© The Institution of Engineering and Technology
This study designs a model predictive controller for linear, discrete-time, stochastic systems with multiplicative noise and probabilistic constraints. The probabilistic invariance has shown its advantage in characterising the stochastic dynamics of the controlled state. Here multi-step probabilistic sets strengthen probabilistic invariance to further satisfy infinite-horizon probabilistic constraints. In addition, multi-step probabilistic sets offer some degrees of freedom to enlarge the feasible region ensured by probabilistic invariance. The controller satisfies given constraints and guarantees closed-loop mean-square stability. Moreover, a simplified controller with lower on-line computational burden is presented. Numerical examples show the performance of the proposed approach.
References
-
-
1)
-
16. Wu, Y., Shen, Z., Liu, Y.: ‘Mean square detectability of multi-output systems over stochastic multiplicative channels’, IET Control Theory Appl., 2012, 6, (6), pp. 796–802 (doi: 10.1049/iet-cta.2011.0477).
-
2)
-
7. Primbs, J.A.: ‘A soft constraint approach to stochastic receding horizon control’. 2007 46th IEEE Conf. on Decision and Control, IEEE, 2007, pp. 4797–4802.
-
3)
-
8. Primbs, J.A., Sung, C.H.: ‘Stochastic receding horizon control of constrained linear systems with state and control multiplicative noise’, IEEE Trans. Autom. Control, 2009, 54, (2), pp. 221–230 (doi: 10.1109/TAC.2008.2010886).
-
4)
-
2. Henriksen, L.C., Hansen, M.H., Poulsen, N.K.: ‘Wind turbine control with constraint handling: a model predictive control approach’, IET Control Theory Appl., 2012, 6, (11), pp. 1722–1734 (doi: 10.1049/iet-cta.2011.0488).
-
5)
-
10. Chatterjee, D., Hokayem, P., Lygeros, J.: ‘Stochastic receding horizon control with bounded control inputs: a vector space approach’, IEEE Trans. Autom. Control, 2011, 56, (11), pp. 2704–2710 (doi: 10.1109/TAC.2011.2159422).
-
6)
-
5. Ding, B.: ‘Stabilization of linear systems over networks with bounded packet loss and its use in model predictive control’, Automatica, 2011, 47, (11), pp. 2526–2533 (doi: 10.1016/j.automatica.2011.08.038).
-
7)
-
19. Williams, D.: ‘Probability with martingales’ (Cambridge University Press, 1991).
-
8)
-
23. Li, D., Xi, Y.: ‘Design of robust model predictive control based on multi-step control set’, Acta Autom. Sin., 2009, 35, (4), pp. 433–437.
-
9)
-
12. Hokayem, P., Cinquemani, E., Chatterjee, D., Ramponi, F., Lygeros, J.: ‘Stochastic receding horizon control with output feedback and bounded controls’, Automatica, 2012, 48, (1), pp. 77–88 (doi: 10.1016/j.automatica.2011.09.048).
-
10)
-
13. Cannon, M., Kouvaritakis, B., Wu, X.: ‘Model predictive control for systems with stochastic multiplicative uncertainty and probabilistic constraints’, Automatica, 2009, 45, (1), pp. 167–172 (doi: 10.1016/j.automatica.2008.06.017).
-
11)
-
M.V. Kothare ,
V. Balakrishnan ,
M. Morari
.
Robust constrained model predictive control using linear matrix inequalities.
Automatica
,
10 ,
1361 -
1379
-
12)
-
25. Han, C.S., Wu, L.G., Shi, P., et al: ‘Passivity and passification of T–S fuzzy descriptor systems with stochastic perturbation and time delay’, IET Control Theory Appl., 2013, 7, (13), pp. 1711–1724 (doi: 10.1049/iet-cta.2013.0211).
-
13)
-
23. Li, D., Xi, Y., Gao, F.: ‘Synthesis of dynamic output feedback RMPC with saturated inputs’, Automatica, 2013, 49, (4), pp. 949–954 (doi: 10.1016/j.automatica.2013.01.010).
-
14)
-
18. Hou, T., Zhang, W., Chen, B.-S.: ‘Study on general stability and stabilizability of linear discrete-time stochastic systems’, Asian J. Control, 2011, 13, (6), pp. 977–987 (doi: 10.1002/asjc.238).
-
15)
-
15. Jiwei, L., Dewei, L., Yugeng, X.: ‘On design of mpc with soft constraint based on multistep control set for stochastic multiplicative system’. 2012 31st Chinese Control Conf. (CCC), IEEE, 2012, pp. 4120–4125.
-
16)
-
14. Su, Y., Tan, K.K., Lee, T.H.: ‘Comments on “model predictive control for systems with stochastic multiplicative uncertainty and probabilistic constraints” (Automatica 45 2009 167–172)’ Automatica, 2011, 47, (2), pp. 427–428 (doi: 10.1016/j.automatica.2010.10.042).
-
17)
-
D.W. Li ,
Y.G. Xi ,
P.Y. Zheng
.
Constrained robust feedback model predictive control for uncertain systems with polytopic description.
Int. J. Control
,
7 ,
1267 -
1274
-
18)
-
1. Alessio, A., Bemporad, A.: ‘A survey on explicit model predictive control’ In Nonlinear Model Predictive Control, SpringerBerlin Heidelberg, 2009, vol. 384, pp. 345–369.
-
19)
-
20. Kushner, H.: ‘Introduction to stochastic control’ (Holt Rinehart and Winston, 1971).
-
20)
-
11. Zou, Y., Niu, Y.: ‘Predictive control of constrained linear systems with multiple missing measurements’, Circuits Syst. Signal Process., 2013, 32, 2 pp. 615–630 (doi: 10.1007/s00034-012-9482-2).
-
21)
-
9. Kouvaritakis, B., Cannon, M., Rakovic, S.V., Cheng, Q.: ‘Explicit use of probabilistic distributions in linear predictive control’, Automatica, 2010, 46, (10), pp. 1719–1724 (doi: 10.1016/j.automatica.2010.06.034).
-
22)
-
3. Jerez, J.L., Ling, K.-V., Constantinides, G.A., Kerrigan, E.C.: ‘Model predictive control for deeply pipelined field-programmable gate array implementation: algorithms and circuitry’, IET Control Theory Appl., 2012, 6, (8), pp. 1029–1041 (doi: 10.1049/iet-cta.2010.0441).
-
23)
-
21. Cannon, M., Kouvaritakis, B.: ‘Optimizing prediction dynamics for robust mpc’, IEEE Trans. Autom. Control, 2005, 50, (11), pp. 1892–1897 (doi: 10.1109/TAC.2005.858679).
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