Observer-based model following sliding mode tracking control of discrete-time linear networked systems with two-channel event-triggered schemes and quantizations. (English) Zbl 1428.93066
Summary: This paper addresses the problem of \(H_\infty\) observer-based model following sliding mode tracking control for a class of linear discrete-time networked systems subject to event-triggered transmission schemes and quantizations occurring in both input and output channels. First, a dynamic event-triggered scheme and a static event-triggered scheme on sensor and controller sides are proposed, respectively, to reduce the number of unnecessary data transmission. Then, an observer is designed to estimate the system state. Considering the effects of quantization, networked conditions, external disturbance and event-triggered transmission schemes, the state error system and sliding mode dynamics are modeled as a new networked time-delay system. Based on this model and Lyapunov-Krasovskii functional method, sufficient conditions are derived to guarantee the resulting closed-loop system to be asymptotically stable with prescribed \(H_\infty\) performance. And then, a co-design method is present to obtain the observer gain, triggering parameter and sliding mode parameter, simultaneously. Furthermore, a sliding mode controller for reaching motion is developed to ensure the reachability of the sliding surface. Finally, simulation examples are present to verify the effective of the proposed design method.
MSC:
| 93C55 | Discrete-time control/observation systems |
| 93B07 | Observability |
| 93B12 | Variable structure systems |
| 93C62 | Digital control/observation systems |
Keywords:
event-triggered control; quantization; model following and output tracking; sliding mode control; networked control systems (NCSs)References:
| [1] | Luan, X.; Shi, P.; Liu, F., Stabilization of networked control systems with random delays, IEEE Trans. Autom. Control, 58, 9, 4323-4330 (2011) |
| [2] | Zhang, D.; Shi, P.; Wang, Q. G.; Yu, L., Analysis and synthesis of networked control systems: a survey of recent advances and challenges, ISA Trans., 66, 376-392 (2017) |
| [3] | Zhang, L.; Ning, Z.; Zheng, W. X., Observer-based control for piecewise-affine systems with both input and output quantization, IEEE Trans. Autom. Control, 62, 11, 5858-5865 (2017) · Zbl 1390.93520 |
| [4] | Zhang, L.; Ning, Z.; Wang, Z., Distributed filtering for fuzzy time-delay systems with packet dropouts and redundant channels, IEEE Trans. Syst. Man Cybern. Syst., 46, 4, 559-572 (2016) |
| [5] | Yue, D.; Tian, E.; Han, Q. L., A delay system method for designing event-triggered controllers of networked control systems, IEEE Trans. Autom. Control, 58, 2, 475-481 (2013) · Zbl 1369.93183 |
| [6] | Peng, C.; Yang, T. C., Event-triggered communication and \(H_∞\) control co-design for networked control systems, Automatica, 49, 5, 1326-1332 (2013) · Zbl 1319.93022 |
| [7] | Wu, L.; Gao, Y.; Liu, J.; Li, H., Event-triggered sliding mode control of stochastic systems via output feedback, Automatica, 82, 79-92 (2017) · Zbl 1376.93030 |
| [8] | Gu, Z.; Yue, D.; Liu, J., \(H_∞\) tracking control of nonlinear networked systems with a novel adaptive event-triggered communication, J. Frankl. Inst., 354, 8, 3540-3553 (2017) · Zbl 1364.93212 |
| [9] | Li, Q.; Shen, B.; Wang, Z.; Huang, T.; Luo, J., Synchronization control for a class of discrete time-delay complex dynamical networks: a dynamic event-triggered approach, IEEE Trans. Cybern., 49, 5, 1979-1986 (2019) |
| [10] | Ge, X.; Han, Q. L.; Wang, Z., A dynamic event-triggered transmission scheme for distributed set-membership estimation over wireless sensor networks, IEEE Trans. Cybern., 99, 1-13 (2017) |
| [11] | Zhong, Z.; Zhu, Y., Observer-based output-feedback control of large-scale networked fuzzy systems with two channel event-triggering, J. Frankl. Inst., 354, 13, 5398-5420 (2017) · Zbl 1395.93339 |
| [12] | Fu, M.; Xie, L., The sector bound approach to quantized feedback control, IEEE Trans. Autom. Control, 50, 11, 1698-1711 (2005) · Zbl 1365.81064 |
| [13] | Chang, X. H.; Li, Z. M.; Xiong, J.; Wang, Y. M., LMI approaches to input and output quantized feedback stabilization of linear systems, Appl. Math. Comput., 315, 162-175 (2017) · Zbl 1426.93257 |
| [14] | Guo, X. G.; Wang, J. L.; Liao, F., Adaptive quantised \(H_∞\) observer-based output feedback control for nonlinear systems with input and output quantisation, IET Control Theory Appl., 11, 2, 263-272 (2017) |
| [15] | Yan, H.; Yan, S.; Zhang, H., \(l_2\) control design of event-triggered networked control systems with quantizations, J. Frankl. Inst., 352, 1, 332-345 (2015) · Zbl 1307.93259 |
