1,828
Views
69
CrossRef citations to date
0
Altmetric
Original Articles

Stochastic model predictive control with joint chance constraints

, , &
Pages 126-139 | Received 25 Mar 2016, Accepted 23 Apr 2017, Published online: 10 May 2017

References

  • Balas, G.J. , Doyle, J.C. , Glover, K. , Packard, A. , & Smith, R. (1994). μ-Analysis and synthesis toolbox. Natick, MA: The MathWorks Inc.
  • Bemporad, A. , & Morari, M . (1999). Robust model predictive control: A survey. In Robustness in identification and control (pp. 207–226). London: Springer.
  • Ben-Tal, A. , El Ghaoui, L. , & Nemirovski, A . (2009). Robust optimization . Princeton, NJ: Princeton University Press.
  • Ben-Tal, A. , & Goryashko, A. (2004). Adjustable robust solutions of uncertain linear programs. Mathematical Programming, 99 , 351–376.
  • Bertsimas, D. , Brown, D.B. , & Caramanis, C. (2009). Theory and applications of robust optimization. SIAM Review, 53 , 464–501.
  • Bertsimas, D. , & Sim, M. (2006). Tractable approximations to robust conic optimization problems. Mathematical Programming, 107 , 5–36.
  • Blackmore, L. , & Ono, M . (2009). Convex chance constrained predictive control without sampling. In Proceedings of the AIAA guidance, navigation, and control conference (pp. 7–21). Chicago, Illinoise.
  • Blackmore, L. , Ono, M. , Bektassov, A. , & Williams, B.C. (2010). A probabilistic particle-control approximation of chance-constrained stochastic predictive control. IEEE Transactions on Robotics, 26 , 502–517.
  • Buehler, E.A. , & Mesbah, A. (2016). Kinetic study of acetone-butanol-ethanol fermentation in continuous culture. PLOS One, 0158243.
  • Calafiore, G.C. , & El Ghaoui, L. (2006). On distributionally robust chance-constrained linear programs. Journal of Optimization Theory and Applications, 130 , 1–22.
  • Calfiore, G.C. , & Fagiano, L. (2013). Robust model predictive control via scenario optimization. IEEE Transactions on Automatic Control, 58 , 219–224.
  • Chatterjee, D. , & Lygeros, J. (2015). On stability and performance of stochastic predictive control techniques. IEEE Transactions on Automatic Control, 60 , 509–514.
  • Chatterjee, D. , Ramponi, F. , Hokayem, P. , & Lygeros, J. (2012). On mean-square boundedness of stochastic linear systems with bounded controls. System and Control Letters, 61 , 375–280.
  • Cherukuri, A. , Chatterjee, D. , Hokayem, P. , & Lygeros, J . (2011). Stochastic receding horizon control: Stability results. In Proceedings of the 18th IFAC world congress on automatic control, Milano, Italy (pp. 150–155). Milano, Italy.
  • 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.
  • Goulart, P.J. , Kerrigan, E.C. , & Maciejowski, J.M. (2006). Optimization over state feedback policies for robust control with constraints. Automatica, 42 , 523–533.
  • Grant, M. , & Boyd, S. (2014). CVX: Matlab software for disciplined convex programming, version 2.1. March 2014. Retrieved from http://cvxr.com/cvx
  • Haus, S. , Jabbari, S. , Millat, T. , Janssen, H. , Fischer, R.J. , Bahl, H. , … Wolkenhauer, O . (2011). A systems biology approach to investigate the effect of pH-induced gene regulation on solvent production by Clostridium acetobutylicum in continuous culture. BMC Systems Biology, 5 (10), 21247470.
  • Hokayem, P. , Chatterjee, D. , & Lygeros, J . (2009). On stochastic receding horizon control with bounded control inputs. In Proceedings of the 48th IEEE conference on decision and control held jointly with the 28th chinese control conference, Shanghai, China (pp. 6359–6364). Shanghai, China.
  • Hokayem, P. , Cinquemani, E. , Chatterjee, D. , Ramponi, F. , & Lygeros, J. (2012). Stochastic receding horizon control with output feedback and bounded controls. Automatica, 48 , 77–88.
  • Kerrigan, E.C. , & Maciejowski, J.M. (2000). Soft constraints and exact penalty functions in model predictive control. In Proceedings of UKACC international conference (Control 2000) . Cambridge, UK.
  • Kouvaritakis, B. , & Cannon, M . (2015). Developments in robust and stochastic predictive control in the presence of uncertainty. ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part B: Mechanical Engineering, 1 (2), 021003.
  • Kouvaritakis, B. , Rossiter, J.A. , & Schuurmans, J. (2000). Efficient robust predictive control. IEEE Transactions on Automatic Control, 45 , 1545–1549.
  • Ma, Y. , Vichik, S. , & Borrelli, F . (2012). Fast stochastic MPC with optimal risk allocation applied to building control systems. In Proceedings of the 51st IEEE conference on decision and control, Maui, HI, USA (pp. 7559–7564). Maui, HI.
  • Marshall, A. , & Olkin, I . (1979). Inequalities: Theory and majorization and its applications . New York, NY: Academic Press.
  • Mayne, D.Q. (2014). Model predictive control: Recent developments and future promise. Automatica, 50 , 2967–2986.
  • Mayne, D.Q. , Rawlings, J.B. , Rao, C.V. , & Scokaert, P.O. M. (2000). Constrained model predictive control: Stability and optimality. Automatica, 36 , 798–814.
  • Mesbah, A. (2016). Stochastic model predictive control: An overview and perspectives for future research. IEEE Control Systems Magazine, 36 , 30–44.
  • Nemirovski, A. , & Shapiro, A. (2006). Convex approximations of chance constrained programs. SIAM Journal on Optimization, 17 , 969–996.
  • Oldewurtel, F. , Jones, C.N. , & Morari, M . (2008). A tractable approximation of chance constrained stochastic MPC based on affine disturbance feedback. In Proceedings of the 47th IEEE conference on decision and control, Cancun, Mexico (pp. 4731–4736). Cancun, Mexico.
  • Paulson, J.A. , Streif, S. , & Mesbah, A . (2015). Stability for receding-horizon stochastic model predictive control. In Proceedings of the american control conference, Chicago, IL, USA (pp. 937–943). Chicago, IL.
  • Primbs, J.A. , & Hwan Sung, C. (2009). Stochastic receding horizon control of constrained linear systems with state and control multiplicative noise. IEEE Transactions on Automatic Control, 54 , 221–230.
  • Simon, E. , R-Ayerbe, P. , Stoica, C. , Dumur, D. , & Wertz, V . (2011). LMIs-based coordinate descent method for solving BMIs in control design. In Proceedings of the 18th IFAC world congress on automatic control, Milano, Italy (pp. 10180–10186). Milano, Italy.
  • Vitus, M.P. , & Tomlin, C.J . (2011). On feedback design and risk allocation in chance constrained control. In Proceedings of the 50th IEEE conference on decision and control and European control conference, Orlando, FL, USA (pp. 734–739). Orlando, FL.
  • Wang, Y. , & Boyd, S. (2010). Fast model predictive control using online optimization. IEEE Transactions on Control Systems Technology, 18 , 267–278.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.