Restricted accessResearch articleFirst published online 2025
LMI-based robust iterative learning control for leader–follower consensus of delayed singular heterogeneous multi-agent systems with uncertainties and initial shifts
This study deals with the leader–follower consensus for delayed singular heterogeneous multi-agent systems (DSHMASs) with norm-bounded uncertainties by proposing a robust iterative learning control (RILC) approach. The proposed RILC law guarantees zero-convergence of the tracking error despite norm-bounded uncertainties and unknown time-varying delays. Furthermore, it is shown that the control input vector achieves monotonic convergence under the L2-norm. A rectifying reference mechanism is employed to relax the requirement for identical initial conditions. Stability criteria are derived utilizing the performance index and Lyapunov–Krasovskii functional. The gains of the RILC are obtained by solving linear matrix inequalities (LMIs). Ultimately, the theoretical framework is verified via numerical and real-world examples, highlighting the method’s efficacy and robustness.
ArimotoSKawamuraSMiyazakiF (1984) Bettering operation of Robots by learning. Journal of Robotic Systems1(2): 123–140.
2.
AyatiniaMForouzanfarMRamezaniA (2023) Robust iterative learning control for linear discrete-time systems with initial state learning. Journal of Vibration and Control29(9-10): 2242–2254.
3.
CampbellS (1982) Singular systems of differential equations II. Pitman.
4.
Campos-MartínezSNHernández-GonzálezOGuerrero-SánchezME, et al. (2024) Consensus tracking control of multiple unmanned aerial vehicles subject to distinct unknown delays. Machines12(5): 337.
5.
CaoWQiaoJ (2023) Robust iterative learning control for random switched singular systems in time domain. Measurement and Control56: 1114–1125.
6.
CaoWQiaoJSunM (2020) Consensus tracking via iterative learning for multi-agent systems with random initial states. IEEE Access8: 215582–215591.
7.
CaoWQiaoJSunM (2021) Consensus control via iterative learning for singular multi-agent systems with switching topologies. IEEE Access9(Ilc): 81412–81420.
8.
ChenJLiJChenW, et al. (2024a) Neural networks-based iterative learning control consensus for periodically time-varying multi-agent systems. Science China Technological Sciences67(2): 464–474.
9.
ChenJXieJLiJ, et al. (2024b) Human-in-The-Loop fuzzy iterative learning control of consensus for unknown mixed-order nonlinear multi-agent systems. IEEE Transactions on Fuzzy Systems32(1): 255–265.
10.
DaiL (1989) Singular Control Systems. Springer.
11.
DuanGR (2010) Analysis and Design of Descriptor Linear Systems. Springer Science & Business Media, Vol. 23.
12.
EsmaeiliBMadaniSSSalimM, et al. (2022) Model-free adaptive iterative learning integral terminal sliding mode control of exoskeleton robots. Journal of Vibration and Control28(21-22): 3120–3139.
13.
FallahnejadMKazemyAShafieeM (2024) H∞ stabilization of singular networked cascade control systems subject to periodic dos attack. Journal of Vibration and Control31(15-16): 3091–3103.
14.
FuQGuPPWuJR (2017) Decentralized iterative learning control for large-scale interconnected linear systems with fixed initial shifts. International Journal of Control, Automation and Systems15(5): 1991–2000.
15.
GritliHZemoucheABelghithS (2021) On lmi conditions to design robust static output feedback controller for continuous-time linear systems subject to norm-bounded uncertainties. International Journal of Systems Science52(1): 12–46.
16.
GuPTianS (2020) Consensus control of singular multi-agent systems based on iterative learning approach. IMA Journal of Mathematical Control and Information37(2): 535–558.
17.
GuPTianSLiuQ (2018) Iterative learning control for switched singular time-delay systems. Journal of Vibration and Control24(20): 4839–4849.
18.
GuPTianSLiuQ (2019a) Closed-Loop iterative learning control for discrete singular systems with fixed initial shift. Journal of Systems Science and Complexity32(2): 577–587.
19.
GuPTianSLiuQ (2019b) Iterative learning control for discrete singular time-delay systems. IMA Journal of Mathematical Control and Information36(2): 623–637.
20.
HassanabadiAHPourdadashi KomachaliFShafieeM, et al. (2022) Simultaneous actuator and sensor fault reconstruction of singular delayed linear parameter varying systems in the presence of unknown time varying delays and inexact parameters. International Journal of Adaptive Control and Signal Processing36(12): 3043–3065.
21.
Hernández-GonzálezOTarguiBValencia-PalomoG, et al. (2024) Robust cascade observer for a disturbance unmanned aerial vehicle carrying a load under multiple time-varying delays and uncertainties. International Journal of Systems Science55(5): 1056–1072.
22.
HockASchoelligAP (2019) Distributed iterative learning control for multi-agent systems Theoretic developments and application to formation flying. Autonomous Robots43(8): 1989–2010.
