© The Institution of Engineering and Technology
This study presents a novel robust model predictive control (MPC) method for constrained non-linear systems with control constraints and external disturbances. The control signal is obtained by optimising an objective function consisting of two terms: an integral non-squared stage cost and a non-squared terminal cost. The terminal weighting matrix is designed appropriately such that: (i) the terminal cost serves as a control Lyapunov function; and (ii) the resultant finite horizon cost can be treated as a quasi-infinite horizon cost. Provided that the Jacobian linearisation of the system to be controlled is stabilisable and the optimisation is initially feasible, sufficient conditions ensuring the recursive feasibility of the optimisation and the robust stability of the closed-loop system are established. It is shown that the conditions rely on an appropriate design of the sampling interval with respect to a certain given disturbance level. The effectiveness of the proposed method is illustrated through a numerical example.
References
-
-
1)
-
36. Nešić, D., Grüne, L.: ‘A receding horizon control approach to sampled-data implementation of continuous-time controllers’, Syst. Control Lett., 2006, 55, (8), pp. 660–672 (doi: 10.1016/j.sysconle.2005.09.013).
-
2)
-
37. Khalil, H.K.: ‘Nonlinear systems’ (Upper Saddle River, NJ, Prentice–Hall, 2002).
-
3)
-
18. Rakovic, S.V., Kouvaritakis, B., Cannon, M., Panos, C., Findeisen, R.: ‘Parameterized tube model predictive control’, IEEE Trans. Autom. Control, 2012, 57, (11), pp. 2746–2761 (doi: 10.1109/TAC.2012.2191174).
-
4)
-
11. Dunbar, W., Caveney, D.S.: ‘Distributed receding horizon control of vehicle platoons: stability and string stability’, IEEE Trans. Autom. Control, 2012, 57, (3), pp. 620–633 (doi: 10.1109/TAC.2011.2159651).
-
5)
-
16. Findeisen, R., Imsland, L., Allgöwer, F., Foss, B.: ‘Towards a sampled-data theory for nonlinear model predictive control’. In Kang, W., Borges, C., Xiao, M. (Eds): ‘New trends in nonlinear dynamics and control and their applications’, , New York, Springer-Verlag, 295, pp. 295–311, 2003.
-
6)
-
8. Mayne, D.Q., Langson, W.: ‘Robustifying model predictive control of constrained linear systems’, Electron. Lett., 2001, 37, (23), pp. 1422–1423 (doi: 10.1049/el:20010951).
-
7)
-
20. Rawlings, J.B., Mayne, D.Q.: ‘Model predictive control: theory and design’ (Nob Hill publishing, Madison, Wisconsin, 2009).
-
8)
-
S.L. de Oliveira Kothare ,
M. Morari
.
Contractive model predictive control for constrainted nonlinear systems.
IEEE Trans. Autom. Control
,
1053 -
1071
-
9)
-
39. Russo, G., di Bernardo, M., Sontag, E.D.: ‘A contraction approach to the hierarchical analysis and design of networked systems’, IEEE Trans. Autom. Control, 2013, 58, (5), pp. 1328–1331 (doi: 10.1109/TAC.2012.2223355).
-
10)
-
P. Mhaskar ,
N. El-Farra ,
P. Christofides
.
Predictive control of switched nonlinear systems with scheduled mode transitions.
IEEE Trans. Autom. Control
,
11 ,
1670 -
1680
-
11)
-
17. Findeisen, R., Raff, T., Allgöwer, F.: ‘Sampled-data nonlinear model predictive control for constrained continuous time systems’. In Tarbouriech, S., Garcia, G., Glattfelder, A.H. (Eds): ‘Advanced strategies in control systems with input and output constraints’, , Springer-Verlag, New York, 346, pp. 207–235, 2007.
-
12)
-
13. Kerrigan, E.C., Maciejowski, J.M.: ‘Feedback min–max model predictive control using a single linear program: Robust stability and the explicit solution’, Int. J. Robust Nonlinear Control, 2004, 14, (4), pp. 395–413 (doi: 10.1002/rnc.889).
-
13)
-
28. Marruedo, D.L., Álamo, T., Camacho, E.F.: ‘Input-to-state stable MPC for constrained discrete-time nonlinear systems with bounded additive uncertainties’. Proc. 41st IEEE Conf. on Decision and Control, Las Vegas, Nevada, USA, 2002, pp. 4619–4624.
-
14)
-
D.Q. Mayne ,
H. Michalska
.
Receding horizon control of nonlinear systems.
IEEE Trans. Autom. Control
,
7 ,
814 -
824
-
15)
-
D.M. Raimondo ,
D. Limon ,
M. Lazar ,
L. Magni ,
E.F. Camacho
.
Min–max model predictive control of nonlinear systems: a unifying overview on stability.
Eur. J. Control
,
1 ,
5 -
21
-
16)
-
33. Li, H., Shi, Y.: ‘Network-based predictive control for constrained nonlinear systems with two-channel packet dropouts’, IEEE Trans. Ind. Electron., 2014, 61, (3), pp. 1574–1582 (doi: 10.1109/TIE.2013.2261039).
-
17)
-
F. Blanchini
.
Set invariance in control.
Automatica
,
11 ,
1747 -
1767
-
18)
-
18. Yu, S., Reble, M., Chen, H., Allgöwer, F.: ‘Inherent robustness properties of quasi-infinite horizon MPC’. Proc. 18th IFAC World Congress, Milano, Italy, 2011, pp. 179–184.
