Observer-based fuzzy adaptive stabilization of uncertain switched stochastic nonlinear systems with input quantization. (English) Zbl 1409.93062
Summary: This paper proposes an observer-based fuzzy adaptive output feedback control scheme for a class of uncertain single-input and single-output (SISO) nonlinear stochastic systems with quantized input signals and arbitrary switchings. The SISO system under consideration contains completely unknown nonlinear functions, unmeasured system states and quantized input signals quantized by a hysteretic quantizer. By adopting a new nonlinear disposal of the quantized input, the relationship between the control input and the quantized input is established. The hysteretic quantizer that we take can effectively avoid the chattering phenomena. Furthermore, the introduction of a linear observer makes the estimation of the states possible. Based on the universal approximation ability of the fuzzy logic systems (FLSs) and backstepping recursive design with the common stochastic Lyapunov function approach, a quantized output feedback control scheme is constructed, where the dynamic surface control (DSC) is explored to alleviate the computation burden. The proposed control scheme cannot only guarantee the boundedness of signals but also make the output of the system converge to a small neighborhood of the origin. The simulation results are exhibited to demonstrate the validity of the control scheme.
MSC:
| 93D21 | Adaptive or robust stabilization |
| 93C42 | Fuzzy control/observation systems |
| 93C41 | Control/observation systems with incomplete information |
| 93C30 | Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems) |
| 93B52 | Feedback control |
| 93E03 | Stochastic systems in control theory (general) |
| 93C10 | Nonlinear systems in control theory |
References:
| [1] | Zhao, J.; Hill, D. J.; Liu, T., Synchronization of complex dynamical networks with switching topology: a switched system point of view, Automatica, 45, 11, 2502-2511 (2009) · Zbl 1183.93032 |
| [2] | Bao, W.; Li, B.; Chang, J.; Niu, W.; Yu, D., Switching control of thrust regulation and inlet buzz protection for ducted rocket, Acta Astronaut., 67, 7-8, 764-773 (2010) |
| [3] | Homaee, O.; Zakariazadeh, A.; Jadid, S., Real-time voltage control algorithm with switched capacitors in smart distribution system in presence of renewable generations, Int. J. Electr. Power Energy Syst. (2014) |
| [4] | Lin, A.; Silvester, J. A., Priority queueing strategies and buffer allocation protocols for traffic control at an ATM integrated broadband switching system, IEEE J. Sel. Areas Commun., 9, 9, 1524-1536 (1991) |
| [5] | Zhao, C. R.; Xie, X. J., Output feedback stabilization using small-gain method and reduced-order observer for stochastic nonlinear systems, IEEE Trans. Autom. Control, 58, 2, 523-529 (2013) · Zbl 1369.93711 |
| [6] | Liu, L.; Xu, S.; Xie, X., New results on the fourth moment exponentially stable for a class of stochastic nonlinear systems and its application, Nonlinear Dyn., 89, 2, 1-9 (2017) · Zbl 1384.93124 |
| [7] | Niu, B.; Karimi, H. R.; Wang, H.; Liu, Y., Adaptive output-feedback controller design for switched nonlinear stochastic systems with a modified average dwell-time method, IEEE Trans. Syst. Man Cybern. Syst., 47, 7, 1371-1382 (2017) |
| [8] | Li, Y.; Sui, S.; Tong, S., Adaptive fuzzy control design for stochastic nonlinear switched systems with arbitrary switchings and unmodeled dynamics., IEEE Trans. Syst. Man Cybern., 47, 2, 403-414 (2017) |
| [9] | Sui, S.; Li, Y.; Tong, S., Observer-based adaptive fuzzy control for switched stochastic nonlinear systems with partial tracking errors constrained, IEEE Trans. Syst. Man Cybern. Syst., 46, 12, 1605-1617 (2016) |
| [10] | Liu, Y.; Ma, H.; Ma, H., Adaptive fuzzy fault-tolerant control for uncertain nonlinear switched stochastic systems with time-varying output constraints, IEEE Trans. Fuzzy Syst. (2018) |
| [11] | Hou, M.; Fu, F.; Duan, G., Global stabilization of switched stochastic nonlinear systems in strict-feedback form under arbitrary switchings, Automatica, 49, 8, 2571-2575 (2013) · Zbl 1364.93847 |
