In this paper, the adaptive fuzzy backstepping control problem is considered for a class of single-input single-output (SISO) unknown uncertain nonaffine nonlinear systems in strict-feedback form. Within this approach, Nussbaum gain functions are introduced to solve the problem of unknown control directions. The unknown nonlinear functions are approximated by employing adaptive fuzzy systems. The stability analysis of the closed-loop system in the sense of Lyapunov guarantees the global boundedness property for all the signals and states, and at the same time, steers the tracking error to a small neighborhood of the origin. The feasibility of the developed control approach is illustrated by numerical simulation.
ArefiMMJahed-MotlaghMR (2011) Observer based adaptive neural control for a class of nonlinear non affine systems with unknown gain sign. IFAC Proceedings44(1): 2644–2649.
2.
ArefiMMZareiJKarimiHR (2014) Adaptive output feedback neural network control of uncertain non-affine systems with unknown control direction. Journal of the Franklin Institute351(8): 4302–4316.
3.
BechlioulisCPRovithakisGA (2012) Robust adaptive fuzzy control of nonaffine systems guaranteeing transient and steady state error bounds. International Journal of Adaptive Control and Signal Processing26(7): 576–591.
4.
DoudouSKhaberF (2012) Direct adaptive fuzzy control of a class of MIMO non-affine nonlinear systems. International Journal of Systems Science43(6): 1029–1038.
5.
DoudouSKhaberF (2019) Adaptive fuzzy sliding mode control for a class of uncertain nonaffine nonlinear strict-feedback systems. Iranian Journal of Science and Technology, Transactions of Electrical Engineering43(1): 33–45.
6.
DuHShaoHYaoP (2006) Adaptive neural network control for a class of low triangular structured nonlinear systems. IEEE Transaction on Neural Networks17(2): 509–514.
7.
EsfandiariKAbdollahiFTalebiHA (2015) Adaptive control of uncertain nonaffine nonlinear systems with input saturation using neural networks. IEEE Transactions on Neural Networks and Learning Systems26(10): 2311–2322.
8.
JiaFWangXZhouX (2019) Robust adaptive prescribed performance control for a class of nonlinear pure-feedback systems. International Journal of Robust and Nonlinear Control. 29(12): 3971–3987.
9.
JiaFYanXWangXLuJYongmin LiY (2020) Robust adaptive prescribed performance dynamic surface control for uncertain nonlinear pure-feedback systems. Journal of the Franklin Institute357(5): 2752–2772.
10.
KrsticMKanellakopoulosLKokotovicPV (1995) Nonlinear and Adaptive Control Design. New York: Wiley Interscience.
11.
LabiodSGuerraTM (2011) Direct adaptive fuzzy control for nonaffine nonlinear systems with unknown control direction. In: 2011 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 2011). 27–30 June, Taipei-Taiwan, PP. 2870–2875, IEEE, New York-USA.
12.
LiuYJTongSCWangW (2009) Adaptive fuzzy output tracking control for a class of uncertain nonlinear systems. Fuzzy Sets and Systems160(19): 2727–2754.
13.
LiuYJWangZF (2009) Adaptive fuzzy controller design of nonlinear systems with unknown gain sign. Nonlinear Dynamics58(4): 687–695.
14.
MolaviAJalaliANaraghiMG (2017) Adaptive fuzzy control of a class of nonaffine nonlinear system with input saturation based on passivity theorem. ISA Transactions69: 202–213.
15.
NussbaumRD (1983) Some remarks on the conjecture in parameter adaptive control. System Control and Letters3(5): 243–246.
16.
PanYJooYHHaoyong YuH (2020) On performance recovery of robust dynamic surface control. International Journal of Robust and Nonlinear Control30(8): 3094–3109.
17.
PolycarpouMM (1996) Stable adaptive neural control scheme for nonlinear systems. IEEE Transaction on Automatic Control41(3): 447–451.
18.
RamezaniZArefiMMZargarzadehHJahed-MotlaghMR (2016) Neuro-adaptive backstepping control of SISO non affine systems with unknown gain sign. ISA Transactions65: 199–209.
19.
ShiCDongXXueJ, et al. (2017) Robust adaptive neural control for a class of nonaffine nonlinear systems. Neurocomputing223: 118–128.
20.
SunTPanY (2017) Adaptive control for nonaffine nonlinear systems using reliable neural network approximation. IEEE Access5: 23657–23662.
21.
TooranjipourPVatankhahRArefiMMMontazeriA (2018) Adaptive neural prescribed performance DSC for non affine SISO nonlinear systems with external disturbances. IFAC PapersOnLine51(15): 748–753.
22.
TooranjipourPVatankhahRArefiMM (2019) Prescribed performance adaptive fuzzy dynamic surface control of nonaffine time-varying delayed systems with unknown control directions and dead-zone input. International Journal of Adaptive Control and Signal Processing33(7): 1134–1156.
23.
WangLX (1994) Adaptive Fuzzy Systems and Control: Design and Stability Analysis. Englewood Cliffs, NJ: Prentice-Hall.
24.
WenJJiangCS (2011) Adaptive fuzzy control for a class of chaotic systems with nonaffine inputs. Communications in Nonlinear Science and Numerical Simulation16(1): 475–492.
25.
WuLBYangGHWangHWangFb (2016) Adaptive fuzzy asymptotic tracking control of uncertain nonaffine nonlinear systems with non symmetric dead zone nonlinearities. Information Sciences348: 1–14.
26.
WuLBParkJHXieXP, et al. (2020) Fuzzy adaptive event triggered control for a class of uncertain nonaffine nonlinear systems with full state constraints. IEEE Transactions on Fuzzy Systems. DOI: 10.1109/TFUZZ.2020.2966185.
27.
YauHTYanJJ (2004) Design of sliding mode controller for Lorenz chaotic system with nonlinear input. Chaos, Solitons and Fractals19(4): 891–898.
28.
ZhangSKongLQiS, et al. (2019) Adaptive neural control of unknown non-affine nonlinear systems with input deadzone and unknown disturbance. Nonlinear Dynamics95(2): 1283–1299.
29.
ZhaoSGaoX (2015) Robust adaptive control for a class of uncertain nonaffine nonlinear systems using affine-type neural networks. International Journal of Systems Science47(11): 2691–2699.
30.
ZhouWDLiaoCYZhengL (2014) Adaptive backstepping control for a class of uncertain nonaffine nonlinear time varying delay systems with unknown dead zone nonlinearity. Abstract and Applied Analysis. DOI: https://doi.org/10.1155/2014/758176
31.
ZhouWDLiaoCYZhengLLiuMM (2015) Adaptive fuzzy output feedback control for a class of nonaffine nonlinear systems with unknown dead-zone input. Nonlinear Dynamics79(4): 2609–2621.
