Prescribed-time control of stochastic high-order nonlinear systems

Hui Wang; Hui Wang

doi:10.3934/mbe.2022531

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 11: 11399-11408. doi: 10.3934/mbe.2022531

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Research article Special Issues

Prescribed-time control of stochastic high-order nonlinear systems

Hui Wang ^,

School of Mathematics and Statistics Science, Ludong University, Yantai 264025, China

Received: 19 July 2022 Revised: 29 July 2022 Accepted: 07 August 2022 Published: 09 August 2022

In this paper, the prescribed-time stabilization is studied for stochastic high-order nonlinear systems. Different from the previous research results on stochastic high-order nonlinear systems where only asymptotic stabilization or finite-time stabilization is considered, this paper proposes a new design to achieve stabilization in the prescribed-time. Specifically, the designed controller can ensure that the closed-loop system has an almost surely unique strong solution and the equilibrium of the closed-loop system is prescribed-time mean-square stable. The design method is verified by an example.
- prescribed-time stabilization,
- high-order nonlinear,
- stochastic
Citation: Hui Wang. Prescribed-time control of stochastic high-order nonlinear systems[J]. Mathematical Biosciences and Engineering, 2022, 19(11): 11399-11408. doi: 10.3934/mbe.2022531

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Abstract

In this paper, the prescribed-time stabilization is studied for stochastic high-order nonlinear systems. Different from the previous research results on stochastic high-order nonlinear systems where only asymptotic stabilization or finite-time stabilization is considered, this paper proposes a new design to achieve stabilization in the prescribed-time. Specifically, the designed controller can ensure that the closed-loop system has an almost surely unique strong solution and the equilibrium of the closed-loop system is prescribed-time mean-square stable. The design method is verified by an example.

