An evolutionary algorithm based approach for selection of topologies in hierarchical fuzzy systems

Abstract

EVWUDFW²This paper presents an evolutionary algorithm based approach for selection of topologies in hierarchical fuzzy systems (HFS). The different topologies of HFS for a given dynamical system such as inverted pendulum are investigated and analysed to address the problem of how input configuration in multi-layered structure affects the controller performance. The experiments are conducted to test controller performance for different topologies of the hierarchical fuzzy system. The impact of different topologies on control process is discussed. The results from case study (inverted pendulum) can be extended to other dynamical systems, in particular to a robotic manipulator. , ,1752'8&7,21 ,QFUHDVLQJ WKH QXPEHU RI LQSXW YDULDEOHV RU LQSXW IX]]\ VHWV UHVXOWV LQ DQ H[SRQHQWLDO LQFUHDVH LQ FRPSOH[LW\ RI WKH UXOH EDVH 7KH GHFRPSRVLWLRQ RI WKH V\VWHP LQWR KLHUDUFKLFDO IX]]\ V\VWHP LV LQWHQGHG WR UHGXFH WKH VL]H RI WKH UXOH EDVH ZKLOH PDLQWDLQLQJ DQ DGHTXDWH DFFXUDF\ /D\HUHG IX]]\ ORJLF V\VWHPV XWLOL]H WKH PRGXODULW\ FKDUDFWHULVLQJ PDQ\ SK\VLFDO V\VWHPV DQG WKHLU PDWKHPDWLFDO PRGHOV 7KH RXWSXW LQÀ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µ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

Selection and impact of different topologies in multi-layered hierarchical fuzzy systems

“…In this paper (extended version of [9,10]) different topologies of HFS for a given dynamical system (the inverted pendulum system) are investigated and analysed to address the problem of how input configuration in multilayered structure affects the controller performance. The research presented in this paper has originated in research work by Stonier et al [11].…”