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.
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]. Journal of Shanghai Jiaotong University(Science), 2024
, 29(3)
: 436
-449
.
DOI: 10.1007/s12204-022-2550-2
[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.
