State feedback and output feedback control strategies are developed for discrete-time periodic systems with state delay via periodic preview control (PPC) technique in this article. To utilize future reference information for the controller design, a periodic augmented error system (PAES) with delay is constructed using the state augmentation technique and difference operator approach. Then, the PPC problem is converted into a stabilization problem. Furthermore, the state feedback and static output preview controllers are designed and sufficient conditions that guarantee the closed-loop stability of PAES are derived via the linear matrix inequality (LMI) approach. Finally, two examples are presented to illustrate the effectiveness of the proposed method.
BirlaNSwarupA (2015) Optimal preview control: A review. Optimal Control Applications and Methods6: 241–268.
2.
CaoMLiaoF (2015) Design of an optimal preview controller for linear discrete-time descriptor systems with state delay. International Journal of Systems Science46: 932–943.
3.
CarlosESouzaDCoutinhoD (2014) Robust stability and control of uncertain linear discrete-time periodic systems with time-delay. Automatica50: 431–441.
4.
ChangXZhangLParkH (2015) Robust static output feedback H∞ control for uncertain fuzzy systems. Fuzzy Sets Systems273: 87–104.
5.
GershonEShakedU (2014) H∞ preview tracking control of retarded state-multiplicative stochastic systems. International Journal of Robust and Nonlinear Control24: 2119–2135.
6.
GuoYLiaoF (2017) Robust preview control for multirate uncertain discrete-time systems with input delay. Control and Decision32: 2113–2126.
7.
HanYKaoYGaoC, et al. (2019) H∞ sliding mode control of discrete switched systems with time-varying delays. ISA Transactions89: 12–19.
8.
KatayamaTOhkiTInoueT, et al. (1985) Design of an optimal controller for a discrete-time system subject to previewable demand. International Journal of Control41: 677–699.
9.
KojimaA (2015) H∞ controller design for preview and delayed systems. IEEE Transactions on Automatic Control60: 404–419.
10.
LiGZhangWChenM (2015) Robust H2/H∞ control for periodic stochastic difference systems with mutiplicative noise. IET Control Theory and Application9: 2451–2457.
11.
LiLLiaoF (2018) Robust preview control for a class of uncertain discrete-time systems with time-varying delay. ISA Transactions73: 11–21.
12.
LiLLuYGuL (2021) Preview control for a class of linear discrete-time periodic systems. International Journal of Control94: 823–833.
13.
LiaoFSunMUsman (2019) Optimal preview control for linear discrete-time periodic systems. Mathematical Problems in Engineering2019: 8434293.
14.
LuYLiaoFDengJ, et al. (2017) Cooperative global optimal preview tracking control of linear multi-agent systems: An internal model approach. International Journal of Systems Science48: 2451–2462.
15.
LuYLiaoFDengJ, et al. (2019) Cooperative optimal preview tracking for linear descriptor multi-agent systems. Journal of the Frank Institute356: 908–934.
16.
MaHJiaY (2013) H2 control of discrete-time periodic systems with Markovian jumps and multiplicative noise. International Journal of Control86: 1837–1849.
17.
NguyenHBourdaisRGutmanP (2017) Fast model predictive control for linear periodic systems with state and control constraints. International Journal of Robust and Nonlinear Control27: 3703–3726.
18.
PaunonenL (2017) Robust output regulation for continuous-time periodic systems. IEEE Transactions on Automatic Control62: 4363–4375.
19.
ShimmyoSSatoTOhnishiK (2013) Biped walking pattern generation by using preview control based on three-mass model. IEEE Transactions on Industrial Electronics60: 5137–5147.
20.
SubudhiBOgetiP (2018) Optimal preview stator voltage-oriented control of DFIG WECS. IET Generation Transmission & Distribution12: 1004–1013.
21.
TakabaK (2000) Robust servomechanism with preview action for polytopic uncertain systems. International Journal of Robust and Nonlinear Control10: 101–111.
22.
TehraniHAEsmaeiliJ (2017) Stability of fractional-order periodic discrete-time linear systems. IMA Journal of Mathematical Control and Information34: 271–281.
23.
WangSJiangYLiY, et al. (2015) Reliable observer-based H∞ control for discrete-time fuzzy systems with time-varying delays and stochastic actuator faults via scaled small gain theorem. Neurocomputing147: 251–259.
24.
WuJLiaoFTomizukaM (2017) Optimal preview control for a linear continuous-time stochastic control system in finite-time horizon. International Journal of Systems Science48: 129–137.
25.
XieXLamJFanC (2018) Robust time-weighted guaranteed cost control of uncertain periodic piecewise linear systems. Information Sciences460: 238–253.
26.
XieXLamJLiP (2017) Finite-time H∞ control of periodic piecewise linear systems. International Journal of Systems Science48: 2333–2344.
27.
XuYLiaoF (2013) Preview control for a class of time-varying discrete systems with input time-delay. Control and Decision28: 466–470.
28.
YimS (2019) Active roll preview control with V2V communication. International Journal of Automotive Technology20: 169–175.
29.
ZhangPDingXWangG, et al. (2005) Fault detection of linear discrete-time periodic systems. IEEE Transactions on Automatic Control50: 239–244.
30.
ZhaoLSunF-QRenJ-C, et al. (2016) Optimal preview control for a class of continuous time-invariant descriptor systems. Optimal Control Applications and Methods37: 279–289.
31.
ZhenZJiangSJiangJ (2018) Preview control and particle filtering for automatic carrier landing. IEEE Transactions on Aerospace & Electronic Systems54: 2662–2674.
32.
ZhouB (2015) Global stabilization of periodic linear systems by bounded controls with applications to spacecraft magnetic attitude control. Automatica60: 145–154.
33.
ZhouLChengLSheJ, et al. (2019) Generalized extended state observer-based repetitive control for systems with mismatched disturbances. International Journal of Robust and Nonlinear Control29: 3777–3792.
34.
ZouQDevasiaS (1999) Preview-based output tracking for periodic switching systems. In: Proceeding of the 38th conference on decision and control, Phoenix, AZ, 7–10 December 1999, pp. 2930–2935. New York: IEEE.