| [12] | Ren, H.; Zong, G.; Li, T., Event-triggered finite-time control for networked switched linear systems with asynchronous switching, IEEE Trans. Syst. Man Cybern. Syst. (2018) |
| [13] | Cheng, J.; Park, J. H.; Cao, J.; Zhang, D., Quantized \(H_∞\) filtering for switched linear parameter-varying systems with sojourn probabilities and unreliable communication channels, Inf. Sci., 466, 289-302 (2018) · Zbl 1448.93323 |
| [14] | Cheng, J.; Chang, X.; Park, J. H.; Li, H.; Wang, H., Fuzzy-model-based \(H_∞\) control for discrete-time switched systems with quantized feedback and unreliable links, Inf. Sci., 436, 181-196 (2018) · Zbl 1448.93180 |
| [15] | Zhao, X.; Yin, Y.; Zhang, L.; Yang, H., Control of switched nonlinear systems via T-S fuzzy modeling, IEEE Trans. Fuzzy Syst., 24, 1, 235-241 (2016) |
| [16] | Vu, L.; Liberzon, D., Common Lyapunov functions for families of commuting nonlinear systems, Syst. Control Lett., 54, 5, 405-416 (2005) · Zbl 1129.34321 |
| [17] | Zhao, X.; Zheng, X.; Niu, B.; Liu, L., Adaptive tracking control for a class of uncertain switched nonlinear systems, Automatica, 52, 185-191 (2015) · Zbl 1309.93081 |
| [18] | Wang, X.; Li, H.; Zong, G.; Zhao, X., Adaptive fuzzy tracking control for a class of high-order switched uncertain nonlinear systems, J. Frankl. Inst., 354, 15, 6567-6587 (2017) · Zbl 1373.93196 |
| [19] | Tong, S.; Zhang, L.; Li, Y., Observed-based adaptive fuzzy decentralized tracking control for switched uncertain nonlinear large-scale systems with dead zones, IEEE Trans. Syst. Man Cybern. Syst., 46, 1, 37-47 (2016) |
| [20] | Zhao, X.; Wang, X.; Zong, G.; Zheng, X., Adaptive neural tracking control for switched high-order stochastic nonlinear systems, IEEE Trans. Cybern., 47, 10, 3088-3099 (2017) |
| [21] | Ma, R.; Zhao, J., Backstepping design for global stabilization of switched nonlinear systems in lower triangular form under arbitrary switchings, Automatica, 46, 11, 1819-1823 (2010) · Zbl 1218.93075 |
| [22] | Wu, J., Stabilizing controllers design for switched nonlinear systems in strict-feedback form, Automatica, 45, 4, 1092-1096 (2009) · Zbl 1162.93030 |
| [23] | Yin, Y.; Zong, G.; Zhao, X., Improved stability criteria for switched positive linear systems with average dwell time switching, J. Frankl. Inst., 354, 8, 3472-3484 (2017) · Zbl 1364.93693 |
| [24] | Yin, Y.; Zhao, X.; Zheng, X., New stability and stabilization conditions of switched systems with mode-dependent average dwell time, Circuits Syst. Signal Process., 36, 1, 82-98 (2017) · Zbl 1368.93581 |
| [25] | Zhou, J.; Wen, C.; Yang, G., Adaptive backstepping stabilization of nonlinear uncertain systems with quantized input signal, IEEE Trans. Autom. Control, 59, 2, 460-464 (2014) · Zbl 1360.93626 |
| [26] | Yu, X.; Lin, Y., Adaptive backstepping quantized control for a class of nonlinear systems., IEEE Trans. Autom. Control, 62, 2, 981-985 (2017) · Zbl 1364.93353 |
| [27] | Li, Y.; Yang, G., Adaptive asymptotic tracking control of uncertain nonlinear systems with input quantization and actuator faults, Automatica (2016) · Zbl 1344.93061 |
| [28] | Xing, L.; Wen, C.; Su, H.; Liu, Z.; Cai, J., Robust control for a class of uncertain nonlinear systems with input quantization, Int. J. Robust Nonlinear Control, 26, 8, 1585-1596 (2016) · Zbl 1342.93044 |
| [29] | Xing, L.; Wen, C.; Zhu, Y.; Su, H.; Liu, Z., Output feedback control for uncertain nonlinear systems with input quantization, Automatica, 65, 191-202 (2016) · Zbl 1328.93148 |
| [30] | Chang, X.; Xiong, J.; Li, Z.; Park, J. H., Quantized static output feedback control for discrete-time systems, IEEE Trans. Ind. Inf., 14, 8, 3426-3435 (2018) |
| [31] | X. Chang, Y. Wang, Peak-to-peak filtering for networked nonlinear DC motor systems with quantization, IEEE Trans. Ind. Inf.DOI:10.1109/TII.2018.2805707.; X. Chang, Y. Wang, Peak-to-peak filtering for networked nonlinear DC motor systems with quantization, IEEE Trans. Ind. Inf.DOI:10.1109/TII.2018.2805707. |
| [32] | Sun, H.; Hou, L.; Zong, G.; Yu, X., Fixed-time attitude tracking control for spacecraft with input quantization, IEEE Trans. Aerosp. Electron. Syst. (2018) |
