具有状态时滞的奇异随机系统基于滚动时域控制的镇定

doi:10.1007/s12204-022-2550-2

摘要/Abstract

摘要： 针对一类具有多重状态延迟的离散时间奇异随机系统，本研究关注滚动时域控制的稳定性问题。由于所提优化问题的求解难度较大，此类系统的滚动时域控制稳定性问题尚未得到解决。通过采用前向和后向方程技术，本研究完全解决了这一优化问题。在满足正则化和无脉冲条件下，给出了优化控制器具有唯一解的充分必要条件。基于这一控制器，推导出了滚动时域控制的稳定性条件，该条件以线性矩阵不等式的形式表示。证明了在适当假设下，当终端加权矩阵满足给定不等式时，具有多重状态延迟的奇异随机系统在均方意义下是稳定的。数值算例表明，所提滚动时域控制方法对于稳定具有多重状态延迟的奇异随机系统是有效的。

关键词: 滚动时域控制（RHC），奇异随机系统，状态时滞，稳定性

Abstract: For a class of discrete-time singular stochastic systems with multi-state delay, the stabilization problem of receding horizon control (RHC) is concerned. Due to the difficulty in solving the proposed optimization problem, the RHC stabilization for such systems has not been solved. By adopting the forward and backward equation technique, the optimization problem is solved completely. A sufficient and necessary condition for the optimization controller to have a unique solution is given when the regularization and pulse-free conditions are satisfied. Based on this controller, an RHC stabilization condition is derived, which is in the form of linear matrix inequality. It is proved that the singular stochastic system with multi-state delay is stable in the mean-square sense under appropriate assumptions when the terminal weighting matrix satisfies the given inequality. Numerical examples show that the proposed RHC method is effective in stabilizing singular stochastic systems with multi-state delay.

Key words: receding horizon control (RHC), singular stochastic system, state delay, stabilization

中图分类号:

TP273

王晓静1，刘晓华2，高荣2. 具有状态时滞的奇异随机系统基于滚动时域控制的镇定[J]. J Shanghai Jiaotong Univ Sci, 2024, 29(3): 436-449.

WANG Xiaojing(王晓静),LIU Xiaohua(刘晓华), GAO Rong（高荣）. Receding Horizon Control-Based Stabilization of Singular Stochastic Systems with State Delay[J]. J Shanghai Jiaotong Univ Sci, 2024, 29(3): 436-449.

参考文献

[1] DAI L Y. Singular control systems [M]. Berlin, Heidelberg: Springer-Verlag, 1989.
[2] DAI L Y. Filtering and LQG problems for discretetime stochastic singular systems [J]. IEEE Transactions on Automatic Control, 1989, 34(10): 1105-1108.
[3] FARHAT C, GERADIN M. On the general solution by a direct method of a large-scale singular system of linear equations: Application to the analysis of floating structures [J]. International Journal for Numerical Methods in Engineering, 1998, 41(4): 675-696.
[4] XU S Y, LAM J, ZOU Y. An improved characterization of bounded realness for singular delay systems and its applications [J]. International Journal of Robust and Nonlinear Control, 2008, 18(3): 263-277.
[5] FANG C H, CHANG F R. Robust control analysis and design for discrete-time singular systems [J]. IFAC Proceedings Volumes, 1993, 26(2): 83-88.
[6] AMATO F, MATTEI M, PIRONTI A. Solution of the state feedback singular H∞ control problem for linear time-varying systems [J]. Automatica, 2000, 36(10): 1469-1479.
[7] YAN J J, CHANG W D, YAU H T, et al. Decentralized adaptive control for large-scale singular systems with series nonlinearities [J]. IFAC Proceedings Volumes, 2004, 37(11): 49-54.
[8] LIU X H, YANG Y H. Observer-based robust predictive control of singular systems with time-delay and parameter uncertainties [J]. Journal of Systems Engineering and Electronics, 2009, 20(3): 590-597.
[9] WANG F, LIANG J L, WANG F. Optimal control for discrete-time singular stochastic systems with input delay [J]. Optimal Control Applications and Methods, 2016, 37(6): 1282-1313.
[10] ECH-CHARQY A, OUAHI M, TISSIR E H. Delaydependent robust stability criteria for singular timedelay systems by delay-partitioning approach [J]. International Journal of Systems Science, 2018, 49(14): 2957-2967.
[11] FENG Z G, LAM J, GAO H J. Delay-dependent robust H∞ controller synthesis for discrete singular delay systems [J]. International Journal of Robust and Nonlinear Control, 2011, 21(16): 1880-1902.
[12] GU P P, TIAN S P, LIU Q. Iterative learning control for discrete singular time-delay systems [J]. IMA Journal of Mathematical Control and Information, 2019, 36(2): 623-637.
[13] FENG J E, CUI P, HOU Z S. Singular linear quadratic optimal control for singular stochastic discrete-time systems [J]. Optimal Control Applications and Methods, 2013, 34(5): 505-516.
[14] ZHANG W H, LIN Y N, XUE L R. Linear quadratic Pareto optimal control problem of stochastic singular systems [J]. Journal of the Franklin Institute, 2017, 354(2): 1220-1238.
[15] CARABALLO T, EZZINE F, HAMMAMI M A. New stability criteria for stochastic perturbed singular systems in mean square [J]. Nonlinear Dynamics, 2021, 105(1): 241-256.
[16] WANG G L, ZHANG Q L, YANG C Y. Exponential stability of stochastic singular delay systems with general Markovian switchings [J]. International Journal of Robust and Nonlinear Control, 2015, 25(17): 3478-3494.
[17] ZHANG W H, ZHAO Y, SHENG L. Some remarks on stability of stochastic singular systems with statedependent noise [J]. Automatica, 2015, 51: 273-277.
[18] CHEN X, ZHU Y G. Optimal control for uncertain random singular systems with multiple time-delays [J]. Chaos, Solitons & Fractals, 2021, 152: 111371.
[19] KWON W H, LEE Y S, HAN S H. General receding horizon control for linear time-delay systems [J]. Automatica, 2004, 40(9): 1603-1611.
[20] GAO R, LIU X H, ZHANG H S. Receding horizon control for discrete-time multiple input delay systems [J]. Optimal Control Applications and Methods, 2017, 38(6): 1187-1192.
[21] GAO R, XU J J, ZHANG H S. Receding horizon control for multiplicative noise stochastic systems with input delay [J]. Automatica, 2017, 81: 390-396.
[22] LI L, ZHANG H S. Linear quadratic regulation for discrete-time systems with state delays and multiplicative noise [J]. Control Theory and Technology, 2015, 13(4): 348-359.
[23] LIU X H, WANG X J, GAO R. Receding horizon control-based stabilization of discrete-time stochastic systems with state delay [J]. IEEE Access, 2019, 7: 136232-136238.