| [16] | Liu, Y.; Wang, Z.; He, X.; Zhou, D. H., Finite-horizon quantized \(H_∞\) filter design for a class of time-varying systems under event-triggered transmissions, Syst. Control Lett., 103, 38-44 (2017) · Zbl 1370.93284 |
| [17] | Pai, M. C., Discrete-time output feedback quasi-sliding mode control for robust tracking and model following of uncertain systems, J. Frankl. Inst., 351, 5, 2623-2639 (2014) · Zbl 1372.93069 |
| [18] | Chen, L.; Liu, M.; Huang, X.; Fu, S.; Qiu, J., Adaptive fuzzy sliding mode control for network-based nonlinear systems with actuator failures, IEEE Trans. Fuzzy Syst., 26, 3, 1311-1323 (2018) |
| [19] | Su, X.; Liu, X.; Shi, P.; Song, Y. D., Sliding mode control of hybrid switched systems via an event-triggered mechanism, Automatica, 90, 294-303 (2018) · Zbl 1387.93055 |
| [20] | Su, X.; Liu, X.; Shi, P.; Yang, R., Sliding mode control of discrete-time switched systems with repeated scalar nonlinearities, IEEE Trans. Autom. Control, 62, 9, 4604-4610 (2017) · Zbl 1390.93508 |
| [21] | Han, Y.; Kao, Y.; Gao, C., Robust sliding mode control for uncertain discrete singular systems with time-varying delays and external disturbances, Automatica, 75, 210-216 (2017) · Zbl 1351.93035 |
| [22] | Ran, S.; Xue, Y.; Zheng, B. C.; Wang, Z., Quantized feedback fuzzy sliding mode control design via memory-based strategy, Appl. Math. Comput., 298, 283-295 (2017) · Zbl 1411.93045 |
| [23] | Liu, M.; Cao, X.; Zhang, S., Sliding mode control of quantized systems against bounded disturbances, Inf. Sci., 274, 261-272 (2014) · Zbl 1339.93037 |
| [24] | Zheng, B. C.; Yu, X.; Xue, Y., Quantized feedback sliding mode control: an event-triggered approach, Automatica, 91, 126-135 (2018) · Zbl 1387.93056 |
| [25] | Chu, X.; Li, M., \(H_∞\) observer-based event-triggered sliding mode control for a class of discrete-time nonlinear networked systems with quantizations, ISA Trans., 79, 13-26 (2018) |
| [26] | Zhang, D.; Han, Q. L.; Jia, X. C., Observer-based \(H_∞\) output tracking control for networked control systems, Int. J. Robust Nonlinear Control, 24, 14, 2741-2760 (2014) · Zbl 1305.93068 |
| [27] | Wu, H., Adaptive robust tracking and model following of uncertain dynamical systems with multiple time delays, IEEE Trans. Autom. Control, 49, 4, 611-616 (2004) · Zbl 1365.93227 |
| [28] | Pai, M. C., Discrete-time sliding mode control for robust tracking and model following of systems with state and input delays, Nonlinear Dyn., 76, 3, 1769-1779 (2014) · Zbl 1314.93040 |
| [29] | Pai, M. C., Observer-based adaptive sliding mode control for robust tracking and model following, Int. J. Control Autom. Syst., 11, 2, 225-232 (2013) |
| [30] | Rahmani, B., Robust output feedback sliding mode control for uncertain discrete time systems, Nonlinear Anal. Hybrid Syst., 24, 83-99 (2017) · Zbl 1377.93055 |
| [31] | Chang, J. L., Robust discrete-time model reference sliding-mode controller design with state and disturbance estimation, IEEE Trans. Ind. Electron., 55, 11, 4065-4074 (2008) |
| [32] | Tang, Z., Event-triggered consensus of linear discrete-time multi-agent systems with time-varying topology, Int. J. Control Autom. Syst., 16, 3, 1179-1185 (2018) |
| [33] | Yang, G. H.; Ye, D., Reliable \(H_∞\) control of linear systems with adaptive mechanism, IEEE Trans. Autom. Control, 55, 1, 242-247 (2010) · Zbl 1368.93161 |
| [34] | Seuret, A.; Gouaisbaut, F.; Fridman, E., Stability of discrete-time systems with time-varying delays via a novel summation inequality, IEEE Trans. Autom. Control, 60, 10, 2740-2745 (2015) · Zbl 1360.93612 |
| [35] | Park, P.; Ko, J. W.; Jeong, C., Reciprocally convex approach to stability of systems with time-varying delays, Automatica, 47, 1, 235-238 (2011) · Zbl 1209.93076 |
| [36] | Xie, L., Output feedback \(H_∞\) control of systems with parameter uncertainty, Int. J. Control, 63, 4, 741-750 (1996) · Zbl 0841.93014 |
| [37] | de Souza, C. E., Robust stability and stabilization of uncertain discrete-time Markovian jump linear systems, IEEE Trans. Autom. Control, 51, 5, 836-841 (2006) · Zbl 1366.93479 |
| [38] | Chang, X. H.; Yang, G. H., New results on output feedback \(H_∞\) control for linear discrete-time systems, IEEE Trans. Autom. Control, 59, 5, 1355-1359 (2014) · Zbl 1360.93383 |
| [39] | Yun, S. W.; Choi, Y. J.; Park, P., \(H_2\) control of continuous-time uncertain linear systems with input quantization and matched disturbances, Automatica, 45, 10, 2435-2439 (2009) · Zbl 1183.93117 |
| [40] | Khandekar, A. A.; Malwatkar, G. M.; Patre, B. M., Discrete sliding mode control for robust tracking of higher order delay time systems with experimental application, ISA Trans., 52, 1, 36-44 (2013) |
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