Finite-time stabilization for uncertain nonlinear systems with impulsive disturbance via aperiodic intermittent control. (English) Zbl 1511.93115
Summary: This paper ensures finite-time stabilization (FTS) and finite-time contractive stabilization (FTCS) for impulsive systems with time-varying parametric uncertainties by investigating the design of an aperiodic intermittent controller, where uncertain impulsive disturbance is generated at the instants caused by the control action to the plant. Based on the Lyapunov methods, several sufficient conditions are proposed to guarantee the FTS and FTCS. In the framework of finite-time, two relationships between impulsive disturbance, aperiodic control periods, and aperiodic control widths are established to guarantee the FTS and FTCS for the system, respectively. Moreover, such two relationships can potentially increase the freedom of the designed control periods and control widths. Finally, two numerical simulations and a practical application are given to show the validity of the aperiodic intermittent controller.
MSC:
| 93D40 | Finite-time stability |
| 34A37 | Ordinary differential equations with impulses |
| 34D20 | Stability of solutions to ordinary differential equations |
Keywords:
finite-time stabilization; contractive stabilization; impulsive disturbance; aperiodic intermittent control; uncertaintiesReferences:
| [1] | Haddad, W.; Chellaboina, V.; Nersesov, S., Impulsive and Hybrid Dynamcial Systems: Stability, Dissipativity and Control (2006), Princeton University Press: Princeton University Press New Jersey · Zbl 1114.34001 |
| [2] | Masutani, Y.; Matsushita, M.; Miyazaki, F., Flyaround maneuvers on a satellite orbit by impulsive thrust control, Proceedings 2001 ICRA. IEEE International Conference on Robotics and Automation (Cat. No. 01CH37164), vol. 1, 421-426 (2001), IEEE |
| [3] | Yang, T., Impulsive Control Theory, vol. 272 (2001), Springer Science & Business Media · Zbl 0996.93003 |
| [4] | Suo, J.; Sun, J., Asymptotic stability of differential systems with impulsive effects suffered by logic choice, Automatica, 51, 302-307 (2015) · Zbl 1309.93132 |
| [5] | Shen, Z.; Li, C.; Li, H.; Cao, Z., Estimation of the domain of attraction for discrete-time linear impulsive control systems with input saturation, Appl. Math. Comput., 362, 124502 (2019) · Zbl 1433.93113 |
| [6] | Amato, F.; De Tommasi, G.; Pironti, A., Necessary and sufficient conditions for finite-time stability of impulsive dynamical linear systems, Automatica, 49, 8, 2546-2550 (2013) · Zbl 1364.93737 |
| [7] | Yang, X.; Lam, J.; Ho, D. W.; Feng, Z., Fixed-time synchronization of complex networks with impulsive effects via nonchattering control, IEEE Trans. Autom. Control, 62, 11, 5511-5521 (2017) · Zbl 1390.93393 |
| [8] | He, X.; Li, X.; Song, S., Finite-time input-to-state stability of nonlinear impulsive systems, Automatica, 135, 109994 (2022) · Zbl 1480.93367 |
| [9] | Dorato, P., Short Time Stability in Linear Time-varying Systems (1961), Polytechnic Institute of Brooklyn |
| [10] | Weiss, L.; Infante, E., On the stability of systems defined over a finite time interval, Proc. Natl. Acad. Sci. USA, 54, 1, 44 (1965) · Zbl 0134.30702 |
| [11] | Tan, F.; Zhou, B.; Duan, G.-R., Finite-time stabilization of linear time-varying systems by piecewise constant feedback, Automatica, 68, 277-285 (2016) · Zbl 1334.93144 |
| [12] | Mei, Z.; Fang, T.; Shen, H., Finite-time \(l_2 - l_\infty\) filtering for persistent dwell-time switched piecewise-affine systems against deception attacks, Appl. Math. Comput., 427, 127088 (2022) · Zbl 1510.93323 |
| [13] | Wu, K.-N.; Na, M.-Y.; Wang, L.; Ding, X.; Wu, B., Finite-time stability of impulsive reaction-diffusion systems with and without time delay, Appl. Math. Comput., 363, 124591 (2019) · Zbl 1433.35176 |
| [14] | Guan, K.; Luo, R., Finite-time stability of impulsive pantograph systems with applications, Syst. Control Lett., 157, 105054 (2021) · Zbl 1480.93365 |
| [15] | Yang, X.; Li, X., Finite-time stability of nonlinear impulsive systems with applications to neural networks, IEEE Trans. Neural Netw. Learn. Syst. (2021) |
| [16] | Guo, Y.; Yao, Y.; Wang, S.; Ma, K.; Liu, K.; Guo, J., Input-output finite-time stabilization of linear systems with finite-time boundedness, ISA Trans., 53, 4, 977-982 (2014) |
| [17] | Amato, F.; Ambrosino, R.; Ariola, M.; Cosentino, C.; De Tommasi, G., Finite-Time Stability and Control, vol. 453 (2014), Springer · Zbl 1297.93001 |