References

[1]	Z. G. Pan, T. Basar, Adaptive controller design for tracking and disturbance attenuation in parametric strict-feedback nonlinear systems, IEEE Trans. Autom. Control, 43 (1998), 1066–1083. https://doi.org/10.1109/9.704978 doi: 10.1109/9.704978
[2]	Z. G. Pan, T. Basar, Backstepping controller design for nonlinear stochastic systems under a risk-sensitive cost criterion, SIAM J. Control Optim., 37 (1999), 957–995. https://doi.org/10.1137/S0363012996307059 doi: 10.1137/S0363012996307059
[3]	Z. G. Pan, Y. Liu, S. Shi, Output feedback stabilization for stochastic nonlinear systems in observer canonical form with stable zero-dynamics, Sci. China, 44 (2001), 292–308. https://doi.org/10.1007/BF02714717 doi: 10.1007/BF02714717
[4]	H. Deng, M. Krsti$\acute{c}$, Stochastic nonlinear stabilization, part i: a backstepping design, Syst. Control Lett., 32 (1997), 143–150. https://doi.org/10.1016/S0167-6911(97)00068-6 doi: 10.1016/S0167-6911(97)00068-6
[5]	H. Deng, M. Krsti$\acute{c}$, Output-feedback stochastic nonlinear stabilization, IEEE Trans. Autom. Control, 44 (1999), 328–333. https://doi.org/10.1109/9.746260 doi: 10.1109/9.746260
[6]	H. Deng, M. Krsti$\acute{c}$, Output-feedback stabilization of stochastic nonlinear systems driven by noise of unknown covariance, Syst. Control Lett., 39 (2000), 173–182. https://doi.org/10.1016/S0167-6911(99)00084-5 doi: 10.1016/S0167-6911(99)00084-5
[7]	H. Deng, M. Krsti$\acute{c}$, R. J. Williams, Stabilization of stochastic nonlinear driven by noise of unknown covariance, IEEE Trans. Autom. Control, 46 (2001), 1237–1253. https://doi.org/10.1109/9.940927 doi: 10.1109/9.940927
[8]	M. Krsti$\acute{c}$, H. Deng, Stabilization of Uncertain Nonlinear Systems, Springer, New York, 1998.
[9]	W. Q. Li, L. Liu, G. Feng, Cooperative control of multiple nonlinear benchmark systems perturbed by second-order moment processes, IEEE Trans. Cybern., 50 (2020), 902–910. https://doi.org/10.1109/TCYB.2018.2869385 doi: 10.1109/TCYB.2018.2869385
[10]	W. Q. Li, M. Krsti$\acute{c}$, Stochastic adaptive nonlinear control with filterless least-squares, IEEE Trans. Autom. Control, 66 (2021), 3893–3905. https://doi.org/10.1109/TAC.2020.3027650 doi: 10.1109/TAC.2020.3027650
[11]	W. Q. Li, X. X. Yao, M. Krsti$\acute{c}$, Adaptive-gain observer-based stabilization of stochastic strict-feedback systems with sensor uncertainty, Automatica, 120 (2020), 109112. https://doi.org/10.1016/j.automatica.2020.109112 doi: 10.1016/j.automatica.2020.109112
[12]	W. Q. Li, M. Krsti$\acute{c}$, Mean-nonovershooting control of stochastic nonlinear systems, IEEE Trans. Autom. Control, 66 (2021), 5756–5771. https://doi.org/10.1109/TAC.2020.3042454 doi: 10.1109/TAC.2020.3042454
[13]	X. J. Xie, N. Duan, Output tracking of high-order stochastic nonlinear systems with application to benchmark mechanical system, IEEE Trans. Autom. Control, 55 (2010), 1197–1202. https://doi.org/10.1109/TAC.2010.2043004 doi: 10.1109/TAC.2010.2043004
[14]	X. J. Xie, J. Tian, State-feedback stabilization for high-order stochastic nonlinear systems with stochastic inverse dynamics, Int. J. Robust Nonlinear, 17 (2007), 1343–1362. https://doi.org/10.1002/rnc.1177 doi: 10.1002/rnc.1177
[15]	W. Q. Li, X. J. Xie, S. Y. Zhang, Output-feedback stabilization of stochastic high-order nonlinear systems under weaker conditions, SIAM J. Control Optim., 49 (2011), 1262–1282. https://doi.org/10.1137/100798259 doi: 10.1137/100798259
[16]	W. Q. Li, L. Liu, G. Feng, Output tracking of stochastic nonlinear systems with unstable linearization, Int. J. Robust Nonlinear, 28 (2018), 466–477. https://doi.org/10.1002/rnc.3877 doi: 10.1002/rnc.3877
[17]	R. H. Cui, X. J. Xie, Adaptive state-feedback stabilization of state-constrained stochastic high-order nonlinear systems, Sci. China Inf. Sci., 64 (2021), 200203. https://linkspringer.53yu.com/article/10.1007/s11432-021-3293-0
[18]	Y. D. Song, Y. J. Wang, J. C. Holloway, M. Krsti$\acute{c}$, Time-varying feedback for robust regulation of normal-form nonlinear systems in prescribed finite time, Automatica, 83 (2017), 243–251. https://doi.org/10.1016/j.automatica.2017.06.008 doi: 10.1016/j.automatica.2017.06.008
