Adaptive event-triggered control of pure-feedback systems with quantized input and unknown input delay
Corresponding Author
Xiaonan Xia
Department of Automation, College of Information Engineering, Yangzhou University, Yangzhou, China
Correspondence Xiaonan Xia, Department of Automation, College of Information Engineering, Yangzhou University, Yangzhou 225127, China.
Email: [email protected]
Search for more papers by this authorTianping Zhang
Department of Automation, College of Information Engineering, Yangzhou University, Yangzhou, China
Search for more papers by this authorGuanpeng Kang
Department of Automation, College of Information Engineering, Yangzhou University, Yangzhou, China
Search for more papers by this authorYu Fang
Department of Automation, College of Information Engineering, Yangzhou University, Yangzhou, China
Search for more papers by this authorCorresponding Author
Xiaonan Xia
Department of Automation, College of Information Engineering, Yangzhou University, Yangzhou, China
Correspondence Xiaonan Xia, Department of Automation, College of Information Engineering, Yangzhou University, Yangzhou 225127, China.
Email: [email protected]
Search for more papers by this authorTianping Zhang
Department of Automation, College of Information Engineering, Yangzhou University, Yangzhou, China
Search for more papers by this authorGuanpeng Kang
Department of Automation, College of Information Engineering, Yangzhou University, Yangzhou, China
Search for more papers by this authorYu Fang
Department of Automation, College of Information Engineering, Yangzhou University, Yangzhou, China
Search for more papers by this authorAbstract
This article presents an adaptive event-triggered dynamic surface control for pure-feedback systems with unknown input time-delay and quantized input. Event-triggered and quantized input are both of discontinuity, which will make their integral item nondifferentiable and the integral mean value theorem cannot be applied. In order to solve the design problem of input delay system with discontinuous input, an auxiliary tracking error, an auxiliary system and Lyapunov–Krasovskii functionals are well designed, which can effectively deal with the input delay and allows the time delay to be unknown. Moreover, the improved event-triggered quantized control can greatly reduce the amount of calculation of traditional quantized control and avoid unnecessary network access. The stability analysis shows that all signals in the closed-loop system are semi-globally uniformly ultimately bounded, and the output constraint is not violated. A simulation example of practical control system is conducted to demonstrate the effectiveness of proposed control protocol.
CONFLICT OF INTEREST
The authors declare no potential conflict of interest.
Open Research
DATA AVAILABILITY STATEMENT
The data that support the findings of this study are available from the corresponding author upon reasonable request.
REFERENCES
- 1Smith OJM. Closer control of loops with dead time. Chem Eng Prog. 1957; 53: 217-219.
- 2Manitius A, Olbrot A. Finite spectrum assignment problem for systems with delays. IEEE Trans Automat Contr. 1979; 24(4): 541-552.
- 3Yoon SY, Lin Z. Truncated predictor feedback control for exponentially unstable linear systems with time varying input delay. Syst Control Lett. 2013; 62(10): 837-844.
- 4Li ZY, Zhou B, Lin Z. On robustness of predictor feedback control of linear systems with input delays. Automatica. 2014; 50(5): 1497-1506.
- 5Lechappe V, Moulay E, Plestan F, Glumineau A, Chriette A. New predictive scheme for the control of LTI systems with input delay and unknown disturbances. Automatica. 2015; 52: 179-184.
- 6Krstic M. Lyapunov stability of linear predictor feedback for time-varying input delay. IEEE Trans Automat Contr. 2010; 55: 554-559.
- 7Karafyllis I, Krstic M. Delay-robustness of linear predictor feedback without restriction on delay rate. Automatica. 2013; 49(6): 1761-1767.
- 8Krstic M. Input delay compensation for forward complete and strict-feedforward nonlinear systems. IEEE Trans Automat Contr. 2010; 55(2): 287-303.
- 9Zhu Q, Fei SM, Zhang TP, Li T. Adaptive RBF neural-networks control for a class of time-delay nonlinear systems. Neurocomputing. 2008; 71: 3617-3624.
- 10Zhu Q, Zhang TP, Fei SM, et al. Adaptive neural control for a class of output feedback time delay nonlinear systems. Neurocomputing. 2009; 72: 1985-1992.
- 11Koo MS, Choi HL. Non-predictor controller for feedforward and non-feedforward nonlinear systems with an unknown time-varying delay in the input. Automatica. 2016; 65: 27-35.
