Abstract

A novel self-triggered model predictive control (STMPC) strategy for linear constrained systems with additive disturbance is presented in this paper. The actuator adopts the control input from the controller by sample-and-hold fashion. At the same time, the triggering threshold is designed to ensure the feasibility of the algorithms and the stability of the closed-loop system. Furthermore, two different ways to generate the event triggered input signal, namely, using single sample and multiple samples, are proposed and it is shown that better triggering performance can be obtained as the number of samples increases. In the last, the effectiveness and applicability of the proposed methods are verified by simulation.

References

1.
Hill
,
E.
,
Gadsden
,
S. A.
, and
Biglarbegian
,
M.
,
2022
, “
Robust Nonlinear Model Predictive Control With Model Predictive Sliding Mode for Continuous-Time Systems
,”
ASME J. Dyn. Syst., Meas., Control
,
144
(
3
), p. 031006.10.1115/1.4053026
2.
Liu
,
C.
,
Li
,
H.
,
Gao
,
J.
, and
Xu
,
D.
,
2018
, “
Robust Self-Triggered Min–Max Model Predictive Control for Discrete-Time Nonlinear Systems
,”
Automatica
,
89
, pp.
333
339
.10.1016/j.automatica.2017.12.034
3.
Kumar
,
P.
,
Anoohya
,
B. B.
, and
Padhi
,
R.
,
2019
, “
Model Predictive Static Programming for Optimal Command Tracking: A Fast Model Predictive Control Paradigm
,”
ASME J. Dyn. Syst., Meas., Control
,
141
(
2
), p.
021014
.10.1115/1.4041356
4.
Mayne
,
D. Q.
,
Seron
,
M. M.
, and
Raković
,
S.
,
2005
, “
Robust Model Predictive Control of Constrained Linear Systems With Bounded Disturbances
,”
Automatica
,
41
(
2
), pp.
219
224
.10.1016/j.automatica.2004.08.019
5.
Luo
,
Y.
,
Xia
,
Y.
, and
Sun
,
Z.
,
2018
, “
Self-Triggered Model Predictive Control for Continue Linear Constrained System: Robustness and Stability
,”
37th Chinese Control Conference (CCC)
,
IEEE
, Wuhan, China, July 25–27, pp.
3612
3617
.10.23919/ChiCC.2018.8484210
6.
Lu
,
L.
, and
Maciejowski
,
J. M.
,
2020
, “
Self-Triggered MPC With Performance Guarantee Using Relaxed Dynamic Programming
,”
Automatica
,
114
, p.
108803
.10.1016/j.automatica.2020.108803
7.
Eqtami
,
A.
,
Heshmati-Alamdari
,
S.
,
Dimarogonas
,
D. V.
, and
Kyriakopoulos
,
K. J.
,
2013
, “
Self-Triggered Model Predictive Control for Nonholonomic Systems
,”
2013 European Control Conference (ECC)
, Zurich, Switzerland, July 17–19, pp.
638
643
.10.23919/ECC.2013.6669628
8.
Anta
,
A.
, and
Tabuada
,
P.
,
2010
, “
To Sample or Not to Sample: Self-Triggered Control for Nonlinear Systems
,”
IEEE Trans. Autom. Control
,
55
(
9
), pp.
2030
2042
.10.1109/TAC.2010.2042980
9.
Aydiner
,
E.
,
Brunner
,
F. D.
,
Heemels
,
W.
, and
Allgower
,
F.
,
2015
, “
Robust Self-Triggered Model Predictive Control for Constrained Discrete-Time LTI Systems Based on Homothetic Tubes
,”
2015 European Control Conference (ECC)
,
IEEE
, Linz, Austria, July 15–17, pp.
1587
1593
.10.1109/ECC.2015.7330764
10.
Lu
,
L.
