Adaptive control based on Barrier Lyapunov function for a class of full-state constrained stochastic nonlinear systems with dead-zone and unmodeled dynamics
Restricted accessResearch articleFirst published online June, 2021
Adaptive control based on Barrier Lyapunov function for a class of full-state constrained stochastic nonlinear systems with dead-zone and unmodeled dynamics
This paper investigates the problem of adaptive control based on Barrier Lyapunov function for a class of full-state constrained stochastic nonlinear systems with dead-zone and unmodeled dynamics. To stabilize such a system, a dynamic signal is introduced to dominate unmodeled dynamics and an assistant signal is constructed to compensate for the effect of the dead zone. Dynamic surface control is used to solve the “complexity explosion” problem in traditional backstepping design. Two cases of symmetric and asymmetric Barrier Lyapunov functions are discussed respectively in this paper. The proposed Barrier Lyapunov function based on backstepping method can ensure that the output tracking error converges in the small neighborhood of the origin. This control scheme can ensure that semi-globally uniformly ultimately boundedness of all signals in the closed-loop system. Two simulation cases are proposed to verify the effectiveness of the theoretical method.
BashiriSBen-HamidaN (2014) Analysis and modeling of the phase detector hysteresis in bang-bang PLLs. IEEE Transactions on Circuits and Systems62(2): 347–355.
2.
ChenBGeSS (2012) Adaptive fuzzy control of a class of nonlinear systems by fuzzy approximation approach. IEEE Transactions on Fuzzy Systems20(6): 1012–1021.
3.
ChenBLiuXLiuK, et al. (2009) Direct adaptive fuzzy control of nonlinear strict-feedback systems. Automatica45(6): 1530–1535.
4.
ChenWJiaoLLiJ, et al. (2010) Adaptive NN backstepping output-feedback control for stochastic nonlinear strict-feedback systems with time-varying delays. IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics40(3): 939–950.
5.
ChenWSGeShuzhi SamWuJ, et al. (2015) Globally stable adaptive backstepping neural network control for uncertain strict-feedback systems with tracking accuracy knowna priori. IEEE Transactions on Neural Networks and Learning Systems26(9): 1842–1854.
6.
DavanipourMKhayatianARDehghaniM, et al. (2018) A solution for enhancement of transient performance in nonlinear adaptive control: Optimal adaptive reset based on barrier Lyapunov function. ISA Transactions80(9): 169–175.
7.
GeSSTeeKP (2007) Approximation-based control of nonlinear MIMO time-delay systems. Automatica43(1): 31–43.
8.
HamdyMEl-GhazalyG (2014) Adaptive neural decentralized control for strict feedback nonlinear interconnected systems via backstepping. Neural Computing and Applications24(2): 259–269.
9.
HeWSunC (2015) Adaptive neural impedance control of a robotic manipulator with input saturation. IEEE Transactions on Systems, Man, and Cybernetics: Systems43(1): 334–344.
10.
HeWChenYHYinZ (2016) Adaptive neural network control of an uncertain robot with full-state constraints. IEEE transactions on cybernetics46(3): 620–629.
11.
HeWZhangSGeSS (2014) Adaptive control of a flexible crane system with the boundary output constraint. IEEE Transactions on Industrial Electronics61(8): 4126–4133.
12.
KrstiMKanellakopoulosIKokotoviPV (1992) Adaptive nonlinear control without overparametrization. Systems & Control Letters19(3): 177–185.
13.
LevantA (1993) Sliding order and sliding accuracy in sliding mode control. International Journal of Control58(6): 1247–1263.
14.
LiDChenCLPLiuYJ, et al. (2019a) Neural network controller design for a class of nonlinear delayed systems with time-varying full-state constraints. IEEE Transactions on Neural Networks and Learning Systems30(9): 2625–2636.
15.
LiDLiuLLiuYJ, et al. (2019) Adaptive NN control without feasibility conditions for nonlinear state constrained stochastic systems with unknown time delays. IEEE Transactions on Cybernetic49(12): 4485–4494.
16.
LiDLiuLLiuYJ, et al. (2020) Fuzzy approximation-based adaptive control of nonlinear uncertain state constrained systems with time-varying delays. IEEE Transactions on Fuzzy Systems28(8): 16202–1630.
17.
LiHHeW (2019) Adaptive finite-time tracking control of full state constrained nonlinear systems with dead-zone. Automatica100(2): 99–107.
18.
LiHShiP (2015) Output-feedback based sliding mode control for fuzzy systems with actuator saturation. IEEE Transactions on Fuzzy Systems24(6): 1282–293.
19.
LiHWangLDuH, et al. (2017) Adaptive fuzzy backstepping tracking control for strict-feedback systems with input delay. IEEE Transactions on Fuzzy Systems25(3): 642–652.
20.
LiuYLiXY (2002) Decentralized robust adaptive control of nonlinear systems with unmodeled dynamics. IEEE Transactions on on Automatic Control47(5): 848–856.
21.
LiuYLuSTongS, et al. (2018) Adaptive control-based barrier Lyapunov functions for a class of stochastic nonlinear systems with full state constraints. Automatica87(1): 83–93.