23.
JiangALiangDWangC, et al. (2025) Finite-time output regulation of singular heterogeneous linear multi-agent systems. International Journal of Systems Science: 1–10.
24.
LiJZhangYJinZ (2021) The approximation of the nonlinear singular system with impulses and sliding mode control via a singular polynomial fuzzy model approach. Symmetry13(8): 1409.
25.
LiangMLiJLiJ (2022) Coordinated fuzzy adaptive iterative learning control of consensus for unknown nonlinear multi-agent systems. International Journal of Fuzzy Systems24(6): 3000–3014.
26.
LiuTShengAQiG, et al. (2023) Fully distributed bipartite output formation tracking for heterogeneous singular multiagent systems on signed digraphs. International Journal of Robust and Nonlinear Control33(17): 10698–10715.
27.
LiuXShengKYanY (2025) Output formation containment of heterogeneous singular multiagent systems using adaptive protocols. International Journal of Robust and Nonlinear Control35(6): 2156–2169.
28.
MaYChenM (2017) Memory feedback H∞ control of uncertain singular T–S fuzzy time-delay system under actuator saturation. Computational and Applied Mathematics36(1): 493–511.
29.
PereidaKKooijmanDDuivenvoordenRR, et al. (2019) Transfer learning for high-precision trajectory tracking through L1 adaptive feedback and iterative learning. International Journal of Adaptive Control and Signal Processing33(2): 388–409.
30.
RiazSQiRTutsoyO, et al. (2023) A novel adaptive PD-type iterative learning control of the PMSM servo system with the friction uncertainty in low speeds. PLoS One18(1): e0279253.
31.
TangXLiuZ (2022) Sliding mode observer-based adaptive control of uncertain singular systems with unknown time-varying delay and nonlinear input. ISA Transactions128: 133–143.
32.
UchiyamaM (1978) Formation of high-speed motion pattern of a mechanical arm by trial. Transactions of the Society of Instrument and Control Engineers14(6): 706–712.
33.
Vazquez TrejoJAPonsartJCAdam-MedinaM, et al. (2025) Fault-tolerant observer-based leader-following consensus control for lpv multi-agent systems using virtual actuators. International Journal of Systems Science56(8): 1816–1833.
34.
WangJZhouJMoY, et al. (2020) Consensus tracking via iterative learning control for singular fractional-order multi-agent systems under iteration-varying topologies and initial state errors. IEEE Access8: 168812–168824.
35.
WangCZhouZDaiX, et al. (2022a) Iterative learning approach for consensus tracking of partial difference multi-agent systems with control delay under switching topology. ISA Transactions136: 46–60.
36.
WangLChenGYangT, et al. (2022b) Sampled-data synchronization of singular markovian jump system: application to dc motor model. IET Cyber-Physical Systems: Theory & Applications7(4): 171–182.
37.
WangZTangSGuoG, et al. (2023) Event-triggered data-and knowledge-driven adaptive quality iterative learning control with uncertainty for a pharmaceutical cyber-physical system. The Canadian Journal of Chemical Engineering101(10): 5844–5857.
38.
WangGWangRYiD, et al. (2024) Iterative learning formation control via input sharing for fractional-order singular multi-agent systems with local lipschitz nonlinearity. Fractal and Fractional8(6): 347.
39.
XuJNiuYLamHK (2023) Adaptive distributed attitude consensus of a heterogeneous multiagent quadrotor system: singular perturbation approach. IEEE Transactions on Aerospace and Electronic Systems59(6): 9722–9732.
40.
YangSLiXD (2025) Quantized iterative learning control for consensus of switched nonlinear heterogeneous multi-agent systems. Nonlinear Dynamics113(7): 6695–6716.
41.
YuYLaiS (2022) Initial-Rectification barrier iterative learning control for pneumatic artificial muscle systems with nonzero initial errors and iteration-varying reference trajectories. IEEE Access10: 24194–24202.
42.
ZhangSWangLWangH, et al. (2021) Consensus control for heterogeneous multivehicle systems: an iterative learning approach. IEEE Transactions on Neural Networks and Learning Systems32(12): 5356–5368.
43.
ZhouXWangHTianY, et al. (2021) Consensus tracking via quantized iterative learning control for singular nonlinear multi-agent systems with state time-delay and initial state error. Nonlinear Dynamics103(3): 2701–2719.
44.
ZhouXWangHWangK, et al. (2023) Quantized iterative learning control for singular nonlinear fractional-order time-delay multi-agent systems with iteration-varying reference trajectories and switching topologies. Communications in Nonlinear Science and Numerical Simulation125(2021): 107359.
45.
ZhouXWangGZhangS (2025) Event-triggered iterative learning containment control for one-sided lipschitz nonlinear singular switched multi-agent systems with multiple leaders and error quantization. Communications in Nonlinear Science and Numerical Simulation140: 108429.
