Abstract
This paper presents an efficient stochastic model predictive control (SMPC) framework for quasi-linear parameter varying (qLPV) systems. The framework applies to general nonlinear systems that are driven by stochastic additive disturbances and subject to chance constraints. The qLPV form is featured by a composition of a set of linear time-invariant (LTI) models with state-/control-dependent scheduling variables, which can be obtained by the spatial–temporal filtering-based system identification approach developed in our earlier work. The overall framework can then be transformed into a tube-based MPC optimization problem which can be efficiently handled by a series of quadratic programing (QP) problems. A case study on automotive engine control is presented as a pilot demonstration of the proposed qLPV–SMPC where we show its advantage over the zone-based MPC, much greater computational efficiency than nonlinear MPC (NMPC) and less conservativeness of the proposed method as compared to its robust MPC (RMPC) counterpart.
Issue Section:
Research Papers
References
1.
Mayne
,
D. Q.
, 2014
, “
Model Predictive Control: Recent Developments and Future Promise
,” Automatica
,
50
(12
), pp. 2967
–2986
.10.1016/j.automatica.2014.10.1282.
Li
,
N.
,
Girard
,
A.
, and
Kolmanovsky
,
I.
, 2019
, “
Stochastic Predictive Control for Partially Observable Markov Decision Processes With Time-Joint Chance Constraints and Application to Autonomous Vehicle Control
,” ASME J. Dyn. Syst., Meas., Control
,
141
(7
), p. 071007
.10.1115/1.40431153.
Eaton
,
J. W.
, and
Rawlings
,
J. B.
, 1992
, “
Model Predictive Control of Chemical Processes
,” Chem. Eng. Sci.
,
47
(4
), pp. 705
–720
.10.1016/0009-2509(92)80263-C4.
Herzog
,
F.
,
Dondi
,
G.
, and
Geering
,
H. P.
, 2007
, “
Stochastic Model Predictive Control and Portfolio Optimization
,” Int. J. Theor. Appl. Finance
,
10
(02
), pp. 203
–233
.10.1142/S02190249070041965.
Alexis
,
K.
,
Nikolakopoulos
,
G.
, and
Tzes
,
A.
, 2011
, “
Model Predictive Control Scheme for the Autonomous Flight of an Unmanned Quadrotor
,” 2011 IEEE International Symposium on Industrial Electronics
, Gdansk, Poland, June 27–30, pp. 2243
–2248
.10.1109/ISIE.2011.59845106.
Docimo
,
D. J.
,
Kang
,
Z.
,
James
,
K. A.
, and
Alleyne
,
A. G.
, 2021
, “
Plant and Controller Optimization for Power and Energy Systems With Model Predictive Control
,” ASME J. Dyn. Syst., Meas., Control
,
143
(8
), p. 081009
.10.1115/1.40503997.
Tóth
,
R.
, 2010
, Modeling and Identification of Linear Parameter-Varying Systems
,
Springer
,
Berlin
.8.
Morato
,
M. M.
,
Sename
,
O.
, and
Dugard
,
L.
, 2018
, “
LPV-MPC Fault Tolerant Control of Automotive Suspension Dampers
,” IFAC-PapersOnLine
,
51
(26
), pp. 31
–36
.10.1016/j.ifacol.2018.11.1729.
Nandola
,
N. N.
, and
Bhartiya
,
S.
, 2008
, “
A Multiple Model Approach for Predictive Control of Nonlinear Hybrid Systems
,” J. Process Control
,
18
(2
), pp. 131
–148
.10.1016/j.jprocont.2007.07.00310.
Besselmann
,
T.
, and
Morari
,
M.
, 2014
, “
Autonomous Vehicle Steering Using Explicit LPV-MPC
,” European Control Conference
, Budapest, Hungary, Aug. 23–26, pp. 2628
–2633
.10.23919/ECC.2009.707480211.
Ul Haq
,
A. A.
,
Cholette
,
M. E.
, and
Djurdjanovic
,
D.
, 2017
, “
A Dual-Mode Model Predictive Control Algorithm Trajectory Tracking in Discrete-Time Nonlinear Dynamic Systems
,” ASME J. Dyn. Syst., Meas., Control
,
139
(4
), p. 044501
.10.1115/1.403509612.