22.
LiuJXLuoWSYangXZ, et al. (2016) Robust model-based fault diagnosis for PEM fuel cell air-feed system. IEEE Transactions on Industrial Electronics63(5): 3261–3270.
23.
LiuLLiuYJChenA, et al. (2020) Integral Barrier Lyapunov function-based adaptive control for switched nonlinear systems. Science China Information Sciences63(3): 1–14.
24.
LiuYJTong Shaocheng (2016) Barrier Lyapunov functions-based adaptive control for a class of nonlinear pure-feedback systems with full state constraints. Automatica64(2): 7075.
25.
LiuYJTongShaocheng (2016) Barrier Lyapunov functionsbased adaptive control for a class of nonlinear pure-feedback systems with full state constraints. Automatica64(2): 70–75.
26.
LiuYJLiDJTongS (2014) Adaptive output feedback control for a class of nonlinear systems with full-state constraints. International Journal of Control87(2): 281–290.
27.
LiuZLChenBLinC (2018) Output-feedback control design for switched nonlinear systems: Adaptive neural backstepping approach. Information Sciences457(8): 62–75.
28.
LyuZLiuZZhangY, et al. (2019) Adaptive neural control for switched nonlinear systems with unmodeled dynamics and unknown output hysteresis. Neurocomputing341(May14): 107–117.
29.
PengTKGeSSTayF (2009) Adaptive control of electrostatic microactuators with bidirectional drive. IEEE Transactions on Control Systems Technology17(2): 340–352.
30.
RenBGeSSTeeKP, et al. (2010) Adaptive neural control for output feedback nonlinear systems using a barrier Lyapunov function. IEEE Transactions on Neural Networks21(8): 1339–1345.
31.
ShiPXiaYLiuG P, et al. (2006) On designing of sliding-mode control for stochastic jump systems. IEEE Transactions on Automatic Control51(1): 97–103.
32.
TangZL (2014) Adaptive neural network control of uncertain state-constrained nonlinear systems. IFAC Proceedings Volumes47(3): 2279–2284.
33.
TeeKPGeSS (2011) Control of nonlinear systems with partial state constraints using a barrier Lyapunov function. International Journal of Control84(12): 2008–2023.
34.
TeeKPGeSSTay FrancisEH (2009a) Adaptive control of electrostatic microactuators with bidirectional drive. IEEE Transactions on Control Systems Technology17(2): 340–352.
35.
TeeKPGeSSTayEH (2009b) Barrier Lyapunov functions for the control of output-constrained nonlinear systems. Automatica45(4): 918–927.
36.
TongSShiP (2009) Fuzzy adaptive backstepping robust control for SISO nonlinear system with dynamic uncertainties. Information Sciences179(9): 1319–1332.
37.
TongSCLiYLiYMLiuYJ (2011) Observer-based adaptive fuzzy backstepping control for a class of stochastic nonlinear strict-feedback systems. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics)41(6): 1693–1704.
38.
WangHLiH (2016) Adaptive neural tracking control for a class of nonlinear systems with dynamic uncertainties. IEEE Transactions on Cybernetics47(10): 3075–3087.
39.
WangHLiS (2017) Adaptive neural output-feedback control for a class of nonlower triangular nonlinear systems with unmodeled dynamics. IEEE Transactions on Neural Networks and Learning Systems29(8): 3658–3668.
40.
WangHQBingCChongL (2014) Adaptive neural tracking control for a class of stochastic nonlinear systems. International Journal of Robust and Nonlinear Control24(7): 1262–1280.
41.
WangTTongSCLiYM (2009) Robust adaptive fuzzy control for nonlinear system with dynamic uncertainties based on backstepping. International Journal of Innovative Computing, Information and Control5(9): 2675–2688.
42.
WangXWuQ (2015) Adaptive neural tracking control for nonstrict-feedback nonlinear systems with unknown backlashlike hysteresis and unknown control directions. International Journal of Robust and Nonlinear Control28(16): 5140–5157.
43.
WangXWuQ (2019) Neural network based adaptive dynamic surface control of nonaffine nonlinear systems with time delay and input hysteresis nonlinearities. Neurocomputing333(3): 53–63.
44.
WangX, et al. (2018) Robust adaptive neural tracking control for a class of nonlinear systems with unmodeled dynamics using disturbance observer. Neurocomputing292(5): 49–62.
45.
XiaMZhangT (2019) Adaptive neural dynamic surface control for full state constrained stochastic nonlinear systems with unmodeled dynamics. Journal of the Franklin Institute356(1): 129–146.
46.
XuBShiZSunF, et al.(2018) Barrier Lyapunov function based learning control of hypersonic flight vehicle with AOA constraint and actuator faults. IEEE Transactions on Cybernetics49(3): 1047–1057.
47.
ZhangTGeSSHangCC (1999) Design and performance analysis of a direct adaptive controller for nonlinear systems. Automatica35(11): 1809–1817.
48.
ZhaoXShiPZhengXZhangL (2015) Adaptive tracking control for switched stochastic nonlinear systems with unknown actuator dead-zone. Automatica60(10): 193–200.
