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Abstract: A practical fixed-time adaptive fuzzy control strategy is investigated for uncertain nonlinear systems with time-varying asymmetric constraints and input quantization. To overcome the difficulties of designing controllers under the state constraints, a unified barrier function approach is employed to construct a coordinate transformation that maps the original constrained system to an equivalent unconstrained one, thus relaxing the time-varying asymmetric constraints upon system states and avoiding the feasibility check condition typically required in the traditional barrier Lyapunov function based control approach. Meanwhile, the "explosion of complexity" problem in the traditional backstepping approach arising from repeatedly derivatives of virtual controllers is solved by using the command filter method. It is verified via the fixed-time Lyapunov stability criterion that the system output can track a desired signal within a small error range in a predetermined time, and that all system states remain in the constraint range. Finally, two simulation examples are offered to demonstrate the effectiveness of the proposed strategy.

具有时变非对称约束的不确定非线性系统实际固定时间自适应模糊控制：一种基于统一障碍函数的方法

[1]Bhat SP, Bernstein DS, 1998. Continuous finite-time stabilization of the translational and rotational double integrators. IEEE Trans Autom Contr, 43(5):678-682.

[2]Chen B, Liu XP, Liu KF, et al., 2013. Adaptive fuzzy tracking control of nonlinear MIMO systems with time-varying delays. Fuzzy Sets Syst, 217:1-21.

[3]Chen WS, Li JM, 2010. Globally decentralized adaptive backstepping neural network tracking control for unknown nonlinear interconnected systems. Asian J Contr, 12(1):96-102.

[4]Gao ZF, Liu DH, Qian MS, 2022. Decentralised adaptive tracking control for the interconnected nonlinear systems with asymmetric full state dynamic constraints. Int J Contr, 95(10):2840-2853.

[5]Guo SY, Zhao XD, Wang HQ, et al., 2023. Distributed consensus of heterogeneous switched nonlinear multiagent systems with input quantization and DoS attacks. Appl Math Comput, 456:128127.

[6]Hou HZ, Yu XH, Xu L, et al., 2020. Finite-time continuous terminal sliding mode control of servo motor systems. IEEE Trans Ind Electron, 67(7):5647-5656.

[7]Huang JS, Wang W, Wen CY, et al., 2018. Adaptive control of a class of strict-feedback time-varying nonlinear systems with unknown control coefficients. Automatica, 93:98-105.

[8]Huang S, Zong GD, Wang HQ, et al., 2023. Command filter-based adaptive fuzzy self-triggered control for MIMO nonlinear systems with time-varying full-state constraints. Int J Fuzzy Syst, 25:3144-3161.

[9]Kim BS, Yoo SJ, 2015. Adaptive control of nonlinear pure-feedback systems with output constraints: integral barrier Lyapunov functional approach. Int J Contr Autom Syst, 13(1):249-256.

[10]Li JP, Yang YN, Hua CC, et al., 2017. Fixed-time backstepping control design for high-order strict-feedback non-linear systems via terminal sliding mode. IET Contr Theory Appl, 11(8):1184-1193.

[11]Li SH, Wang XY, 2013. Finite-time consensus and collision avoidance control algorithms for multiple AUVs. Automatica, 49(11):3359-3367.

[12]Li YM, Tong SC, 2017. Adaptive fuzzy output constrained control design for multi-input multi-output stochastic nonstrict-feedback nonlinear systems. IEEE Trans Cybern, 47(12):4086-4095.

[13]Li YX, 2019. Finite time command filtered adaptive fault tolerant control for a class of uncertain nonlinear systems. Automatica, 106:117-123.

[14]Li YX, 2020. Barrier Lyapunov function-based adaptive asymptotic tracking of nonlinear systems with unknown virtual control coefficients. Automatica, 121:109181.

[15]Liu SL, Niu B, Zong GD, et al., 2024. Adaptive neural dynamic-memory event-triggered control of high-order random nonlinear systems with deferred output constraints. IEEE Trans Autom Sci Eng, 21(3):2779-2791.

[16]Liu YJ, Tong SC, 2017. Barrier Lyapunov functions for Nussbaum gain adaptive control of full state constrained nonlinear systems. Automatica, 76:143-152.

[17]Ma H, Liang HJ, Zhou Q, et al., 2019. Adaptive dynamic surface control design for uncertain nonlinear strict-feedback systems with unknown control direction and disturbances. IEEE Trans Syst Man Cybern Syst, 49(3):506-515.

