DSC  >> Vol. 6 No. 2 (April 2017)

    一类有限时间稳定的输出反馈预测控制算法
    A Class of Algorithms of Output Feedback Predictive Control of Finite-Time Stability

  • 全文下载: PDF(444KB) HTML   XML   PP.43-53   DOI: 10.12677/DSC.2017.62006  
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作者:  

梁秀兰,刘晓华:鲁东大学数学与统计科学学院,山东 烟台

关键词:
模型预测控制有限时间稳定动态输出反馈线性矩阵不等式Model Predictive Control Finite-Time Stability Dynamic Output Feedback Linear Matrix Inequality

摘要:

本文针对一类离散时间线性时不变系统,研究其有限时间稳定预测控制问题。首先给出了有限时间稳定预测控制的定义,然后,通过构造Lyapunov函数,将有限时域的最小化优化问题转化为具有线性矩阵不等式约束的半正定规划问题。并采用线性矩阵不等式的方法,给出了输出反馈控制律存在的充分条件。证明了优化问题在满足可行性条件下闭环系统是有限时间稳定的。最后,仿真算例验证了所提方法的有效性。

This paper researches the finite-time stable predictive control problem for a class of discrete-time linear time invariant system. Firstly, the definition of finite-time stable predictive control is given. Then by constructing Lyapunov function, minimization-optimization problems of finite-time domain are converted into positive semi-definite programming problems with linear matrix inequality constraints. Using linear matrix inequality approach, a sufficient condition for the existence of output feedback control law is presented. It is proved that the optimization problems is finite-time stable when the feasible condition of closed-loop systems is guaranteed. Finally, a simulation example demonstrates the effectiveness of the proposed method.

文章引用:
梁秀兰, 刘晓华. 一类有限时间稳定的输出反馈预测控制算法[J]. 动力系统与控制, 2017, 6(2): 43-53. https://doi.org/10.12677/DSC.2017.62006

参考文献

[1] Xue, W.P. and Mao, W.J. (2013) Asymptotic Stability and Finite-Time Stability of Networked Control Systems: Analysis and Synthesis. Asian Journal of Control, 15, 1376-1384.
https://doi.org/10.1002/asjc.695
[2] Dorato, P. (1961)Short Time Stability in Linear Time-Varying Systems. Proceedings of the IRE International Convention Record Part 4, New York, 9 May 1961, 83-87.
[3] San, F. and Dorato, P. (1974) Short-Time Parameter Optimization with Fight Control Application. Automatica, 10, 425-430.
[4] Garcia, G., Tarbouriech, S. and Bernussou, J. (2009) Fi-nite-Time Stabilization of Linear Time-Varying Continuous Systems. IEEE Transactions on Atomatic Control, 54, 364-368.
https://doi.org/10.1109/TAC.2008.2008325
[5] Lin, X.Z., Du, H.B. and Li, S.H. (2011) Uniform Fi-nite-Time Stability and Feedback Stabilization for Discrete-Time Switched Linear Systems and Its Application to Networked Control Systems. Control and Decision, 26, 841-846.
[6] Weiss, L. and Infante, E.F. (1965) On the Sta-bility of Systems Defined over a Finite Time Interval. Proceedings of the National Academy of Sciences, 54, 44-48.
https://doi.org/10.1073/pnas.54.1.44
[7] Dorato, P. (2005) An Overview of Finite-Time Stability. Current Trends in Nonlinear Systems and Control. Birkhauser, Boston, 185-194.
[8] Amato, F., Ariola, M. and Dorato P. (2001) Finite-Time Control of Linear Systems Subject to Parametric Uncertainties and Disturbances. Automatica, 37, 1459-1463.
[9] Amato, F., Ariola, M., Amato, F., Ariola, M. and Cosentino, C. (2006) Finite Time Stabilization via Dynamic Output Feedback. Automatica, 42, 337-342.
[10] Amato, F., Ariola, M. and Cosentino, C. (2010) Finite-Time Control of Discrete-Time Linear Systems: Analysis and Design Conditions. Automatica, 46, 919-924.
[11] Haddad, W.M. and L’Afflitto, A. (2015) Finite-Time Partial Stability and Stabilization and Optimal Feedback Control. Journal of the Franklin Institute, 352, 2329-2357.
[12] Wang, L. and Shen, Y. (2016) Finite-Time Robust Stabilization of Uncertain Delayed Neural Networks with Discontinuous Activations via Delayed Feedback Control. The Official Journal of the International Neural Network Society, 76, 46-54.
[13] 严志国, 张国山. 线性随机系统有限时间H∞控制[J]. 控制与决策, 2011, 26(8): 1224-1228.
[14] 席裕庚, 耿晓军, 陈虹. 预测控制性能研究的新进展[J]. 控制理论与应用, 2000, 17(4): 469-475.
[15] Amato, F. and Ariola, M. (2005) Finite-Time Control of Discrete-Time Linear Systems. IEEE Transactions on Automatic Control, 50, 724-729.
https://doi.org/10.1109/TAC.2005.847042
[16] Yaz, E.E. (1998) Linear Matrix Inequalities in System and Control Theory. Proceeding of the IEEE, 86, 2473-2474.
https://doi.org/10.1109/JPROC.1998.735454
[17] Gahinet, P. (1994) Explicit Controller Formulas for LMI-Based H∞ Synthesis. Automatica, 32, 1007-1014.
[18] Kothare, M.V., Balakrishnan, V. and Morari, M. (1994) Robust Con-strained Model Predictive Control Using Linear Matrix Inequalities. American Control Conference IEEE, Baltimore, 29 June-1 July 1994, 440-444.
https://doi.org/10.1109/acc.1994.751775