, and
Maciejowski
,
J. M.
,
2019
, “
Robust Self-Triggered Mpc for Constrained Linear Systems With Additive Disturbance
,”
IEEE 58th Conference on Decision and Control (CDC)
,
IEEE
, Nice, France, Dec. 11–13, pp.
445
450
.10.1109/CDC40024.2019.9028889
11.
Heemels
,
W. H.
,
Donkers
,
M.
, and
Teel
,
A. R.
,
2013
, “
Periodic Event-Triggered Control for Linear Systems
,”
IEEE Trans. Autom. Control
,
58
(
4
), pp.
847
861
.10.1109/TAC.2012.2220443
12.
Liu
,
C.
,
Gao
,
J.
,
Li
,
H.
, and
Xu
,
D.
,
2018
, “
Aperiodic Robust Model Predictive Control for Constrained Continuous-Time Nonlinear Systems: An Event-Triggered Approach
,”
IEEE Trans. Cybern.
,
48
(
5
), pp.
1397
1405
.10.1109/TCYB.2017.2695499
13.
Li
,
H.
, and
Shi
,
Y.
,
2014
, “
Event-Triggered Robust Model Predictive Control of Continuous-Time Nonlinear Systems
,”
Automatica
,
50
(
5
), pp.
1507
1513
.10.1016/j.automatica.2014.03.015
14.
Brunner
,
F. D.
,
Heemels
,
W.
, and
Allgöwer
,
F.
,
2014
, “
Robust Self-Triggered MPC for Constrained Linear Systems
,”
IEEE European Control Conference (ECC)
,
IEEE
, Strasbourg, France, June 24–27, pp.
472
477
.10.1109/ECC.2014.6862397
15.
Henriksson
,
E.
,
Quevedo
,
D. E.
,
Sandberg
,
H.
, and
Johansson
,
K. H.
,
2012
, “
Self-Triggered Model Predictive Control for Network Scheduling and Control
,”
IFAC Proc. Volumes
,
45
(
15
), pp.
432
438
.10.3182/20120710-4-SG-2026.00132
16.
Xu
,
Q.
,
Wang
,
J.
,
Zhang
,
F.
, and
Li
,
K.
,
2015
, “
Stability of Networked Control System With Bandwidth Limitation and Bernoulli-Process Packet Loss in Feed-Back
,”
2015 34th Chinese Control Conference (CCC)
,
IEEE
, Hangzhou, China, July 28–30, pp.
7671
7675
.
17.
Heemels
,
W. P.
,
Johansson
,
K. H.
, and
Tabuada
,
P.
,
2012
, “
An Introduction to Event-Triggered and Self-Triggered Control
,”
2012 IEEE 51st IEEE Conference on Decision and Control (CDC)
,
IEEE
, Maui, HI, Dec. 10–13, pp.
3270
3285
.10.1109/ChiCC.2015.7260857
18.
Brunner
,
F. D.
,
Heemels
,
W.
, and
Allgöwer
,
F.
,
2019
, “
Event-Triggered and Self-Triggered Control for Linear Systems Based on Reachable Sets
,”
Automatica
,
101
, pp.
15
26
.10.1016/j.automatica.2018.11.035
19.
Sun
,
Z.
,
Dai
,
L.
,
Liu
,
K.
,
Dimarogonas
,
D. V.
, and
Xia
,
Y.
,
2019
, “
Robust Self-Triggered MPC With Adaptive Prediction Horizon for Perturbed Nonlinear Systems
,”
IEEE Trans. Autom. Control
,
64
(
11
), pp.
4780
4787
.10.1109/TAC.2019.2905223
20.
Li
,
A.
, and
Sun
,
J.
,
2022
, “
Self-Triggered Model Predictive Control for Nonlinear Continuous-Time Networked System Via Ensured Performance Control Samples Selection
,”
Int. J. Control
,
95
(
10
), pp.
2793
2801
.10.1080/00207179.2021.1936189
21.
Brunner
,
F. D.
,
Heemels
,
M.
, and
Allgöwer
,
F.
