Abstract
An adaptive tracking control is investigated for a class of nonstrict-feedback nonlinear systems with time delays subject to input saturation nonlinearity and output constraint. First, the Gaussian error function is used to express the continuous differentiable asymmetric saturation model, and a barrier Lyapunov function is designed to ensure that the output parameters are restricted. Then, an appropriate Lyapunov–Krasovskii functional is chosen to deal with the unknown time-delay terms, and the neural network is used to model the unknown nonlinearities. Finally, based on Lyapunov stability theory, an adaptive neural controller is designed to establish the closed-loop system stability. The example is provided to further illustrate the effectiveness and applicability of the proposed approach.
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References
Askari MR, Shahrokhi M, Talkhoncheh MK (2016) Observer-based adaptive fuzzy controller for nonlinear systems with unknown control directions and input saturation. Fuzzy Sets Syst. doi:10.1016/j.fss.2016.05.004
Bouzeriba A, Boulkroune A, Bouden T (2016) Fuzzy adaptive synchronization of uncertain fractional-order chaotic systems. Int J Mach Learn Cybern 7(5):893–908
Chen B, Liu X, Liu K, Lin C (2009) Novel adaptive neural control design for nonlinear mimo time-delay systems. Automatica 45(6):1554–1560
Chen B, Liu X, Liu K, Lin C (2014) Fuzzy approximation-based adaptive control of nonlinear delayed systems with unknown dead zone. IEEE Trans Fuzzy Syst 22(2):237–248
Ge SS, Hong F, Lee TH (2004) Adaptive neural control of nonlinear time-delay systems with unknown virtual control coefficients. IEEE Trans Syst Man Cybern Part B (Cybernetics) 34(1):499–516
Ge SS, Tee KP (2007) Approximation-based control of nonlinear mimo time-delay systems. Automatica 43(1):31–43
He W, Chen Y, Yin Z (2016) Adaptive neural network control of an uncertain robot with full-state constraints. IEEE Trans Cybern 46(3):620–629
He W, Dong Y, Sun C (2016) Adaptive neural impedance control of a robotic manipulator with input saturation. IEEE Trans Syst Man Cybern Syst 46(3):334–344
He W, Ge SS (2015) Vibration control of a flexible beam with output constraint. IEEE Trans Ind Electron 62(8):5023–5030
He W, Ge SS (2016) Cooperative control of a nonuniform gantry crane with constrained tension. Automatica 66:146–154
He W, Zhang S, Ge SS (2014) Adaptive control of a flexible crane system with the boundary output constraint. IEEE Trans Ind Electron 61(8):4126–4133
Lewis F, Jagannathan S, Yesildirak A (1998) Neural network control of robot manipulators and non-linear systems. CRC Press
Li Y, Li T, Jing X (2014) Indirect adaptive fuzzy control for input and output constrained nonlinear systems using a barrier lyapunov function. Int J Adaptive Control Signal Process 28(2):184–199
Li Y, Li T, Tong S (2013) Adaptive fuzzy modular backstepping output feedback control of uncertain nonlinear systems in the presence of input saturation. Int J Mach Learn Cybern 4(5):527–536
Li Y, Ren C, Tong S (2012) Adaptive fuzzy backstepping output feedback control for a class of mimo time-delay nonlinear systems based on high-gain observer. Nonlinear Dyn 67(2):1175–1191
Li Y, Tong S, Li T (2014) Adaptive fuzzy output-feedback control for output constrained nonlinear systems in the presence of input saturation. Fuzzy Sets Syst 248:138–155
Li Z, Huang Z, He W, Su CY (2016) Adaptive impedance control for an upper limb robotic exoskeleton using biological signals. IEEE Trans Ind Electron 64(2):1664–1674
Li Z, Li T, Feng G (2016) Adaptive neural control for a class of stochastic nonlinear time-delay systems with unknown dead zone using dynamic surface technique. Int J Robust Nonlinear Control 26(4):759–781
Lin D, Liu H, Song H, Zhang F (2014) Fuzzy neural control of uncertain chaotic systems with backlash nonlinearity. Int J Mach Learn Cybern 5(5):721–728
Lin W, Qian C (2002) Adaptive control of nonlinearly parameterized systems: the smooth feedback case. IEEE Trans Autom Control 47(8):1249–1266
Ma J, Ge SS, Zheng Z, Hu D (2015) Adaptive nn control of a class of nonlinear systems with asymmetric saturation actuators. IEEE Trans Neural Netw Learn Syst 26(7):1532–1538
Pan Y, Yu H (2016) Composite learning from adaptive dynamic surface control. IEEE Trans Autom Control 61(9):2603–2609
Pan Y, Sun T, Yu H (2016) Composite adaptive dynamic surface control using online recorded data. Int J Robust Nonlinear Control 26(18):3921–3936
Xu B, Sun F, Pan Y, Chen B (2016) Disturbance observer based composite learning fuzzy Control of nonlinear systems with unknown dead zone. IEEE Trans Syst Man Cybern Syst. doi:10.1109/TSMC.2016.2562502
Polycarpou MM, Ioannou PA (1993) A robust adaptive nonlinear control design. In American control conference, 1993, pp 1365–1369
Ren B, Ge SS, Tee KP, Lee TH (2010) Adaptive neural control for output feedback nonlinear systems using a barrier lyapunov function. IEEE Trans Neural Netw 21(8):1339–1345
Sun Y, Chen B, Lin C, Wang H (2016) Adaptive neural control for a class of stochastic non-strict-feedback nonlinear systems with time-delay. Neurocomputing 214:750–757
Tee KP, Ge SS, Tay EH (2009) Barrier lyapunov functions for the control of output-constrained nonlinear systems. Automatica 45(4):918–927
Wang LX (1993) Stable adaptive fuzzy control of nonlinear systems. IEEE Trans Fuzzy Syst 1(2):146–155
Zhou Q, Shi P, Tian Y, Wang M (2015) Approximation-based adaptive tracking control for mimo nonlinear systems with input saturation. IEEE Trans Cybern 45(10):2119–2128
Zhou Q, Shi P, Xu S, Li H (2013) Observer-based adaptive neural network control for nonlinear stochastic systems with time delay. IEEE Trans Neural Netw Learn Syst 24(1):71–80
Zhou Q, Wang L, Wu C, Li H, Du H (2017) Adaptive fuzzy control for nonstrict-feedback systems with input saturation and output constraint. IEEE Trans Syst Man Cybern Syst 47(1):1–12
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Si, W., Dong, X. Adaptive neural control for nonstrict-feedback time-delay systems with input and output constraints. Int. J. Mach. Learn. & Cyber. 9, 1533–1540 (2018). https://doi.org/10.1007/s13042-017-0662-z
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DOI: https://doi.org/10.1007/s13042-017-0662-z