具有执行器饱和的广义随机系统的滑模自适应控制
Sliding Mode Adaptive Control for Singular Stochastic Systems with Time-Delay and Uncertainty
DOI: 10.12677/PM.2021.115092, PDF,    国家自然科学基金支持
作者: 张钟月, 苏晓明*：沈阳工业大学理学院，辽宁 沈阳
关键词: 广义随机系统；滑模控制；自适应控制；Singular Stochastic System； Sliding Mode Control； Adaptive Control
摘要: 本文主要研究了具有时滞不确定性的广义随机系统的滑模自适应控制问题。首先设计了适合可行的积分型滑模面函数，进一步求得等效控制器，从而得到了闭环系统，利用LMI和李雅普诺夫函数理论，得到闭环系统带有H∞扰动衰减水平的容许性；设计一种新的自适应滑模控制率，保证了滑模面的有限时间可达性。最后，用一个算例仿真证明了本文所提方法的有效性。
Abstract: In this paper, the problem of adaptive sliding mode control for singular stochastic systems with delay uncertainties is studied. Firstly, a suitable and feasible integral sliding mode surface function is designed, and the equivalent controller is obtained to get the closed-loop system. By using LMI and Lyapunov function theory, the permissibility of the closed-loop system with disturbance attenuation level is obtained. A new adaptive sliding mode control rate is designed to ensure the finite time accessibility of the sliding mode surface. Finally, a numerical example is given to demonstrate the effectiveness of the proposed method.
文章引用：张钟月, 苏晓明. 具有执行器饱和的广义随机系统的滑模自适应控制[J]. 理论数学, 2021, 11(5): 776-789. https://doi.org/10.12677/PM.2021.115092

