National Taiwan University, Taiwan. Email: lee@ ntu.edu.tw
4
Department of Electrical Engineering, Indian Institute of Technology, India, Email: sharma@ieee.org
ABSTRACT
A novel approach for solving fuzzy model-based stability problems via evolutionary computation (EC)
is presented. Gain scheduling problem of a multi-model fuzzy system that satisfies the Lyapunov
stability criteria is solved. The generalized eigenvalue problem (GEVP) can be directly introduced to EC
in searching positive definite (PD) or positive semi-definite (PSD) matrices, by making a penalty for an
individual that violates the inequality condition in order to solve the nonlinear constraints or linear
matrix inequalities (LMIs). Four examples for illustrating the proposed methodology are included and
the results show the effectiveness. (Abstract Font Size: 10; Times New Roman; Line Spacing: Single)
Key words: Fuzzy logic, LMI, positive definite, nonlinear
1.
INTRODUCTION
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The many theoretical and practical models of
artificial intelligence (AI) are gleaned from
nature, either by observing human intelligent
behavior or by deriving algorithms from natural
systems. In AI, fuzzy logic and fuzzy set theory
provide a rich and meaningful addition to
standard logic, defining a useful rule base,
especially for the purpose of engineering control.
The basic idea of “fuzzy logic control” (FLC)
was suggested by Zadeh [1]. The first
implementation of an FLC was reported by
Mamdani and Assilian [2, 3]. (Paragraph Font
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2.
METHODOLOGY
2.1. Procedure for Analysis
The studied site was located in the Central
Taiwan and the total experiment area of this site
was 1.3 ha. Soils were contaminated with
combined metals and the total concentration in
the topsoil (0-15 cm) was 46-463 (Cr), 23-152
(Cu), 103-523 (Ni), and 202-958 (Zn) mg kg-1,
respectively. We selected 12 plant species from
33 plant species based on the result of small areaexperiment before the beginning of this large area
study. The selected 12 species are Rainbow pink
(Dianthus chinensis), Serissa (Serissa japonica),
French marigold (Tagetes patula), Chinese ixora
(Ixora chinensis Lam), Sunflower (Helianthus
annuus), Croton (Codialum variegatum),
Kalanchoe (Kalanchoe blossfeldiana), Garden
canna (Canna generalis spp.), Garden verbena
(Verbena hybrida), Purslane (Portulaca oloraua
Linn), Scandent Scheffera umbrella tree
(Schefflera arboricola Hayata), and Bojers spurge
(Euphorbia splendens), respectively eq. (01).
y  mx  c
(01)
Total area of 1.3ha was divided into 12 blocks
and one plant species is planted in one block
(0.1ha). At the 1st stage of large area-experiment,
total amounts of 12,000 seedlings were…
3.
RESULTS
The result indicated that the soil texture of the
contaminated site was silty clay. The CEC and
pH value of the topsoil was 13.2 cmol(+) kg-1
and in the levels of 5.6-7.2, respectively. After
planting in this combined metals-contaminated
site for 33 d, these 12 plant species have no any
toxic symptoms of metals. Figure 1 shows the
initial and final concentration of Cr, Cu, Ni, and
International Research Symposium on Engineering Advancements 2016 (RSEA 2016)
SAITM, Malabe, Sri Lanka
Zn in the shoots of 12 plant species. Except for
Cu concentration of Chinese ixora and Purslane
in shoot, the other 10 plant species have low
metal concentration before planting (initial in
Fig. 1). The initial metal concentration in their
shoots was <20 (Cr), <10 (Cu), <5 (Ni), and <50
(Zn) mg kg-1, respectively. Based on the
experimental results and conditions of this study
(10,000 plants/ha/species), we can probably
calculate the total phytoextraction capacity of
different metals.
Figure 1 shows experience of an individual's state
of mind as interacting with biochemical (internal)
and
environmental
(external)
influences.
Moreover, Table 1 shows the values of the
experiment 1.
addition to those, one of the advantages of this
algorithm is that the LMIs of the fuzzy modelbased controller scheme can be directly solved
without using any particular software tool for
solving LMIs. On the other hand, any of EC
algorithms produces a sub-optimal solution and
we may not even know whether it has a solution
or not.
5.
REFERENCES
[1] L. A. Zadeh, “Fuzzy Sets,” Journal of
Information and Control, vol. 8, pp. 338-353,
1965.
[2] E. H. Mamdani, "Fuzzy sets, 20 years of fuzzy
control: experiences gained and lessons learnt,"
in: Proceedings of IEEE International Conference
on fuzzy systems, pp. 339–344, 1993.
[3] A. Jadbabaaie, “Robust, Non-Fragile
Controller Synthesis Using Model-Based
Systems: A Linear Matrix Inequality Approach,”
Master Thesis, University of Mexico, USA,
October 1997.
[4] X. Ma, Z. Sun, and Y. He, “Analysis and
Design of Fuzzy Controllers and Observers,”
IEEE Transactions on Fuzzy Systems, vol. 6, no.
1, pp. 41–51, 1998.
[5] L. A. Zadeh, “Fuzzy logic,” IEEE Computer
Magazine, pp. 83–93, 1988.
(Reference List Font Size: 10; Times New
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Figure 1: State of mind as interacting with
biochemical (Figure Caption Font Size: 9; Times
New Roman; Line Spacing: Single; bold)
Table 1: Title…(Table Caption Font Size: 9; Times
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Sample 1
1
2
4.
State
Active
Neutral
Value
12.3 [J/m2]
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CONCLUSION
An EC based algorithm has a number of
advantages. It can quickly scan a vast solution
set. Moreover, this EC approach is appropriate
for handling any number of constraints of the
control system, in addition to the stability criteria
guaranteed by the Lyapunov non-linear
constraints or LMIs. For an example, if the
designer wants to keep the gains at high (or law)
it can be easily achieved by setting upper and
lower limits of the genes of EC program. In
International Research Symposium on Engineering Advancements 2016 (RSEA 2016)
SAITM, Malabe, Sri Lanka