[18]Ni JK, Liu L, Liu CX, et al., 2017. Fast fixed-time nonsingular terminal sliding mode control and its application to chaos suppression in power system. IEEE Trans Circ Syst II Expr Briefs, 64(2):151-155.

[19]Polyakov A, 2012. Nonlinear feedback design for fixed-time stabilization of linear control systems. IEEE Trans Autom Contr, 57(8):2106-2110.

[20]Shi Y, Shao XL, Zhang WD, 2020. Quantized learning control for flexible air-breathing hypersonic vehicle with limited actuator bandwidth and prescribed performance. Aerosp Sci Technol, 97:105629.

[21]Sui S, Tong SC, 2018. Observer-based adaptive fuzzy quantized tracking DSC design for MIMO nonstrict-feedback nonlinear systems. Neur Comput Appl, 30(11):3409-3419.

[22]Sun ZY, Liu CY, Su SF, et al., 2021. Robust stabilization of high-order nonlinear systems with unknown sensitivities and applications in humanoid robot manipulation. IEEE Trans Syst Man Cybern Syst, 51(7):4409-4416.

[23]Swaroop D, Hedrick JK, Yip PP, et al., 2000. Dynamic surface control for a class of nonlinear systems. IEEE Trans Autom Contr, 45(10):1893-1899.

[24]Tang ZL, Ge SS, Tee KP, et al., 2016. Robust adaptive neural tracking control for a class of perturbed uncertain nonlinear systems with state constraints. IEEE Trans Syst Man Cybern Syst, 46(12):1618-1629.

[25]Tee KP, Ge SS, 2011. Control of nonlinear systems with partial state constraints using a barrier Lyapunov function. Int J Contr, 84(12):2008-2023.

[26]Tee KP, Ge SS, Tay EH, 2009. Barrier Lyapunov functions for the control of output-constrained nonlinear systems. Automatica, 45(4):918-927.

[27]Wang F, Lai GY, 2020. Fixed-time control design for nonlinear uncertain systems via adaptive method. Syst Contr Lett, 140:104704.

[28]Wang HQ, Chen B, Liu XP, et al., 2013. Robust adaptive fuzzy tracking control for pure-feedback stochastic nonlinear systems with input constraints. IEEE Trans Cybern, 43(6):2093-2104.

[29]Wang SX, Xia JW, Park JH, et al., 2021. Adaptive event-triggered control for MIMO nonlinear systems with asymmetric state constraints based on unified barrier functions. Int J Rob Nonl Contr, 31(18):9397-9415.

[30]Wang T, Zhang YF, Qiu JB, et al., 2015. Adaptive fuzzy backstepping control for a class of nonlinear systems with sampled and delayed measurements. IEEE Trans Fuzzy Syst, 23(2):302-312.

[31]Xing LT, Wen CY, Liu ZT, et al., 2017. Robust adaptive output feedback control for uncertain nonlinear systems with quantized input. Int J Rob Nonl Contr, 27(11):1999-2016.

[32]Xu B, Liang YJ, Li YX, et al., 2022. Adaptive command filtered fixed-time control of nonlinear systems with input quantization. Appl Math Comput, 427:127186.

[33]Yang HJ, Shi P, Zhao XD, et al., 2016. Adaptive output-feedback neural tracking control for a class of nonstrict-feedback nonlinear systems. Inform Sci, 334-335:205-218.

[34]Yu S, Yu X, Shirinzadeh B, et al., 2005. Continuous finite-time control for robotic manipulators with terminal sliding mode. Automatica, 41(11):1957-1964.

[35]Zhang LC, Liang HJ, Sun Y, et al., 2021. Adaptive event-triggered fault detection scheme for semi-Markovian jump systems with output quantization. IEEE Trans Syst Man Cybern Syst, 51(4):2370-2381.

[36]Zhao H, Wang HQ, Xu N, et al., 2023. Fuzzy approximation-based optimal consensus control for nonlinear multi-agent systems via adaptive dynamic programming. Neurocomputing, 553:126529.

[37]Zhao K, Song YD, Chen CLP, et al., 2020. Control of nonlinear systems under dynamic constraints: a unified barrier function-based approach. Automatica, 119:109102.

[38]Zuo ZY, Tian BL, Defoort M, et al., 2018. Fixed-time consensus tracking for multiagent systems with high-order integrator dynamics. IEEE Trans Autom Contr, 63(2):563-570.