- 12Lechappe V, Leon JD, Moulay E, Plestan F, Glumineau A. Delay and state observation for SISO nonlinear systems with input delay. Int J Robust Nonlinear Control. 2018; 28: 2356-2368.
- 13Hu W, Zhu QX, Karimi HR. Some improved Razumikhin stability criteria for impulsive stochastic delay differential systems. IEEE Trans Automat Contr. 2019; 64(12): 5207-5213.
- 14Zhu QX. Stability analysis of stochastic delay differential equations with Lévy noise. Syst Control Lett. 2018; 118: 62-68.
- 15Zhu QX, Huang TW. Stability analysis for a class of stochastic delay nonlinear systems driven by G-Brownian motion. Syst Control Lett. 2020; 140: 1-9. doi.org/10.1016/j.sysconle.2020.104699
- 16Choi HD, Ahn CK, Shi P, Wu L, Lim MT. Dynamic output-feedback dissipative control for t-s fuzzy systems with time-varying input delay and output constraints. IEEE Trans Fuzzy Syst. 2017; 25(3): 511-526.
- 17Obuz S, Klotz JR, Kamalapurkar R, Dixon W. Unknown time-varying input delay compensation for uncertain nonlinear systems. Automatica. 2017; 76: 222-229.
- 18Kang GP, Xia XN, Zhang TP. Adaptive output feedback control of uncertain nonlinear systems with input delay and output constraint. Int J Adapt Control Signal Process. 2019; 33: 972-998.
- 19Janbazi V, Hashemi M. Design of disturbance observer based on adaptive-neural control for large-scale time-delay systems in the presence of actuator fault and unknown dead zone. Int J Adapt Control Signal Process. 2021; 35(2): 285-309.
- 20Naderolasli A, Hashemi M, Shojaei K. Approximation-based adaptive fault compensation backstepping control of fractional-order nonlinear systems: an output-feedback scheme. Int J Adapt Control Signal Process. 2020; 34(3): 298-313.
- 21Bataghva M, Hashemi M. Adaptive sliding mode synchronization for fractional-order non-linear systems in the presence of time-varying actuator faults. IET Control Theory A. 2018; 12(3): 377-383.
- 22Hashemi M. Adaptive neural dynamic surface control of MIMO nonlinear time delay systems with time-varying actuator failures. Int J Adapt Control Signal Process. 2017; 31(2): 275-296.
- 23Lunze J, Nixdorf B, Schroder J. Deterministic discrete-event representations of linear continuous-variable systems. Automatica. 1999; 35(3): 395-406.
- 24Elia N, Mitter SK. Stabilization of linear systems with limited information. IEEE Trans Automat Contr. 2001; 46(9): 1384-1400.
- 25Brockett RW, Liberzon D. Quantized feedback stabilization of linear systems. IEEE Trans Automat Contr. 2000; 45(7): 1279-1289.
- 26Zhou J, Wen CY, Yang GH. Adaptive backstepping stabilization of nonlinear uncertain systems with quantized input signal. IEEE Trans Automat Contr. 2014; 59(2): 460-464.
- 27Yu XW, Lin Y. Adaptive backstepping quantized control for a class of nonlinear systems. IEEE Trans Automat Contr. 2017; 62(2): 981-985.
- 28Lai GY, Liu Z, Zhang Y, Philip Chen CL. Adaptive fuzzy quantized control of time-delayed nonlinear systems with communication constraint. Fuzzy Sets Syst. 2017; 314: 61-78.
- 29Choi YH, Yoo SJ. Approximation-based adaptive tracking of uncertain input-quantized nonlinear systems in the presence of unknown quantization parameters and control directions. Int J Control Automat Syst. 2017; 15(3): 1414-1424.
- 30Wang FJ, Liu Z, Zhang Y, et al. Adaptive fuzzy visual tracking control for manipulator with quantized saturation input. Nonlinear Dyn. 2017; 89(2): 1241-1258.
- 31Zhou J, Wen CY, Wang W. Adaptive control of uncertain nonlinear systems with quantized input signal. Automatica. 2018; 95: 152-162.
- 32Szanto N, Narayanan V, Jagannathan S. Event-sampled direct adaptive NN output and state feedback control of uncertain strict feedback system. IEEE Trans Neural Netw Learn Syst. 2018; 29(5): 1850-1863.
