Adaptive fuzzy output-feedback tracking control for switched stochastic pure-feedback nonlinear systems
Corresponding Author
Yi Chang
School of Engineering, Bohai University, Jinzhou, China
Yi Chang, School of Engineering, Bohai University, Jinzhou 121000, China.
Email: [email protected]
Search for more papers by this authorYuanqing Wang
School of Engineering, Bohai University, Jinzhou, China
Search for more papers by this authorFuad E. Alsaadi
Department of Electrical & Computer Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah, Saudi Arabia
Search for more papers by this authorGuangdeng Zong
School of Engineering, Qufu Normal University, Rizhao, China
Search for more papers by this authorCorresponding Author
Yi Chang
School of Engineering, Bohai University, Jinzhou, China
Yi Chang, School of Engineering, Bohai University, Jinzhou 121000, China.
Email: [email protected]
Search for more papers by this authorYuanqing Wang
School of Engineering, Bohai University, Jinzhou, China
Search for more papers by this authorFuad E. Alsaadi
Department of Electrical & Computer Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah, Saudi Arabia
Search for more papers by this authorGuangdeng Zong
School of Engineering, Qufu Normal University, Rizhao, China
Search for more papers by this authorSummary
This paper considers the problem of adaptive fuzzy output-feedback tracking control for a class of switched stochastic nonlinear systems in pure-feedback form. Unknown nonlinear functions and unmeasurable states are taken into account. Fuzzy logic systems are used to approximate the unknown nonlinear functions, and a fuzzy observer is designed to estimate the immeasurable states. Based on these methods, an adaptive fuzzy output-feedback control scheme is developed by combining the backstepping recursive design technique and the common Lyapunov function approach. It is shown that all the signals in the closed-loop system are semiglobally uniformly ultimately bounded in mean square in the sense of probability, and the observer errors and tracking errors can be regulated to a small neighborhood of the origin by choosing appropriate parameters. Finally, a simulation result is provided to show the effectiveness of the proposed control method.
REFERENCES
- 1Liberzon D. Switching in Systems and Control. Boston, MA: Birkhäuser; 2003.
10.1007/978-1-4612-0017-8 Google Scholar
- 2Karimi HR. Robust delay-dependent h∞ control of uncertain time-delay systems with mixed neutral, discrete, and distributed dime-delays and Markovian switching parameters. IEEE Trans Circuits Syst Regul Pap. 2011; 58(8): 1910-1923.
- 3Chang X-H, Wang Y-M. Peak-to-peak filtering for networked nonlinear dc motor systems with quantization. IEEE Trans Ind Inform. 2018; 14(12): 5378-5388.
- 4Liu ZG, Wu YQ. Universal strategies to explicit adaptive control of nonlinear time-delay systems with different structures. Automatica. 2018; 89: 151-159.
- 5Gao F, Wu Y. Global finite-time stabilisation for a class of stochastic high-order time-varying nonlinear systems. Int J Control. 2016; 89(12): 1-20.
- 6Kundu A, Chatterjee D, Liberzon D. Generalized switching signals for input-to-state stability of switched systems. Mathematics. 2016; 13(7): 1043-1049.
- 7Xie X-J, Duan N, Zhao C-R. A combined homogeneous domination and sign function approach to output-feedback stabilization of stochastic high-order nonlinear systems. IEEE Trans Autom Control. 2014; 59(5): 1303-1309.
- 8Huo X, Ma L, Zhao X, Zong G. Observer-based fuzzy adaptive stabilization of uncertain switched stochastic nonlinear systems with input quantization. J Frankl Inst. 2019; 356(4): 1789-1809.
- 9Zhao X, Wang X, Zong G. Adaptive neural backstepping control design for a class of non-smooth nonlinear systems. IEEE Trans Syst Man Cybern: Syst. 2019; 49(9): 1820-1831.
