Model Predictive Control of Stochastic Linear Systems with Probability Constraints
Keywords:
probability constraints, stochastic systems, linear systems, controlAbstract
This paper presents a strategy for computing model predictive control of linear Gaussian noise systems with probability constraints. As usual, constraints are taken on the system state and control input. The novelty relies on setting bounds on the underlying cumulative probability distribution, and showing that the model predictive control can be computed in an efficient manner through these novel bounds– an application confirms this assertion. Indeed real-time experiments were carried out to control a direct current (DC) motor. The corresponding data show the effectiveness and usefulness of the approach.References
Bazaraa, M.S.; Sherali, H.D.; Shetty, C.M. (2006). Nonlinear programming: theory and algorithms, 3rd edn., Wiley-Interscience, New Jersey, 2006. https://doi.org/10.1002/0471787779
Bernardini, D.; Bemporad, A. (2012). Stabilizing model predictive control of stochastic constrained linear systems, IEEE Trans. Autom. Control, 57, 1468-1480, 2012. https://doi.org/10.1109/TAC.2011.2176429
Blackmore, L.; Ono, M. (2009). Convex chance constrained predictive control without sampling, In: AIAA Guidance, Navigation and Control Conference, Chicago, Illinois, USA, 1-17, 2009. https://doi.org/10.2514/6.2009-5876
Boyd, S.; El Ghaoui, L.; Feron, E.; Balakrishnan, V. (1994). Linear matrix inequalities in system and control theory, SIAM, Philadelphia, 1994. https://doi.org/10.1137/1.9781611970777
Cannon, M.; Kouvaritakis, B.; Rakovic, S.; Cheng Q. (2011). Stochastic tubes in model predictive control with probabilistic constraints, IEEE Trans. Autom. Control, 56, 194-200, 2011. https://doi.org/10.1109/TAC.2010.2086553
Cao, G.; Lai, E.M.-K.; Alam, F. (2017). Gaussian process model predictive control of unknown non-linear systems, IET Control Theory Appl., 11, 703-713, 2017. https://doi.org/10.1049/iet-cta.2016.1061
Caruntu, C.F.; Balau, A.E.; Lazar, M.; van den Bosch, P.P.J.; Di Cairano, S. (2016). Driveline oscillations damping: A tractable predictive control solution based on a piecewise affine model, Nonlinear Analysis: Hybrid Systems, 19, 168-185, 2016. https://doi.org/10.1016/j.nahs.2015.10.001
Costa Junior, A.G.; Riul J.A.; Montenegro, P.H.M. (2016). Application of the subspace identification method using the N4SID technique for a robotic manipulator, IEEE Latin America Transactions, 14, 1588-1993, 2016. https://doi.org/10.1109/TLA.2016.7483487
Farina, M.; Giulioni, L.; Scattolini, R. (2016). Stochastic linear model predictive control with chance constraints-A review, Journal of Process Control, 44, 53-67, 2016. https://doi.org/10.1016/j.jprocont.2016.03.005
Farina, M.; Giulioni, L.; Magni, L.; Scattolini, R. (2015). An approach to output-feedback MPC of stochastic linear discrete-time systems, Automatica, 55, 140-149, 2015. https://doi.org/10.1016/j.automatica.2015.02.039
Farina, M.; Scattolini, R. (2016). Model predictive control of linear systems with multiplicative unbounded uncertainty and chance constraints, Automatica, 70, 258-265, 2016. https://doi.org/10.1016/j.automatica.2016.04.008
Hashorva, E.; Hüsler, J. (2003). On multivariate Gaussian tails, Annals of the Institute of Statistical Mathematics, 55, 507-522, 2003. https://doi.org/10.1007/BF02517804
Katayama, T. (2005). Subspace methods for system identification, communications and control engineering, Springer-Verlag, London, 2005. https://doi.org/10.1007/1-84628-158-X
Kwon, W.H., Han, S.H. (2005). Receding horizon control: model predictive control for state models, Springer-Verlag, New York, 2005.