Kothare
,
M. V.
,
Balakrishnan
,
V.
, and
Morari
,
M.
, 1996
, “
Robust Constrained Model Predictive Control Using Linear Matrix Inequalities
,” Automatica
,
32
(10
), pp. 1361
–1379
.10.1016/0005-1098(96)00063-513.
Kim
,
T. H.
,
Park
,
J. H.
, and
Sugie
,
T.
, 2006
, “
Output-Feedback Model Predictive Control for LPV Systems With Input Saturation Based on Quasi-Min-Max Algorithm
,” Proceedings of the IEEE Conference on Decision and Control
, San Diego, CA, Dec. 13–15, pp. 1454
–1459
.10.1109/CDC.2006.37703814.
Abbas
,
H. S.
,
Tóth
,
R.
,
Meskin
,
N.
,
Mohammadpour
,
J.
, and
Hanema
,
J.
, 2016
, “
A Robust MPC for Input-Output LPV Models
,” IEEE Trans. Autom. Control
,
61
(12
), pp. 4183
–4188
.10.1109/TAC.2016.255314315.
Casavola
,
A.
,
Famularo
,
D.
, and
Franze
,
G.
, 2002
, “
A Feedback Min-Max MPC Algorithm for LPV Systems Subject to Bounded Rates of Change of Parameters
,” IEEE Trans. Autom. Control
,
47
(7
), pp. 1147
–1153
.10.1109/TAC.2002.80066216.
Li
,
D.
, and
Xi
,
Y.
, 2010
, “
The Feedback Robust MPC for LPV Systems With Bounded Rates of Parameter Changes
,” IEEE Trans. Autom. Control
,
55
(2
), pp. 503
–507
.10.1109/TAC.2009.203746417.
Abbas
,
H. S.
,
Männel
,
G.
,
Herzog né Hoffmann
,
C.
, and
Rostalski
,
P.
, 2019
, “
Tube-Based Model Predictive Control for Linear Parameter-Varying Systems With Bounded Rate of Parameter Variation
,” Automatica
,
107
, pp. 21
–28
.10.1016/j.automatica.2019.04.04618.
Mesbah
,
A.
, 2016
, “
Stochastic Model Predictive Control: An Overview and Perspectives for Future Research
,” IEEE Control Syst.
,
36
(6
), pp. 30
–44
.10.1109/MCS.2016.260208719.
Farina
,
M.
,
Giulioni
,
L.
, and
Scattolini
,
R.
, 2016
, “
Stochastic Linear Model Predictive Control With Chance Constraints—A Review
,” J. Process Control
,
44
, pp. 53
–67
.10.1016/j.jprocont.2016.03.00520.
Cannon
,
M.
,
Kouvaritakis
,
B.
, and
Wu
,
X.
, 2009
, “
Probabilistic Constrained MPC for Multiplicative and Additive Stochastic Uncertainty
,” IEEE Trans. Autom. Control
,
54
, pp. 1626
–1632
.10.1109/TAC.2009.201797021.
Cannon
,
M.
,
Kouvaritakis
,
B.
, and
Ng
,
D.
, 2009
, “
Probabilistic Tubes in Linear Stochastic Model Predictive Control
,” Syst. Control Lett.
,
58
(10–11
), pp. 747
–753
.10.1016/j.sysconle.2009.08.00422.
Cannon
,
M.
,
Kouvaritakis
,
B.
,
Raković
,
S. V.
, and
Cheng
,
Q.
, 2011
, “
Stochastic Tubes in Model Predictive Control With Probabilistic Constraints
,” IEEE Trans. Autom. Control
,
56
(1
), pp. 194
–200
.10.1109/TAC.2010.208655323.
Kouvaritakis
,
B.
,
Cannon
,
M.
,
Raković
,
S. V.
, and
Cheng
,
Q.
, 2010
, “
Explicit Use of Probabilistic Distributions in Linear Predictive Control
,” Automatica
,
46
(10
), pp. 1719
–1724
.10.1016/j.automatica.2010.06.03424.
Bernardini
,
D.
, and
Bemporad
,
A.
