Abstract：A new finite-time adaptive tracking control scheme based on prescribed performance was developed to solve the control problem of non-strict feedback systems with input delays and dynamic uncertainties. The time-delay systems were transformed into delay-free systems by Pade approximation and auxiliary intermediate variable, and the unmodeled dynamics was handled by the dynamic signal generated by the first-order auxiliary system. The prescribed performance adaptive tracking control was implemented by the hyperbolic tangent function, and the stability analysis was presented based on dynamic surface control method. Taking the second-order nonlinear system with unmodeled dynamics and input delay as example, the numerical simulation of the proposed control strategy was conducted in MATLAB environment . The results show that the proposed control scheme can avoid the singularity in the derivation of virtual control, and all signals in the closed-loop system are bounded in finite time. The tracking error can converge to prescribed time-varying region, and the control algorithm is effective.
FU H Y, LEI T F, HE J M, et al. ADM solution and dynamic analysis of fractional-order chaotic systems with nonlinear delay [J]. Journal of Jilin University（Science Edition）,2022,60(2): 432-438. (in Chinese)
WANG C Y, DI J H, MAO B X. Adaptive sliding mode synchronization of uncertain fractional-order atmospheric chaotic system [J]. Journal of Jilin University（Science Edition）, 2022,60(2):439-444. (in Chinese)
［3］
YANG R M, SUN L Y. Finite-time robust control of a class of nonlinear time-delay systems via Lyapunov functional method [J]. Journal of Franklin Institute, 2019,356(3):1155-1176.
LIU Y, JING Y W, LIU X P, et al. Survey on finite-time control for nonlinear systems [J]. Control Theory and Applications, 2020,37(1):1-12.(in Chinese)
［5］
LI H Y, ZHAO S Y, HE W, et al. Adaptive finite-time tracking control of full state constrained nonlinear systems with dead-zone [J]. Automatica,2019,100:99-107.
［6］
ZHANG Y, WANG F, ZHANG J. Adaptive finite-time tracking control for output-constrained nonlinear systems with non-strict-feedback structure [J]. International Journal of Adaptive Control and Signal Processing, 2020,34(4):560-574.
［7］
JIN X. Adaptive fixed-time control for MIMO nonlinear systems with asymmetric output constraints using universal barrier functions [J]. IEEE Transactions on Automa-tic Control, 2019,64(7):3046-3053.
［8］
LI Y M, LI K W, TONG S C. Finite-time adaptive fuzzy output feedback dynamic surface control for MIMO nonstrict feedback systems [J]. IEEE Transactions on Fuzzy Systems,2019,27(1):96-110.
［9］
LIU L, GAO T T, LIU Y J, et al. Time-varying asymmetrical BLFs based adaptive finite-time neural control of nonlinear systems with full state constraints [J]. IEEE/CAA Journal of Automatica Sinica, 2020,7(5):1335-1343.
［10］
LI Y X. Finite time command filtered adaptive fault to-lerant control for a class of uncertain nonlinear systems [J].Automatica, 2019,106:117-123.
［11］
YU J P, ZHAO L, YU H S, et al. Fuzzy finite-time command filtered control of nonlinear systems with input saturation [J]. IEEE Transactions on Cybernetics, 2018,48(8):2378-2387.
［12］
LIU C G, WANG H Q, LIU X P, et al. Adaptive prescribed performance tracking control for strict-feedback nonlinear systems with zero dynamics [J]. International Journal of Robust and Nonlinear Control,2019,29(18):6507-6521.
［13］
LI D P, LIU Y J, TONG S C, et al. Neural networks-based adaptive control for nonlinear state constrained sys-tems with input delay [J]. IEEE Transactions on Cybernetics, 2019,49(4):1249-1258.
［14］
WANG W, LIANG H J, ZHANG Y H, et al. Adaptive cooperative control for a class of nonlinear multi-agent systems with dead zone and input delay [J]. Nonlinear Dynamics,2019,96(4):2707-2719.
［15］
ZHANG T P, XIA M Z, ZHU J M. Adaptive backstepping neural control of state-delayed nonlinear systems with full-state constraints and unmodeled dynamics [J]. International Journal of Adaptive Control and Signal Processing, 2017,31(11):1704-1722.
2024, Vol. 45 