Li, P.; Wendt, M.; Wozny, G. (2002). A probabilistically constrained model predictive controller, Automatica, 38, 1171-1176, 2002. https://doi.org/10.1016/S0005-1098(02)00002-X
Li, J.W.; Li, D.W.; Xi, Y.G. (2017). H1 predictive control with probability constraints for linear stochastic systems, IET Control Theory Appl., 11, 557-566, 2017. https://doi.org/10.1049/iet-cta.2016.0915
Lu, D.; Li, W.V. (2009). A note on multivariate Gaussian estimates, Journal of Mathematical Analysis and Applications,354, 704-707, 2009. https://doi.org/10.1016/j.jmaa.2009.01.046
Oliveira, R.C.L.; Vargas, A.N.; do Val, J.B.R.; Peres, P.L.D. (2014). Mode-independent H2-control of a DC motor modeled as a Markov jump linear system, IEEE Transactions on Control Systems Technology, 22, 1915-1919, 2014. https://doi.org/10.1109/TCST.2013.2293627
Rubagotti, M.; Patrinos, P.; Guiggiani, A.; Bemporad, A. (2016). Real-time model predictive control based on dual gradient projection: theory and fixed-point FPGA implementation, Int. J. Robust Nonlinear Control, 26, 3292-3310, 2016. https://doi.org/10.1002/rnc.3507
Schwarm, A.T.; Nikolaou, M. (1999). Chance-constrained model predictive control, AIChE Journal, 45, 1743-1752, 1999. https://doi.org/10.1002/aic.690450811
Vargas, A.N.; Costa, E.F.; do Val, J.B.R. (2013). On the control of Markov jump linear systems with no mode observation: application to a DC motor device, Int. J. Robust Nonlinear Control, 23, 1136-1950, 2013. https://doi.org/10.1002/rnc.2911
Vargas, A. N.; do Val, J.B.R. (2010). Average cost and stability of time-varying linear systems, IEEE Trans. Autom. Control, 55, 714-720, 2010. https://doi.org/10.1109/TAC.2010.2040423
Wang, S.; Yu, M.; Sun, X. (2015). Robust H1 control for time-delay networked control systems with probability constraints, IET Control Theory Appl., 9, 482-2489, 2015. https://doi.org/10.1049/iet-cta.2015.0143
Yang, H.; Guo, M.C.; Xia, Y.; Cheng, L. (2018). Trajectory tracking for wheeled mobile robots via model predictive control with softening constraints, IET Control Theory Appl., 12, 206-214, 2018. https://doi.org/10.1049/iet-cta.2017.0395
Yan, J.; Bitmead, R.R. (2005). Incorporating state estimation into model predictive control and its application to network traffic control, Automatica, 41, 595-604, 2005. https://doi.org/10.1016/j.automatica.2004.11.022
Zeilinger, M.N.; Raimondo, D.M.; Domahidi, A.; Morari, M.; Jones, C.N. (2014). Flocking of multi-agents with a virtual leader, Automatica, 50, 683-694, 2014. https://doi.org/10.1016/j.automatica.2013.11.019
Published
Issue
Section
License
ONLINE OPEN ACCES: Acces to full text of each article and each issue are allowed for free in respect of Attribution-NonCommercial 4.0 International (CC BY-NC 4.0.
You are free to:
-Share: copy and redistribute the material in any medium or format;
-Adapt: remix, transform, and build upon the material.
The licensor cannot revoke these freedoms as long as you follow the license terms.
DISCLAIMER: The author(s) of each article appearing in International Journal of Computers Communications & Control is/are solely responsible for the content thereof; the publication of an article shall not constitute or be deemed to constitute any representation by the Editors or Agora University Press that the data presented therein are original, correct or sufficient to support the conclusions reached or that the experiment design or methodology is adequate.