-
19)
-
H. Chen ,
F. Allgöwer
.
Quasi-infinite horizon nonlinear model predictive control scheme with guaranteed stability.
Automatica
,
10 ,
1205 -
1217
-
20)
-
5. Primbs, J. A., Nevistic, V.: ‘Constrained finite receding horizon linear quadratic control’. Technical Report, California Institute of Technology, Pasadena, CA, 1997.
-
21)
-
26. Cheng, X., Krogh, B.H.: ‘Stability-constrained model predictive control’, IEEE Trans. Autom. Control, 2001, 46, (11), pp 1816–1820 (doi: 10.1109/9.964698).
-
22)
-
P.O.M. Scokaert ,
D.Q. Mayne
.
Min-max feedback model predictive control for constrained linear systems.
IEEE Trans. Autom. Control
,
1136 -
1142
-
23)
-
D.Q. Mayne ,
J.B. Rawlings ,
P.M. Scokaert
.
Constraint predictive control: stability and optimality.
Automatica
,
789 -
814
-
24)
-
P. Mhaskar ,
N. El-Farra ,
P. Christofides
.
Stabilization of nonlinear systems with state and control constraints using lyapunov-based predictive control.
Syst. Control Lett.
,
650 -
659
-
25)
-
W. Langson ,
I. Chryssochoos ,
S. Rakovic ,
D.Q. Mayne
.
Robust model predictive control using tubes.
Automatica
,
125 -
133
-
26)
-
J.B. Rawlings ,
K.R. Muske
.
The stability of constrained receding horizon control.
IEEE Trans. Automat. Contr.
,
1512 -
1516
-
27)
-
D.Q. Mayne ,
M.M. Seron ,
S.V. Raković
.
Robust model predictive control of constrained linear systems with bounded disturbance.
Automatica
,
2 ,
219 -
224
-
28)
-
22. Limon, D., Alamo, T., Raimondo, D.M., et al: ‘Input-to-state stability: a unifying framework for robust model predictive control’. In Magni, L., Raimondo, D.M., Allgöwer, F. (Eds): ‘Nonlinear model predictive control: towards new challenging applications’, (Springer–Verlag, New York, 2009), 384, pp. 1–26.
-
29)
-
M. Michalska ,
D. Mayne
.
Robust receding horizon control of constrained nonlinear systems.
IEEE Trans. Autom. Control
,
11 ,
1623 -
1633
-
30)
-
32. Li, H., Shi, Y.: ‘Networked min–max model predictive control of constrained nonlinear systems with delays and packet dropouts’, Int. J. Control, 2013, 86, (4), pp. 610–624 (doi: 10.1080/00207179.2012.751628).
-
31)
-
6. Nevistic, V., Primbs, J.A.: ‘Finite receding horizon linear quadratic control: a unifying theory for stability and performance analysis’. Technical Report, California Institute of Technology, Pasadena, CA, 1997.
-
32)
-
W. Dunbar ,
R. Murray
.
Distributed receding horizon control for multi-vehicle formation stabilization.
Automatica
,
4 ,
549 -
558
-
33)
-
35. Hammer, J.: ‘State feedback control of nonlinear systems: a simple approach’, Int. J. Control, 2014, 87, (1), pp. 143–160 (doi: 10.1080/00207179.2013.824612).
-
34)
-
4. Bitmead, R.R., Gevers, M., Wertz, V.: ‘Adaptive optimal control – the thinking Man's GPC’ (Upper Saddle River, NJ, Prentice–Hall, 1990).
-
35)
-
2. Qin, S.J., Badgwell, T.A.: ‘An overview of nonlinear model predictive control applications’. in Fifth International Conf. on Chemical Process Control, CACHE, AIChE, California, USA, 1997, pp. 232–256.
-
36)
-
J.-S. Kim ,
T.-W. Yoon ,
A. Jadbabaie ,
C. De Persis
.
Input-to-state-stable finite horizon MPC for neutrally stable linear discrete-time systems with input constraints.
Syst. Control Lett.
,
4 ,
293 -
303
-
37)
-
19. Mayne, D.Q., Kerrigan, E.C., Wyk, E.J.V., Falugi, P.: ‘Tube-based robust nonlinear model predictive control’, Int. J. Robust Nonlinear Control, 2011, 21, (11), pp. 1341–1353 (doi: 10.1002/rnc.1758).
-
38)
-
29. Bao, X., Lin, Z., Sontag, E.D.: ‘Finite gain stabilization of discrete-time systems subject to actuator saturation’, Automatica, 2000, 36, (2), pp. 269–277 (doi: 10.1016/S0005-1098(99)00138-7).
-
39)
-
12. Farina, M., Scattolini, R.: ‘Tube-based robust sampled-data MPC for linear continuous-time systems’, Automatica, 2012, 48, (7), pp. 1473–1476 (doi: 10.1016/j.automatica.2012.03.026).
-
40)
-
W. Lohmiller ,
J.J.E. Slotine
.
On contraction analysis for nonlinear systems.
Automatica
,
6 ,
683 -
696
-
41)
-
42. Liu, X., Constantinescu, D., Shi, Y.: ‘Multistage suboptimal model predictive control with improved computational efficiency’, ASME J. Dyn. Syst. Meas. Control, 2014, 136, (3), (doi: 10.1115/1.4026413).
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-cta.2013.1078
Related content
content/journals/10.1049/iet-cta.2013.1078
pub_keyword,iet_inspecKeyword,pub_concept
6
6