参考文献

[1] Gibbs, J.W. (1962) Thermodynamics, Elementary Principles in Statistical Mechanics and Vector Analysis. American Journal of Physics, 30, 313-314. [Google Scholar] [CrossRef] 
[2] Liu, Z., Zhao, L. and Gao, C.C. (2017) Observer-Based Adaptive H∞ Control of Uncertain Stochastic Singular Systems via Integral Sliding Mode Technique. IET Control Theory & Applications, 11, 668-676. [Google Scholar] [CrossRef] 
[3] Xia, J.W. (2007) Robust Filter Design for Uncertain Time-Delay Singular Stochastic Systems with Markovian Jump. Journal of Control Theory and Application, 5, 331-335. [Google Scholar] [CrossRef] 
[4] Xing, S.Y. and Deng, F.Q. (2017) Delay-Dependent Dissipative Filtering for Nonlinear Stochastic Singular Systems with Time-Varying Delays. Science China-Information Science, 60, Article No. 120208. [Google Scholar] [CrossRef] 
[5] Ma, S. and Boukas, E.K. (2009) Stability and Robust Stability of Uncertain Discrete Stochastic Hybrid Singular Systems with Time-Delay. IET Control Theory and Application, 3, 1217-1225. [Google Scholar] [CrossRef] 
[6] Cao, Y.-Y. and Lin, Z.L. (2003) Stability Analysis of Discrete-Time Systems with Actuator Saturation by a Saturation-Dependent Lyapunov Function. Automatica, 39, 1235-1241. [Google Scholar] [CrossRef] 
[7] Li, Y.L. and Lin, Z.L. (2014) Improved Set in Variance Conditions for Singular Linear Systems Subject to Actuator Saturation. Control Theory & Applications, 31, 955-961.
[8] Ma, Y.M. and Yang, G.H. (2010) Stability Analysis for Linear Discrete-Time Systems Subject to Ac-tuator Saturation. Journal of Control Theory and Applications, 8, 245-248. [Google Scholar] [CrossRef] 
[9] Chen, Q., Ni, W. and Wang, L.A. (2012) Stability Analysis and Estimate of Domain of Attraction for Discrete-time Linear Saturated System. Control Engineering of China, A1, 161-164, 171.
[10] Li, Y.L. and Lin, Z.L. (2013) Improvements to the Linear Differential Inclusion Approach to Stability Analysis of Linear Systems with Saturated Linear Feedback. Automatic, 49, 821-828. [Google Scholar] [CrossRef] 
[11] Shi, T., Su, H.Y. and Chu, J. (2009) Stability Analysis for Continuous-Time Systems with Actuator Saturation. Journal of Control Theory and Applications, 7, Article No. 352. [Google Scholar] [CrossRef] 
[12] Zuo, Z.Q., Ho, D.W.C. and Wang, Y.J. (2010) Fault Tolerant Control for Singular Systems with Actuator Saturation and Nonlinear Perturbation. Automatica, 46, 569-576. [Google Scholar] [CrossRef] 
[13] Su, H.Y. and Pan, H.H. (2000) Robust Control for a Class of Uncertain Time-delay Systems Containing Nonlinear Saturating Actuators. Control and Decision, 15, 23-26.
[14] Fu, L. and Ma, Y.C. (2016) Passive Control for Singular Time-Delay System with Actuator Saturation. Applied Mathematics and Computation, 289, 181-193. [Google Scholar] [CrossRef] 
[15] Ma, Y.C., Fu, L., Jing, Y.H. and Zhang, Q.L. (2015) Finite-Time H∞ Control for a Class of Discrete-Time Switched Singular Time-Delay Systems Subject to Actuator Saturation. Applied Mathematics and Computation, 261, 264-283. [Google Scholar] [CrossRef] 
[16] Ma, Y.C. and Fu, L. (2016) H∞ Robust Exponential Stability and Memory State Feedback Control for Uncertain Singular Time-Delay Systems with Saturating Actuators. IET Control Theory & Applications, 10, 328-338. [Google Scholar] [CrossRef] 
[17] Sakthivel, R., Joby, M., Wang, C. and Kaviarasan, B. (2018) Fi-nite-Time Fault-Tolerant Control of Neutral Systems against Actuator Saturation and Nonlinear Actuator Faults. Applied Mathematics and Computation, 332, 425-436. [Google Scholar] [CrossRef] 
[18] Lü, L., Yu, M., Li, C., et al. (2013) Projective Synchronization of a Class of Complex Network Based on High-Order Sliding Mode Control. Nonlinear Dynamics, 73, 411-416. [Google Scholar] [CrossRef] 
[19] Adamy, J. and Flemming, A. (2004) Soft Variable-Structure Controls: A Survey. Automatica, 40, 1821-1844. [Google Scholar] [CrossRef] 
[20] Gao, L., Luo, F. and Yao, X. (2018) Finite-Time Annular Domain Stability of Stochastic Impulsive Systems with Markovian Jumping under Asynchronous Switching. Interna-tional Journal of Control, 24, 156-159.
[21] Yu, X., Yin, J. and Khoo, S. (2019) Generalized Lyapunov Criteria on Finite-Time Stability of Stochastic Nonlinear Systems. Automatica, 107, 183-189. [Google Scholar] [CrossRef] 
[22] Jiang, B., Karimi, H.R., Kao, Y. and Gao, C. (2018) A Novel Robust Fuzzy Integral Sliding Mode Control for Nonlinear Semi-Markov Jump T-S Fuzzy Systems. IEEE Transactions on Fuzzy Systems, 26, 3594-3604. [Google Scholar] [CrossRef] 
[23] Bonfifiglio, A., Cacciacarne, S., Invernizzi, M., et al. (2019) A Sliding Mode Control Approach for Gas Turbine Power Generators. IEEE Transactions on Energy Conversion, 34, 921-932. [Google Scholar] [CrossRef] 
[24] Lin, Y., Balas, V.E., Balas, M.M. and Peng, J. (2019) Adaptive Backstepping Nonsingular Fast Terminal Sliding Mode Control for Hydro-Turbine Governor Design. Energies, 13, 126. [Google Scholar] [CrossRef] 
[25] Zohrabi, N., Zakeri, H., Abolmasoumi, A.H. and Momeni, H.R. (2019) An Adaptive Sliding Mode Approach for Markov Jump Systems with Uncertain Mode-Dependent Time-Varying Delays and Partly Unknown Transition Probabilities. International Journal of Dynamics and Control, 7, 209-225. [Google Scholar] [CrossRef] 
[26] Aurelien, Y.T., Hervé, S.A. and Léandre, N.N. (2019) Application of Higher Order Sliding Mode Observer and Super Twisting Observer Based Super Twisting Control in Hydroelectric Power Plants. International Journal of Recent Technology and Engineering, 8, 3649-3653. [Google Scholar] [CrossRef] 
[27] Shen, M., Zhang, H. and Park, J.H. (2018) Observer-Based Quantized Sliding Mode Infinity Control of Markov Jump Systems. Nonlinear Dynamics, 92, 415-427. [Google Scholar] [CrossRef] 
[28] Liu, M., Shi, P., Zhang, L. and Zhao, X. (2011) Fault-Tolerant Control for Nonlinear Markov Jump Systems via Proportional and Derivative Sliding Mode Observer Technique. IEEE Transactions on Circuits and Systems, 58, 2755-2764. [Google Scholar] [CrossRef] 
[29] Corradini, M.L., Cristofaro, A. and Orlando, G. (2010) Robust Stabilization of Multi-Input Plants with Saturating Actuator. IEEE Transactions on Automatic Control, 55, 419-425. [Google Scholar] [CrossRef] 
[30] Zhu, J.W. and Yang, G.H. (2016) Adaptive Sliding-Mode Con-trol for Stochastic Markovian Jumping Systems with Actuator Faults. IET Control Theory and Applications, 10, 664-673. [Google Scholar] [CrossRef] 
[31] Ma, Y.C., Liu, Y.F., Liu, N. and Wang, Y.N. (2018) Reliable Finite-Time H∞ Control for Singular Markovian Jump System with Actuator Saturation via Sliding-Mode Approach. International Journal of Robust and Nonlinear Control, 28, 5509-5530. [Google Scholar] [CrossRef] 
[32] Kchaou, M., Al Ahmadi, S. and Draou, E. (2020) Integral Sliding-Mode Fault-Tolerant Control for Fuzzy Singular Systems with Actuator Saturation. Circuits, Systems, and Signal Processing, 39, 1307-1334. [Google Scholar] [CrossRef] 
[33] Selvaraj, P., Kaviarasan, B., Sakthivel, R. and Karimi, H.R. (2017) Fault-Tolerant SMC for TakagiıSugeno Fuzzy Systems with Time-Varying Delay and Actuator Saturation. IET Control Theory & Applications, 11, 1112-1123. [Google Scholar] [CrossRef] 

为你推荐