In this paper, the static output periodic preview control problem of discrete-time periodic systems (D-TPSs) is proposed. First, an augmented error periodic system (AEPS) is derived by introducing auxiliary variables related to the system state and input. Consequently, the static output periodic preview control problem is transformed into a stabilization problem. Second, sufficient conditions are derived to ensure asymptotic stability, and these conditions are extended to the D-TPSs with disturbance. Moreover, the corresponding solvability condition for the design of the static output periodic preview control laws is proposed using linear matrix inequality (LMI). Finally, a numerical example is used to illustrate the effectiveness of the results.
XieXLamJFanC.Robust time-weighted guaranteed cost control of uncertain periodic piecewise linear systems. Inf Sci2018; 460: 238–253.
2.
de SouzaCECoutinhoD. Robust stability and control of uncertain linear discrete-time periodic systems with time-delay. Automatica2014; 50(2): 431–441.
3.
ArcaraPBittantiSLoveraM.Periodic control of helicopter rotors for attenuation of vibrations in forward flight. IEEE Trans Control Syst Technol2000; 8(6): 883–894.
4.
BroomheadTJManzieCShekharRC, et al. Robust periodic economic MPC for linear systems. Automatica2015; 60: 30–37.
5.
StolKA. Time-varying control of wind turbines. In: Proceedings of American control conference, Denver, CO, USA, 2003, pp.3796–3796. New York: IEEE.
6.
LiPLiPLiuY, et al. H∞ control of periodic piecewise polynomial time-varying systems with polynomial Lyapunov function. J Franklin Inst2019; 356(13): 6968–6988.
7.
LiPLamJKwokKW, et al. Stability and stabilization of periodic piecewise linear systems: A matrix polynomial approach. Automatica2018; 94: 1–8.
8.
YangJSunJZhengWX, et al. Periodic event-triggered robust output feedback control for nonlinear uncertain systems with time-varying disturbance. Automatica2018; 94: 324–333.
9.
TsuchiyaTEgamiT.Digital preview and predictive control. Beijing: Beijing Science and Technology Press, 1994.
10.
BirlaNSwarupA.Optimal preview control: a review. Optim Control Appl Methods2015; 36(2): 241–268.
TomizukaM.The discrete optimal finite preview control problem-theory and application to a vibration problem. Trans Soc Instrum Control Eng1975; 11(6): 663–668.
13.
KatayamaTOhkiTInoueT, et al. Design of an optimal controller for a discrete-time system subject to previewable demand. Int J Control1985; 41(3): 677–699.
14.
KatayamaTHironoT.Design of an optimal servomechanism with preview action and its dual problem. Int J Control1987; 45(2): 407–420.
15.
SheridanTB.Three models of preview control. IEEE Trans Hum Factors Electron1966; 7(2): 91–102.
16.
NakuraG.Stochastic optimal tracking with preview for linear discrete-time Markovian Jump Systems. Proc ISCIE Int SympStoch Syst Theory Appl2009; 2009: 53–60.
17.
WuJLiaoFXuZ.Preview control for a class of linear stochastic systems with multiplicative noise. Int J Syst Sci2019; 50(14): 2592–2603.
18.
NakuraG.Stochastic optimal tracking with preview for linear continuous-time markovian jump systems by output feedback. Trans Ins Syst Contr Inf Eng2016; 29(11): 497–505.
19.
ChunleiGBinZZhouH.Linear discrete information fusion preview control algorithm based on the observer. Aerosp Control2018; 36(5): 9–13.
20.
ZhenZYWangZSWangDB.Information fusion estimation based preview control for discrete linear system. Zidonghua Xuebao2010; 36(2): 347–352.
21.
ZhishengW.Information fusion optimal preview control for nonlinear discrete system. Control Decis2008; 23(4): 397–402.
22.
LuYLiaoFDengJ, et al. Cooperative optimal preview tracking for linear descriptor multi-agent systems. J Franklin Inst2019; 356(2): 908–934.
23.
ZhaoLSunFQRenJC, et al. Optimal preview control for a class of continuous time-invariant descriptor systems. Optim Control Appl Methods2016; 37(2): 279–289.
24.
CaoMLiaoF.Design of an optimal preview controller for linear discrete-time descriptor systems with state delay. Int J Syst Sci2015; 46(5): 932–943.
25.
LiaoFXueZWuJ.Design of an optimal preview controller for a class of linear discrete-time descriptor systems. Math Probl Eng2017; 2017(1): 9.
26.
LiLLiaoF.Parameter-dependent preview control with robust tracking performance. IET Control Theory Appl2017; 11(1): 38–46.
27.
LanYXieJ.Observer based preview repetitive control for linear discrete systems. Comput Integr Manuf Syst2020; 26(10): 2714–2722.
28.
StrohmJNChristF.Preview H∞ control of a hybrid suspension system. IFAC-PapersOnLine2019; 52(5): 237–242.
29.
PangHWangYZhangX, et al. Robust state-feedback control design for active suspension system with time-varying input delay and wheelbase preview information. J Franklin Inst2019; 356(4): 1899–1923.
30.
LiLYuanY.Output feedback preview control for polytopic uncertain discrete-time systems with time-varying delay. Int J Robust Nonlinear Control2019; 29(9): 2619–2638.
31.
HamadaY.New LMI-based conditions for preview feedforward synthesis. Control Eng Pract2019; 90: 19–26.
32.
SunMLiaoFDengJ.Design of an optimal preview control for linear discrete-time periodic systems. Trans Inst Meas Contr2021; 43(12): 2637–2646.
33.
LiLLuYGuL.Preview control for a class of linear discrete-time periodic systems. Int J Control2019; 94(3): 823–833.
34.
LiLZhangYLiaoY.Preview control for uncertain discrete-time periodic systems. Int J Robust Nonlinear Control2021; 31(18): 9501–9518.
35.
LiLLiaoYMengX.L2-L∞ preview control for discrete-time periodic systems. J Syst Sci Math Sci2022; 42(5): 1113–1128.
36.
ChangXHYangGH.New results on output feedback H∞ control for linear discrete-time systems. IEEE Trans Automat Contr2014; 59(5): 1355–1359.
37.
SilvaRNFrezzattoL.A new parametrization for static output feedback control of LPV discrete-time systems. Automatica2021; 128: 109566.
38.
JiangSFangH.H-infinity output feedback control for nonlinear networked control systems with time delays and packet dropouts. ISA Trans2013; 52(2): 215–222.
39.
ChangXHXiongJLiZM, et al. Quantized static output feedback control for discrete-time systems. IEEE Trans Ind Inform2018; 14(8): 3426–3435.