[19]	Y. D. Song, Y. J. Wang, M. Krsti$\acute{c}$, Time-varying feedback for stabilization in prescribed finite time, Int. J. Robust Nonlinear, 29 (2019), 618–633. https://doi.org/10.1002/rnc.4084 doi: 10.1002/rnc.4084
[20]	Y. J. Wang, Y. D. Song, D. J. Hill, M. Krsti$\acute{c}$, Prescribed finite time consensus and containment control of networked multi-agent systems, IEEE Trans. Cybern., 49 (2019), 1138–1147. https://doi.org/10.1109/TCYB.2017.2788874 doi: 10.1109/TCYB.2017.2788874
[21]	J. Holloway, M. Krsti$\acute{c}$, Prescribed-time observers for linear systems in observer canonical form, IEEE Trans. Autom. Control, 64 (2019), 3905–3912. https://doi.org/10.1109/TAC.2018.2890751 doi: 10.1109/TAC.2018.2890751
[22]	J. Holloway, M. Krsti$\acute{c}$, Prescribed-time output feedback for linear systems in controllable canonical form, Automatica, 107 (2019), 77–85. https://doi.org/10.1016/j.automatica.2019.05.027 doi: 10.1016/j.automatica.2019.05.027
[23]	P. Krishnamurthy, F. Khorrami, M. Krsti$\acute{c}$, Robust adaptive prescribed-time stabilization via output feedback for uncertain nonlinear strict-feedback-like systems, Eur. J. Control, 55 (2020), 14–23. https://doi.org/10.1016/j.ejcon.2019.09.005 doi: 10.1016/j.ejcon.2019.09.005
[24]	W. Q. Li, M. Krsti$\acute{c}$, Stochastic nonlinear prescribed-time stabilization and inverse optimality, IEEE Trans. Autom. Contr., 67 (2022), 1179–1193. https://doi.org/10.1109/TAC.2021.3061646 doi: 10.1109/TAC.2021.3061646
[25]	W. Q. Li, M. Krsti$\acute{c}$, Prescribed-time control of stochastic nonlinear systems with reduced control effort, J. Syst. Sci. Complex., 34 (2021), 1782–1800. https://doi.org/10.1007/s11424-021-1217-7 doi: 10.1007/s11424-021-1217-7
[26]	W. Q. Li, M. Krsti$\acute{c}$, Prescribed-time output-feedback control of stochastic nonlinear systems, IEEE Trans. Autom. Control, 68 (2023). https://doi.org/10.1109/TAC.2022.3151587 doi: 10.1109/TAC.2022.3151587
[27]	W. Q. Li, L. Liu, G. Feng, Distributed output-feedback tracking of multiple nonlinear systems with unmeasurable states, IEEE Trans. Syst. Man Cybern., 51 (2021), 477–486. https://doi.org/10.1109/TSMC.2018.2875453 doi: 10.1109/TSMC.2018.2875453
[28]	X. D. Li, D. W. Ho, J. D. Cao, Finite-time stability and settling-time estimation of nonlinear impulsive systems, Automatica, 99 (2019), 361–368. https://doi.org/10.1016/j.automatica.2018.10.024 doi: 10.1016/j.automatica.2018.10.024
[29]	X. D. Li, S. J. Song, J. H. Wu, Exponential stability of nonlinear systems with delayed impulses and applications, IEEE Trans. Autom. Control, 64 (2019), 4024–4034. https://doi.org/10.1109/TAC.2019.2905271 doi: 10.1109/TAC.2019.2905271
[30]	X. D. Li, D. X. Peng, J. D. Cao, Lyapunov stability for impulsive systems via event-triggered impulsive control, IEEE Trans. Autom. Control, 65 (2020), 4908–4913. https://doi.org/10.1109/TAC.2020.2964558 doi: 10.1109/TAC.2020.2964558
[31]	R. H. Cui, X. J. Xie, Finite-time stabilization of output-constrained stochastic high-order nonlinear systems with high-order and low-order nonlinearities, Automatica, 136 (2022), 110085. https://doi.org/10.1016/j.automatica.2021.110085 doi: 10.1016/j.automatica.2021.110085
[32]	R. H. Cui, X. J. Xie, Finite-time stabilization of stochastic low-order nonlinear systems with time-varying orders and FT-SISS inverse dynamics, Automatica, 125 (2021), 109418. https://doi.org/10.1016/j.automatica.2020.109418 doi: 10.1016/j.automatica.2020.109418
[33]	R. H. Cui, X. J. Xie, Output feedback stabilization of stochastic planar nonlinear systems with output constraint, Automatica, 143 (2022), 110471. https://doi.org/10.1016/j.automatica.2022.110471 doi: 10.1016/j.automatica.2022.110471
[34]	R. H. Cui, X. J. Xie, Adaptive state-feedback stabilization of state-constrained stochastic high-order nonlinear systems, Sci. China Inf. Sci., 64 (2021), 1–11. https://doi.org/10.1007/s11432-021-3293-0 doi: 10.1007/s11432-021-3293-0

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