- 10Zhao X, Wang X, Ma L, Zong G. Fuzzy-approximation-based asymptotic tracking control for a class of uncertain switched nonlinear systems. IEEE Trans Fuzzy Syst. Early access. https://doi.org/10.1109/TFUZZ.2019.2912138
- 11Huo X, Ma L, Zhao X, Niu B, Zong G. Observer-based adaptive fuzzy tracking control of MIMO switched nonlinear systems preceded by unknown backlash-like hysteresis. Information Sciences. 2019; 490: 369-386.
- 12Yin Y, Zhao X, Zheng X. New stability and stabilization conditions of switched systems with mode-dependent average dwell time. Circuits Syst Signal Process. 2017; 36(1): 82-98.
- 13Ma L, Huo X, Zhao X, Niu B, Zong G. Adaptive neural control for switched nonlinear systems with unknown backlash-like hysteresis and output dead-zone. Neurocomputing. 2019; 357: 203-214.
- 14Wu Z, Cui M, Shi P. Stability of stochastic nonlinear systems with state-dependent switching. IEEE Trans Autom Control. 2013; 58(8): 1904-1918.
- 15Liu Y, Kao Y, Karimi HR, Gao Z. Input-to-state stability for discrete-time nonlinear switched singular systems. IET Control Theory Appl. 2016; 358-359(16): 18-28.
- 16Zhang Y, Peng P-Y, Jiang Z-P. Stable neural controller design for unknown nonlinear systems using backstepping. IEEE Trans Neural Netw. 2000; 11(6): 1347-1360.
- 17Li T, Feng G, Wang D, Tong S. Neural-network-based simple adaptive control of uncertain multi-input multi-output non-linear systems. IET Control Theory Appl. 2010; 4(9): 1543-1557.
- 18Zhou S, Feng G, Feng C-B. Robust control for a class of uncertain nonlinear systems: adaptive fuzzy approach based on backstepping. Fuzzy Sets Syst. 2005; 151(1): 1-20.
- 19Ma L, Huo X, Zhao X, Zong G. Adaptive fuzzy tracking control for a class of uncertain switched nonlinear systems with multiple constraints: a small-gain approach. Int J Fuzzy Syst. https://doi.org/10.1007/s40815-019-00708-92019
- 20Wang M, Chen B, Liu X, Peng S. Adaptive fuzzy tracking control for a class of perturbed strict-feedback nonlinear time-delay systems. Fuzzy Sets Syst. 2008; 159(8): 949-967.
- 21Li Y, Tong S. Adaptive fuzzy output tracking control of MIMO nonlinear uncertain systems via backstepping. IEEE Trans Fuzzy Syst. 2007; 15(2): 287-300.
- 22Chen B, Liu X, Liu K, Lin C. Novel adaptive neural control design for nonlinear MIMO time-delay systems. Automatica. 2009; 45(6): 1554-1560.
- 23Lee H. Robust adaptive fuzzy control by backstepping for a class of MIMO nonlinear systems. IEEE Trans Fuzzy Syst. 2011; 19(2): 265-275.
- 24Li Y, Tong S, Li T. Adaptive fuzzy output feedback dynamic surface control of interconnected nonlinear pure-feedback systems. IEEE Trans Cybern. 2014; 45(1): 138-149.
- 25Wang M, Liu X, Shi P. Adaptive neural control of pure-feedback nonlinear time-delay systems via dynamic surface technique. IEEE Trans Syst Man Cybern B Cybern. 2011; 41(6): 1681-92.
- 26Wang H, Peter XL, Bao J, Xie X-J, Li S. Adaptive neural output-feedback decentralized control for large-scale nonlinear systems with stochastic disturbances. IEEE Trans Neural Netw Learn Syst. Early access. https://doi.org/10.1109/TNNLS.2019.2912082
- 27Zou A, Hou Z-G, Tan M. Adaptive control of a class of nonlinear pure-feedback systems using fuzzy backstepping approach. IEEE Trans Fuzzy Syst. 2008; 16(4): 886-897.