| [33] | Zhang, Z.; Ju, H. P.; Shao, H., Adaptive synchronization of uncertain unified chaotic systems via novel feedback controls, Nonlinear Dyn., 81, 1-2, 695-706 (2015) · Zbl 1347.93137 |
| [34] | Liu, Z.; Wu, Y., Universal strategies to explicit adaptive control of nonlinear time-delay systems with different structures, Automatica, 89, 151-159 (2018) · Zbl 1387.93101 |
| [35] | Zhao, Y.; Zhang, W., Observer-based controller design for singular stochastic Markov jump systems with state dependent noise, J. Syst. Sci. Complex., 29, 4, 946-958 (2016) · Zbl 1346.93352 |
| [36] | Lv, W.; Wang, F., Adaptive tracking control for a class of uncertain nonlinear systems with infinite number of actuator failures using neural networks, Adv. Differ. Equ., 2017, 1, 374 (2017) · Zbl 1444.93014 |
| [37] | Zhang, Z.; Shao, H.; Zhen, W.; Hao, S., Reduced-order observer design for the synchronization of the generalized lorenz chaotic systems, Appl. Math. Comput., 218, 14, 7614-7621 (2012) · Zbl 1250.34045 |
| [38] | Zhao, X.; Wang, X.; Zhang, S.; Zong, G., Adaptive neural backstepping control design for a class of nonsmooth nonlinear systems, IEEE Trans. Syst. Man Cybern. Syst. (2018) |
| [39] | Ma, J.; Ge, S. S.; Zheng, Z.; Hu, D., Adaptive NN control of a class of nonlinear systems with asymmetric saturation actuators, IEEE Trans. Neural Netw. Learn. Syst., 26, 7, 1532-1538 (2015) |
| [40] | Zhang, T.; Ge, S. S., Adaptive dynamic surface control of nonlinear systems with unknown dead zone in pure feedback form, Automatica, 44, 7, 1895-1903 (2008) · Zbl 1149.93322 |
| [41] | Sun, H.; Guo, L., Neural network-based DOBC for a class of nonlinear systems with unmatched disturbances, IEEE Trans. Neural Netw. Learn. Syst., 28, 2, 482-489 (2017) |
| [42] | Liu, Z.; Wang, F.; Zhang, Y.; Chen, C. P., Fuzzy adaptive quantized control for a class of stochastic nonlinear uncertain systems, IEEE Trans. Cybern., 46, 2, 524-534 (2016) |
| [43] | Tong, S.; Li, Y.; Li, Y.; Liu, Y., Observer-based adaptive fuzzy backstepping control for a class of stochastic nonlinear strict-feedback systems, IEEE Trans. Syst. Man Cybern. Part B (Cybern.), 41, 6, 1693-1704 (2011) |
| [44] | Sui, S.; Tong, S., Fuzzy adaptive quantized output feedback tracking control for switched nonlinear systems with input quantization, Fuzzy Sets Syst., 290, 56-78 (2016) · Zbl 1374.93158 |
| [45] | Xing, L.; Wen, C.; Su, H.; Cai, J.; Wang, L., A new adaptive control scheme for uncertain nonlinear systems with quantized input signal, J. Frankl. Inst., 352, 12, 5599-5610 (2015) · Zbl 1395.93314 |
| [46] | Xu, Y.; Li, Y.; Tong, S., Fuzzy adaptive actuator failure compensation dynamic surface control of multi-input and multi-output nonlinear systems, Int. J. Innov. Comput. Inf. Control, 9, 12, 4875-4888 (2013) |
| [47] | Li, Y.; Tong, S.; Li, T., Composite adaptive fuzzy output feedback control design for uncertain nonlinear strict-feedback systems with input saturation, IEEE Trans. Cybern., 45, 10, 2299-2308 (2015) |
| [48] | Wang, 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., 43, 6, 2093-2104 (2013) |
| [49] | Zhao, X.; Wang, X.; Zong, G.; Li, H., Fuzzy-approximation-based adaptive output-feedback control for uncertain non-smooth nonlinear systems, IEEE Trans. Fuzzy Syst. (2018) |
| [50] | Wang, H.; Liu, X.; Liu, K.; Karimi, H. R., Approximation-based adaptive fuzzy tracking control for a class of nonstrict-feedback stochastic nonlinear time-delay systems., IEEE Transactions on Fuzzy Systems, 23, 5, 1746-1760 (2015) |
| [51] | Niu, B.; Wang, D.; Alotaibi, N. D.; Alsaadi, F. E., Adaptive neural state-feedback tracking control of stochastic nonlinear switched systems: an average dwell-time method, IEEE Trans. Neural Netw. Learn. Syst. (2018) |
| [52] | Niu, B.; Wang, D.; Li, H.; Xie, X.; Alotaibi, N. D.; Alsaadi, F. E., A novel neural-network-based adaptive control scheme for output-constrained stochastic switched nonlinear systems, IEEE Trans. Syst. Man Cybern. Syst. (2017) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
