×

Direct adaptive fuzzy backstepping control for uncertain discrete-time nonlinear systems using noisy measurements. (English) Zbl 1358.93112

Summary: This paper presents a direct Adaptive Fuzzy Backstepping Control (AFBC) for multi-input multi-output uncertain discrete-time nonlinear systems. It is assumed that the systems are described by a discrete-time state equation with uncertainties to be viewed as the modeling errors and the unknown external disturbances, and the observation of the states is taken with independent measurement noises. The proposed direct AFBC is presented as follows. The proposed direct AFBC is assumed to be the fuzzy logic system by removing the explosion of complexity problem due to repeated computation of nonlinear functions at the first stage. Second, the number of the adjustable parameters is reduced by the fuzzy inference approach based on the extended single input rule modules. Third, the simplified weighted least squares estimator is constructed by reducing the computational burden of the estimation for the unmeasurable states and the adjustable parameters. The effectiveness of the proposed direct AFBC is illustrated through the simulation experiment of a simple numerical system.

MSC:

93C42 Fuzzy control/observation systems
93C40 Adaptive control/observation systems
93C41 Control/observation systems with incomplete information
93E24 Least squares and related methods for stochastic control systems
93C10 Nonlinear systems in control theory
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] DOI: 10.1016/j.fss.2006.12.012 · Zbl 1113.93068
[2] DOI: 10.1109/TFUZZ.2010.2046329
[3] DOI: 10.1080/00207721.2010.547631 · Zbl 1307.93217
[4] DOI: 10.1016/S0967-0661(97)10016-8
[5] DOI: 10.1109/9.100933 · Zbl 0768.93044
[6] Kokotovic, P.V., Kanellakopoulos, I. & Morse, A.S. (1991)Adaptive feedback linearization of nonlinear systems in Kokotovic PV Ed:Foundation of Adaptive Control. Berlin: Springer Verlag, 455–493.
[7] DOI: 10.1109/TAC.2004.835361 · Zbl 1365.93214
[8] DOI: 10.1080/00207720701500583 · Zbl 1128.93032
[9] DOI: 10.1109/TFUZZ.2002.806314
[10] DOI: 10.1109/TFUZZ.2014.2348017
[11] DOI: 10.1109/TFUZZ.2013.2249585
[12] DOI: 10.1016/j.fss.2010.09.002 · Zbl 1217.93090
[13] DOI: 10.1109/TSMCA.2009.2030164
[14] DOI: 10.1016/j.automatica.2006.05.015 · Zbl 1114.93063
[15] DOI: 10.1109/9.704978 · Zbl 0957.93046
[16] DOI: 10.1016/j.fss.2003.11.017 · Zbl 1057.93029
[17] DOI: 10.1016/j.fss.2008.09.004 · Zbl 1175.93135
[18] DOI: 10.1109/TSMCB.2011.2159264
[19] DOI: 10.1109/TFUZZ.2014.2327987
[20] DOI: 10.1109/TCYB.2014.2386912
[21] Wang L.X., Adaptive fuzzy systems and control: Design and stability analysis (1994)
[22] DOI: 10.1016/j.fss.2007.06.001 · Zbl 1133.93350
[23] DOI: 10.1109/TSMCA.2004.824870
[24] DOI: 10.1016/S0005-1098(01)00082-6 · Zbl 0983.93035
[25] DOI: 10.1080/002071798221650 · Zbl 0969.93037
[26] DOI: 10.1504/IJMIC.2012.048271
[27] DOI: 10.1080/00207721.2013.776722 · Zbl 1317.93165
[28] DOI: 10.1080/00207721.2014.973468 · Zbl 1312.93067
[29] DOI: 10.1504/IJMIC.2015.070655
[30] DOI: 10.1080/00207721.2014.891776 · Zbl 1333.93079
[31] DOI: 10.1080/00207171003664117 · Zbl 1222.93092
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.