- 28Li Z, Li T, Gang F. 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. 2016; 26(4): 759-781.
- 29Kang Q, Wang W, Liu Y. Adaptive robust fuzzy control for a class of uncertain nonlinear systems in pure-feedback form. Paper presented at: 2008 International Conference on Intelligent Computation Technology and Automation (ICICTA); 2008; Hunan, China.
- 30Tong S, Li Y, Shi P. Observer-based adaptive fuzzy backstepping output feedback control of uncertain MIMO pure-feedback nonlinear systems. IEEE Trans Fuzzy Syst. 2012; 20(4): 771-785.
- 31Wang D. Neural network-based adaptive dynamic surface control of uncertain nonlinear pure-feedback systems. Int J Robust Nonlinear Control. 2015; 21(5): 527-541.
- 32Li T, Li Z, Wang D, Chen CLP. Output-feedback adaptive neural control for stochastic nonlinear time-varying delay systems with unknown control directions. IEEE Trans Neural Netw Learn Syst. 2015; 26(6): 1188-1201.
- 33Wang H, Chen B, Liu X, Liu K, Lin C. Robust adaptive fuzzy tracking control for pure-feedback stochastic nonlinear systems with input constraints. IEEE Trans Cybern. 2013; 43(6): 2093-2104.
- 34Liu Z, Wang F, Zhang Y, Chen X, Chen CLP. Adaptive tracking control for a class of nonlinear systems with a fuzzy dead-zone input. IEEE Trans Fuzzy Syst. 2015; 23(1): 193-204.
- 35Chang X-L, Li Z-M, Park JH. Fuzzy generalized h2 filtering for nonlinear discrete-time systems with measurement quantization. IEEE Trans Syst Man Cybern Syst. 2018; 48(12): 2419-2430. https://doi.org/10.1109/TSMC.2017.2743012
- 36Li Y, Tong S, Li T. Observer-based adaptive fuzzy tracking control of MIMO stochastic nonlinear systems with unknown control directions and unknown dead zones. IEEE Trans Fuzzy Syst. 2015; 23(4): 1228-1241.
- 37Liu Y-J, Tong S. Adaptive fuzzy identification and control for a class of nonlinear pure-feedback MIMO systems with unknown dead zones. IEEE Trans Fuzzy Syst. 2015; 23(5): 1387-1398.
- 38Huang J, Liu Z, Wu Y. New results on adaptive control for a class of delayed nonholonomic systems. Int J Control Autom Syst. 2017; 15(2): 611-618.
- 39Zhang T-P, Wen H, Zhu Q. Adaptive fuzzy control of nonlinear systems in pure feedback form based on input-to-state stability. IEEE Trans Fuzzy Syst. 2010; 18(1): 80-93.
- 40Wang M, Ge SS, Hong K-S. Approximation-based adaptive tracking control of pure-feedback nonlinear systems with multiple unknown time-varying delays. IEEE Trans Neural Netw. 2010; 21(11): 1804.
- 41Chen B, Tong S, Liu X. Fuzzy approximate disturbance decoupling of MIMO nonlinear systems by backstepping approach. Fuzzy Sets Syst. 2007; 158(10): 1097-1125.
- 42Liu Z, Wu Y. A decoupled adaptive control algorithm for global state feedback stabilization of a class of nonlinear systems. Int J Adapt Control Signal Process. 2015; 29(9): 1165–1188.
- 43Zhao X, Shi P, Zheng X, Zhang L. Adaptive tracking control for switched stochastic nonlinear systems with unknown actuator dead-zone. Automatica. 2015; 60: 193-200.
- 44Shenoi BA. Introduction to Digital Signal Processing and Filter Design. Hoboken, NJ:John Wiley & Sons; 2005.
10.1002/0471656372 Google Scholar