, 2009
, “
Scenario-Based Model Predictive Control of Stochastic Constrained Linear Systems
,” 48th IEEE Conference on Decision and Control
, Shanghai, China, pp. 6333
–6338
.10.1109/CDC.2009.539991725.
Schildbach
,
G.
,
Fagiano
,
L.
,
Frei
,
C.
, and
Morari
,
M.
, 2014
, “
The Scenario Approach for Stochastic Model Predictive Control With Bounds on Closed-Loop Constraint Violations
,” Automatica
,
50
(12
), pp. 3009
–3018
.10.1016/j.automatica.2014.10.03526.
Hewing
,
L.
, and
Zeilinger
,
M. N.
, 2020
, “
Scenario-Based Probabilistic Reachable Sets for Recursively Feasible Stochastic Model Predictive Control
,” IEEE Control Syst. Lett.
,
4
(2
), pp. 450
–455
.10.1109/LCSYS.2019.294919427.
Chitraganti
,
S.
,
Toth
,
R.
,
Meskin
,
N.
, and
Mohammadpour
,
J.
, 2017
, “
Stochastic Model Predictive Control for LPV Systems
,” Proceedings of the American Control Conference
, Seattle, WA, May 24–26, pp. 5654
–5659
.10.23919/ACC.2017.796383528.
Calafiore
,
G. C.
, and
Fagiano
,
L.
, 2013
, “
Stochastic Model Predictive Control of LPV Systems Via Scenario Optimization
,” Automatica
,
49
(6
), pp. 1861
–1866
.10.1016/j.automatica.2013.02.06029.
Cisneros
,
P. G.
,
Voss
,
S.
, and
Werner
,
H.
, 2016
, “
Efficient Nonlinear Model Predictive Control Via Quasi-LPV Representation
,” 2016 IEEE 55th Conference on Decision and Control
, Las Vegas, NV, Dec. 12–14, pp. 3216
–3221
.10.1109/CDC.2016.779875230.
Cisneros
,
P. G.
, and
Werner
,
H.
, 2017
, “
Fast Nonlinear MPC for Reference Tracking Subject to Nonlinear Constraints Via Quasi-LPV Representations
,” IFAC-PapersOnLine
,
50
(1
), pp. 11601
–11606
.10.1016/j.ifacol.2017.08.165031.
Morato
,
M. M.
,
Normey-Rico
,
J. E.
, and
Sename
,
O.
, 2019
, “
Novel qLPV MPC Design With Least-Squares Scheduling Prediction
,” IFAC-PapersOnLine
,
52
(28
), pp. 158
–163
.10.1016/j.ifacol.2019.12.36632.
Cisneros
,
P. S.
,
Sridharan
,
A.
, and
Werner
,
H.
, 2018
, “
Constrained Predictive Control of a Robotic Manipulator Using Quasi-LPV Representations
,” IFAC-PapersOnLine
,
51
(26
), pp. 118
–123
.10.1016/j.ifacol.2018.11.15833.
Morato
,
M. M.
,
Normey-Rico
,
J. E.
, and
Sename
,
O.
, 2020
, “
Sub-Optimal Recursively Feasible Linear Parameter-Varying Predictive Algorithm for Semi-Active Suspension Control
,” IET Control Theory Appl.
,
14
(18
), pp. 2764
–2775
.10.1049/iet-cta.2020.059234.
Li
,
Z.
, and
Filev
,
D.
, 2018
, “
Online Nonlinear System Identification With Evolving Spatial-Temporal Filters
,” Proceedings of the American Control Conference
, Milwaukee, WI, June 27–29, pp. 5274
–5279
.10.23919/ACC.2018.843103635.
Chen
,
K.
,
Li
,
Z.
,
Filev
,
D.
,
Wang
,
Y.
,
Wu
,
K.
, and
Wang
,
J.
, 2021
, “
Online Nonlinear Dynamic System Identification With Evolving Spatial-Temporal Filters: Case Study on Turbocharged Engine Modeling
,” IEEE Trans. Control Syst. Technol.
,
29
(3
), pp. 1364
–1371
.10.1109/TCST.2020.298969336.
Hewing
,
L.