| [18] | Lv, X.; Li, X., Finite time stability and controller design for nonlinear impulsive sampled-data systems with applications, ISA Trans., 70, 30-36 (2017) |
| [19] | Song, J.; Niu, Y.; Zou, Y., Finite-time stabilization via sliding mode control, IEEE Trans. Autom. Control, 62, 3, 1478-1483 (2016) · Zbl 1366.93106 |
| [20] | Wu, Y.; Cao, J.; Alofi, A.; Abdullah, A.-M.; Elaiw, A., Finite-time boundedness and stabilization of uncertain switched neural networks with time-varying delay, Neural Netw., 69, 135-143 (2015) · Zbl 1398.34033 |
| [21] | Joby, M.; Santra, S.; Anthoni, S. M., Finite-time contractive boundedness of extracorporeal blood circulation process, Appl. Math. Comput., 388, 125527 (2021) · Zbl 1508.76135 |
| [22] | Amato, F.; Ambrosino, R.; Cosentino, C.; De Tommasi, G., Finite-time stabilization of impulsive dynamical linear systems, Nonlinear Anal., 5, 1, 89-101 (2011) · Zbl 1371.93159 |
| [23] | Liu, C.; Liu, L.; Cao, J.; Abdel-Aty, M., Intermittent event-triggered optimal leader-following consensus for nonlinear multi-agent systems via actor-critic algorithm, IEEE Trans. Neural Netw. Learn. Syst. (2021) |
| [24] | Liu, X.; Chen, T., Synchronization of complex networks via aperiodically intermittent pinning control, IEEE Trans. Autom. Control, 60, 12, 3316-3321 (2015) · Zbl 1360.93359 |
| [25] | Li, C.; Feng, G.; Liao, X., Stabilization of nonlinear systems via periodically intermittent control, IEEE Trans. Circuits Syst. II, 54, 11, 1019-1023 (2007) |
| [26] | Chen, W.-H.; Zhong, J.; Zheng, W. X., Delay-independent stabilization of a class of time-delay systems via periodically intermittent control, Automatica, 71, 89-97 (2016) · Zbl 1343.93069 |
| [27] | Wang, Q.; He, Y.; Tan, G.; Wu, M., Observer-based periodically intermittent control for linear systems via piecewise Lyapunov function method, Appl. Math. Comput., 293, 438-447 (2017) · Zbl 1411.93085 |
| [28] | Pan, L.; Cao, J., Stochastic quasi-synchronization for delayed dynamical networks via intermittent control, Commun. Nonlinear Sci. Numer. Simul., 17, 3, 1332-1343 (2012) · Zbl 1239.93114 |
| [29] | Zhang, Z.-M.; He, Y.; Wu, M.; Wang, Q.-G., Exponential synchronization of neural networks with time-varying delays via dynamic intermittent output feedback control, IEEE Trans. Syst., Man, Cybern., 49, 3, 612-622 (2017) |
| [30] | Liu, B.; Yang, M.; Xu, B.; Zhang, G., Exponential stabilization of continuous-time dynamical systems via time and event triggered aperiodic intermittent control, Appl. Math. Comput., 398, 125713 (2021) · Zbl 1508.34074 |
| [31] | Liu, B.; Yang, M.; Liu, T.; Hill, D. J., Stabilization to exponential input-to-state stability via aperiodic intermittent control, IEEE Trans. Autom. Control, 66, 6, 2913-2919 (2020) · Zbl 1467.93271 |
| [32] | Liu, D.; Ye, D., Exponential stabilization of delayed inertial memristive neural networks via aperiodically intermittent control strategy, IEEE Trans. Syst., Man, Cybern., 52, 1, 448-458 (2020) |
| [33] | Sang, H.; Zhao, J., Exponential synchronization and \(L_2\)-gain analysis of delayed chaotic neural networks via intermittent control with actuator saturation, IEEE Trans. Neural Netw. Learn. Syst., 30, 12, 3722-3734 (2019) |
| [34] | Wu, Y.; Li, H.; Li, W., Intermittent control strategy for synchronization analysis of time-varying complex dynamical networks, IEEE Trans. Syst., Man, Cybern., 51, 5, 3251-3262 (2019) |
| [35] | Li, X.; Yang, X.; Song, S., Lyapunov conditions for finite-time stability of time-varying time-delay systems, Automatica, 103, 135-140 (2019) · Zbl 1415.93188 |
| [36] | Nie, R.; He, S.; Liu, F.; Luan, X., Sliding mode controller design for conic-type nonlinear semi-Markovian jumping systems of time-delayed Chuas circuit, IEEE Trans. Syst., Man, Cybern., 51, 4, 2467-2475 (2019) |
| [37] | Xu, C.; Yang, X.; Lu, J.; Feng, J.; Alsaadi, F. E.; Hayat, T., Finite-time synchronization of networks via quantized intermittent pinning control, IEEE Trans. Cybern., 48, 10, 3021-3027 (2017) |
| [38] | Chen, W.-H.; Zheng, W. X., Robust stability and \(H_\infty \)-control of uncertain impulsive systems with time-delay, Automatica, 45, 1, 109-117 (2009) · Zbl 1154.93406 |
| [39] | Hu, M.-J.; Wang, Y.-W.; Xiao, J.-W., On finite-time stability and stabilization of positive systems with impulses, Nonlinear Anal., 31, 275-291 (2019) · Zbl 1408.93091 |
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