,
2016
, “
Robust Self-Triggered MPC for Constrained Linear Systems: A Tube-Based Approach
,”
Automatica
,
72
, pp.
73
83
.10.1016/j.automatica.2016.05.004
22.
Berglind
,
J. B.
,
Gommans
,
T.
, and
Heemels
,
W.
,
2012
, “
Self-Triggered MPC for Constrained Linear Systems and Quadratic Costs
,”
IFAC Proc. Vol.
,
45
(
17
), pp.
342
348
.10.3182/20120823-5-NL-3013.00058
23.
Li
,
P.
,
Kang
,
Y.
,
Zhao
,
Y.-B.
, and
Wang
,
T.
,
2021
, “
A Novel Self-Triggered MPC Scheme for Constrained Input-Affine Nonlinear Systems
,”
IEEE Trans. Circuits Syst. II: Express Briefs
,
68
(
1
), pp.
306
310
.10.1109/TCSII.2020.2999408
24.
Xie
,
H.
,
Dai
,
L.
,
Luo
,
Y.
, and
Xia
,
Y.
,
2021
, “
Robust MPC for Disturbed Nonlinear Discrete-Time Systems Via a Composite Self-Triggered Scheme
,”
Automatica
,
127
, p.
109499
.10.1016/j.automatica.2021.109499
25.
Dai
,
L.
,
Cannon
,
M.
,
Yang
,
F.
, and
Yan
,
S.
,
2021
, “
Fast Self-Triggered MPC for Constrained Linear Systems With Additive Disturbances
,”
IEEE Trans. Autom. Control.
,
66
(
8
), pp.
3624
3637
.10.1109/TAC.2020.3022734
26.
Cui
,
D.
, and
Li
,
H.
,
2019
, “
Self-Triggered Model Predictive Control With Adaptive Selection of Sampling Number
,”
IEEE International Conference on Industrial Cyber Physical Systems (ICPS)
,
IEEE
, Taipei, Taiwan, May 6–9, pp.
802
807
.10.1109/ICPHYS.2019.8780233
27.
Cui
,
D.
, and
Li
,
H.
,
2022
, “
Dual Self-Triggered Model-Predictive Control for Nonlinear Cyber-Physical Systems
,”
IEEE Trans. Syst., Man, Cybern.: Syst.
,
52
(
6
), pp.
3442
3452
.10.1109/TSMC.2021.3070229
28.
He
,
N.
, and
Shi
,
D.
,
2015
, “
Event-Based Robust Sampled-Data Model Predictive Control: A Non-Monotonic Lyapunov Function Approach
,”
IEEE Trans. Circuits Syst. I: Regular Papers
,
62
(
10
), pp.
2555
2564
.10.1109/TCSI.2015.2468997
29.
Hashimoto
,
K.
,
Adachi
,
S.
, and
Dimarogonas
,
D. V.
,
2017
, “
Self-Triggered Model Predictive Control for Nonlinear Input-Affine Dynamical Systems Via Adaptive Control Samples Selection
,”
IEEE Trans. Autom. Control
,
62
(
1
), pp.
177
189
.10.1109/TAC.2016.2537741
30.
Hu
,
X.
,
Yu
,
H.
,
Hao
,
F.
, and
Luo
,
Y.
,
2020
, “
Event-Triggered Model Predictive Control for Disturbed Linear Systems Under Two-Channel Transmissions
,”
Int. J. Robust Nonlinear Control
,
30
(
16
), pp.
6701
6719
.10.1002/rnc.5133
31.
Yu
,
S.
,
Maier
,
C.
,
Chen
,
H.
, and
Allgöwer
,
F.
,
2013
, “
Tube MPC Scheme Based on Robust Control Invariant Set With Application to Lipschitz Nonlinear Systems
,”
Syst. Control Lett.
,
62
(
2
), pp.
194
200
.10.1016/j.sysconle.2012.11.004
You do not currently have access to this content.