, and
Zeilinger
,
M. N.
, 2018
, “
Stochastic Model Predictive Control for Linear Systems Using Probabilistic Reachable Sets
,” 57th IEEE Conference on Decision and Control
, Miami Beach, FL, pp. 5182
–5188
.https://www.researchgate.net/publication/325262758_Stochastic_Model_Predictive_Control_for_Linear_Systems_using_Probabilistic_Reachable_Sets37.
Nishio
,
Y.
, and
Shen
,
T.
, 2021
, “
Model Predictive Control With Traffic Information-Based Driver's Torque Demand Prediction for Diesel Engines
,” Int. J. Engine Res.
,
22
(2
), pp. 674
–684
.10.1177/146808741985167838.
Liu
,
Z.
,
Dizqah
,
A. M.
,
Herreros
,
J. M.
,
Schaub
,
J.
, and
Haas
,
O.
, 2021
, “
Simultaneous Control of NOx, Soot and Fuel Economy of a Diesel Engine With Dual-Loop EGR and VNT Using Economic MPC
,” Control Eng. Pract.
,
108
, p. 104701
.10.1016/j.conengprac.2020.10470139.
Liao-McPherson
,
D.
,
Huang
,
M.
,
Kim
,
S.
,
Shimada
,
M.
,
Butts
,
K.
, and
Kolmanovsky
,
I.
, 2020
, “
Model Predictive Emissions Control of a Diesel Engine Airpath: Design and Experimental Evaluation
,” Int. J. Robust Nonlinear Control
,
30
(17
), pp. 7446
–7477
.10.1002/rnc.518840.
Pereira
,
G. C.
,
Lima
,
P. F.
,
Wahlberg
,
B.
,
Pettersson
,
H.
, and
Martensson
,
J.
, 2018
, “
Linear Time-Varying Robust Model Predictive Control for Discrete-Time Nonlinear Systems
,” 57th IEEE Conference on Decision and Control
, Miami, FL, Dec. 17–19, pp. 2659
–2666
.10.1109/CDC.2018.861886641.
Geromel
,
J. C.
,
Peres
,
P. L.
, and
Bernussou
,
J.
, 1991
, “
On a Convex Parameter Space Method for Linear Control Design of Uncertain Systems
,” SIAM J. Control Optim.
,
29
(2
), pp. 381
–402
.10.1137/032902142.
Hewing
,
L.
,
Wabersich
,
K. P.
, and
Zeilinger
,
M. N.
, 2020
, “
Recursively Feasible Stochastic Model Predictive Control Using Indirect Feedback
,” Automatica
,
119
, p. 109095
.10.1016/j.automatica.2020.10909543.
Chen
,
X.
, 2007
, “A New Generalization of Chebyshev Inequality for Random Vectors,” preprint arXiv:0707.0805.44.
Bemporad
,
A.
,
Bernardini
,
D.
,
Long
,
R.
, and
Verdejo
,
J.
, 2018
, “
Model Predictive Control of Turbocharged Gasoline Engines for Mass Production
,” SAE
Paper No. 2018-01-0875.10.4271/2018-01-087545.
Rawlings
,
J. B.
,
Mayne
,
D. Q.
, and
Diehl
,
M.
, 2017
, Model Predictive Control: Theory, Computation, and Design
, Vol.
2
,
Nob Hill Publishing
,
Madison, WI
.46.
Garza-Fabre
,
M.
,
Pulido
,
G. T.
, and
Coello
,
C. A. C.
, 2009
, “
Ranking Methods for Many-Objective Optimization
,” 8th Mexican International Conference on Artificial Intelligence
, Guanajuato, Mexico, Nov. 9–13, pp. 633
–645
.47.
Bumroongsri
,
P.
, 2015
, “
Tube-Based Robust MPC for Linear Time-Varying Systems With Bounded Disturbances
,” Int. J. Control, Autom. Syst.
,
13
(3
), pp. 620
–625
.10.1007/s12555-014-0182-548.
Rakovic
,
S. V.
,
Kerrigan
,
E. C.
,
Kouramas
,
K. I.
, and
Mayne
,
S. V.
, 2005
, “
Invariant Approximation of the Minimal Robust Positively Invariant Set
,” IEEE Trans. Autom. Control
,
50
(3
), pp. 406
–410
.10.1109/TAC.2005.843854Copyright © 2022 by ASME
You do not currently have access to this content.
