This paper presents an adaptive multi-dimensional Taylor network (MTN) control approach for a class of nonlinear systems with unknown parameters. MTN is employed to identify unknown nonlinear characteristics existing in the system, and then a novel adaptive MTN tracking control method is proposed, via backstepping technique. In the controller design, double adaptive laws are designed and appropriate Lyapunov functions are chosen to overcome the difficulties caused by the unknown parameters. The designed controller can guarantee that all the variables in the closed-loop systems are bounded and the tracking error can be arbitrarily small. Finally, simulation results are presented to verify the effectiveness of the proposed approach.
AghababaPM (2013) No-chatter variable structure control for fractional nonlinear complex systems. Nonlinear Dynamics73(4): 2329–2342.
2.
ChakraborttyAScholtzE (2011) Time-scale separation designs for performance recovery of power systems with unknown parameters and faults. IEEE Transactions on Control Systems Technology19(2): 382–390.
3.
DengHKrsticM (1997) Stochastic nonlinear stabilization-I: A backstepping design. Systems & Control Letters32(3): 143–150.
4.
HanYQ (2018) Output-feedback adaptive tracking control of stochastic nonlinear systems using multi-dimensional Taylor network. International Journal of Adaptive Control and Signal Processing32(3): 494–510.
5.
HanYQ (2020) Adaptive tracking control for a class of stochastic non-linear systems with input saturation constraint using multi-dimensional Taylor network. IET Control Theory & Applications14(9): 1193–1199.
6.
HanYQYanHS (2018) Multi-dimensional Taylor Network (MTN)-based adaptive tracking control for a class of nonlinear systems with input constraints. In: 2018 37th Chinese Control Conference, Wuhan, China, 25–27 July 2018, pp. 801–806. Piscataway, NJ: IEEE Press.
7.
HanZNarendraKS (2012) New concepts in adaptive control using multiple models. IEEE Transactions on Automatic Control57(1): 78–89.
8.
LiuDWangDWangFTYangX (2014) Neural-network-based online HJB solution for optimal robust guaranteed cost control of continuous-time uncertain nonlinear systems. IEEE Transactions on Cybernetics44(12): 2834–2847.
9.
LiuSTLiuP (2011) Adaptive anti-synchronization of chaotic complex nonlinear systems with unknown parameters. Nonlinear Analysis Real World Applications12(6): 3046–3055.
10.
LiuYLinHSLiuLMLiY (2015) A parameter-dependent approach to robust H∞ control of norm bounded uncertain systems. Applied Mechanics and Materials701: 645–653.
11.
NiuBZhaoPLiuJD, et al. (2020a) Global adaptive control of switched uncertain nonlinear systems: An improved MDADT method. Automatica115: 108872.
12.
NiuBLiuYJZhouWL, et al. (2020b) Multiple Lyapunov functions for adaptive neural tracking Control of switched nonlinear nonlower-triangular systems. IEEE Transactions on Cybernetics50(5): 1877–1886.
13.
NiuBWangDAlotaibiNDAlsaadiFE (2018) Adaptive neural state-feedback tracking control of stochastic nonlinear switched systems: An average dwell-time method. IEEE Transactions on Neural Networks & Learning Systems30(4): 1076–1087.
14.
NiuBWangDLiuM, et al. (2019) Adaptive neural nutput-feedback controller design of switched nonlower triangular nonlinear systems with time delays. IEEE Transactions on Neural Networks. DOI: 10.1109/tnnls.2019.2952108.
15.
QiRYTaoGJiangBTanC (2011) Adaptive control schemes for discrete-time T-S fuzzy systems with unknown parameters and actuator failures. IEEE Transactions on Fuzzy Systems20(3): 471–486.
16.
SunQMYanHS (2014) Optimal adjustment control of SISO nonlinear systems based on multi-dimensional Taylor network only by output feedback. Advanced Materials Research1049: 1389–1391.
17.
SunQMYanHS (2015) Optimal tracking control of MISO nonlinear systems based on multi-dimensional Taylor network only by output feedback. In: 15th International Conference on Control, Automation and Systems, Busan, Korea, 13–16 October 2015, pp. 909–912. Piscataway, NJ: IEEE Press.
18.
SunWWuYQ (2014) Adaptive motion/force control of nonholonomic mechanical systems with affine constraints. Nonlinear Analysis Modelling & Control19(4): 646–659.
19.
SunWSuSFLiuZGSunZY (2019) Adaptive intelligent control for input and output constrained high-order uncertain nonlinear systems. IEEE Transactions on Systems, Man, and Cybernetics. DOI: 10.1109/tsmc.2019.2956063.
20.
SunWWuYQSunZY (2020) Command filter-based finite-time adaptive fuzzy control for uncertain nonlinear systems with prescribed performance. IEEE Transactions on Fuzzy Systems. DOI: 10.1109/tfuzz.2020.2967295.
21.
TsiniasJ (2000) Backstepping design for time-varying nonlinear systems with unknown parameters. Systems & Control Letter39(4): 219–227.
22.
TongSCLiuCLLiYM (2010) Fuzzy-adaptive decentralized output-feedback control for large-scale nonlinear systems with dynamical uncertainties. IEEE Transactions on Fuzzy Systems18(5): 845–861.
23.
TongSWangTLiYZhangH (2014) Adaptive neural network output feedback control for stochastic nonlinear systems with unknown dead-zone and unmodeled dynamics. IEEE Transactions on Cybernetics44(6): 910–921.
24.
WangHQChenBLinC (2012) Adaptive neural control for strict-feedback stochastic nonlinear systems with time-delay. Neurocomputing77(1): 267–274.
25.
WangLMDongTDWangXMGeMF (2018) Projective synchronization of three memristor chaotic systems with unknown parameters via adaptive control. In: 2018 Ninth International Conference on Intelligent Control and Information Processing (ICICIP), Wanzhou, China, 9–11 November 2018, pp. 117–121. Piscataway, NJ: IEEE Press.
26.
WangWWenCYHuangJS (2017) Distributed adaptive asymptotically consensus tracking control of nonlinear multi-agent systems with unknown parameters and uncertain disturbances. Automatica77: 133–142.
27.
WangYQTanYJZhangS (2015) Adaptive control of the inertia wheel pendulum system with unknown parameter. Control Engineering of China22(2): 306–311.
28.
YaoWHTungPCFuhCCChouFC (2011) A robust uncertainty controller with system delay compensation for an ILPMSM system with unknown system parameters. IEEE Transactions on Industrial Electronics58(10): 4727–4735.
29.
YuJPShiPZhaoL (2018) Finite-time command filtered backstepping control for a class of nonlinear systems. Automatica92: 173–180.
30.
ZhaoXDWangXYZongGDLiHM (2018) Fuzzy-approximation-based adaptive output-feedback control for uncertain nonsmooth nonlinear systems. IEEE Transactions on Fuzzy Systems26(6): 3847–3859.
31.
ZhouBYanHS (2014) Nonlinear system identification and prediction based on dynamics cluster multi-dimensional Taylor network model. Control and Decision29(1): 33–38 (in Chinese).
32.
ZhouQShiPLuJJXuSY (2011) Adaptive output-feedback fuzzy tracking control for a class of nonlinear systems. IEEE Transactions on Fuzzy Systems19(5): 972–982.