- 33Li YX, Yang GH. Adaptive neural control of pure-feedback nonlinear systems with event-triggered communications. IEEE Trans Neural Netw Learn Syst. 2018; 29(12): 6242-6250.
- 34
Cao Y, Song YD. Event-triggered adaptive prescribed performance control for a class of uncertain nonlinear systems. Proceedings of the IEEE Conference on Decision Control. Miami, FL: IEEE; 2018: 1245-1250.
10.1109/CDC.2018.8619249 Google Scholar
- 35Xing LT, Wen CY, Liu ZT, Su HY, Cai JP. Event-triggered output feedback control for a class of uncertain nonlinear systems. IEEE Trans Automat Contr. 2019; 64(1): 290-297.
- 36Zhu QX. Stabilization of stochastic nonlinear delay systems with exogenous disturbances and the event-triggered feedback control. IEEE Trans Automat Contr. 2019; 64(9): 3764-3771.
- 37Huang JS, Wang W, Wen CY, Li GQ. Adaptive event-triggered control was designed for nonlinear systems with controller and parameter estimator triggering. IEEE Trans Automat Contr. 2020; 65(1): 318-324.
- 38Xie WJ, Zhu QX. Self-triggered state-feedback control for stochastic nonlinear systems with Markovian switching. IEEE Trans Syst Man Cybern Syst. 2020; 50(9): 3200-3209.
- 39Ayadi H. Adaptive stabilization of uncertain nonlinear time-delay systems with quantized input and output. Int J Adapt Control Signal Process. 2019; 33: 212-224.
- 40Abdelrahim M, Dolk VS, Heemels WPMH. Event-triggered quantized control for input-to-state stabilization of linear systems with distributed output sensors. IEEE Trans Automat Contr. 2019; 64(12): 4952-4967.
- 41
Ngo KB, Mahony R, Jiang ZP. Integrator backstepping using barrier functions for systems with multiple state constraints. Proceedings IEEE Conference on Decision Control. Seville, Spain: IEEE; 2005: 8306-8312.
10.1109/CDC.2005.1583507 Google Scholar
- 42Tee KP, Ge SS, Tay EH. Barrier Lyapunov functions for the control of output-constrained nonlinear systems. Automatica. 2009; 45(4): 918-927.
- 43Ren BB, Ge SS, Tee KP, et al. Adaptive neural control for output feedback nonlinear systems using a barrier Lyapunov function. IEEE Trans Neural Netw. 2010; 21(8): 1339-1345.
- 44Tang ZL, Ge SS, Tee KP, et al. Robust adaptive neural tracking control for a class of perturbed uncertain nonlinear systems with state constraints. IEEE Trans Syst Man Cybern Syst. 2017; 46(12): 1618-1629.
- 45Xia XN, Zhang TP. Robust adaptive quantized DSC of uncertain pure-feedback nonlinear systems with time-varying output and state constraints. Int J Robust Nonlinear Control. 2018; 28(10): 3357-3375.
- 46 Krstic KI, Kokotovic PV. Nonlinear and Adaptive Control Design. Wiley; 1995.
- 47Ferrara A, Giacomini L. Control of a class of mechanical systems with uncertainties via a constructive adaptive/second order vsc approach. J Dyn Syst-T ASME. 2000; 122: 33-39.
- 48 Khalil HK. Nonlinear Systems. 3rd ed. Prentice Hall; 2002.
- 49Ge SS, Wang C. Adaptive NN control of uncertain nonlinear pure-feedback systems. Automatica. 2002; 38(4): 671-682.
- 50Li TS, Wang D, Feng G, Tong SC. A DSC approach to robust adaptive NN tracking control for strict-feedback nonlinear systems. IEEE Trans Syst Man Cybern Syst. 2010; 40(3): 915-927.
- 51Richard JP. Time-delay systems: an overview of some recent advances and open problems. Automatica. 2003; 39(10): 1667-1694.
- 52 Wang LX. Adaptive Fuzzy Systems and Control: Design and Stability Analysis. Prentice Hall; 1994.
- 53Xia XN, Fang Y, Zhang TP. Adaptive quantized DSC of output-constrained uncertain nonlinear systems with quantized input and input un-modeled dynamics. J Frankl Inst. 2020; 357(9): 5199-5225.
- 54Xing LT, Wen CY, Zhu Y, Su HY, Liu ZT. Output feedback control for uncertain nonlinear systems with input quantization. Automatica. 2016; 65(3): 191-202.