01048885-dfca-454a-99dd-a0f7da72795d20210722030221693wseas:wseasmdt@crossref.orgMDT DepositWSEAS TRANSACTIONS ON SYSTEMS2224-26781109-277710.37394/23202http://wseas.org/wseas/cms.action?id=4067129202112920212010.37394/23202.2021.20https://wseas.org/wseas/cms.action?id=23288Dynamic Programming in Data Driven Model Predictive Control?WangJianhongSchool of Electronic Engineering and Automation, Jiangxi University of Science and Technology, Ganzhou, CHINAIn this short note, one data driven model predictive control is studied to design the optimal control sequence. The idea of data driven means the actual output value in cost function for model predictive control is identi_ed through input-output observed data in case of unknown but bounded noise and martingale di_erence sequence. After substituting the identi_ed actual output in cost function, the total cost function in model predictive control is reformulated as the other standard form, so that dynamic programming can be applied directly. As dynamic programming is only used in optimization theory, so to extend its advantage in control theory, dynamic programming algorithm is proposed to construct the optimal control sequence. Furthermore, stability analysis for data drive model predictive control is also given based on dynamic programming strategy. Generally, the goal of this short note is to bridge the dynamic programming, system identi_cation and model predictive control. Finally, one simulation example is used to prove the e_ciency of our proposed theory7212021721202117017719https://wseas.com/journals/systems/2021/a385103-1078.pdf10.37394/23202.2021.20.19https://wseas.com/journals/systems/2021/a385103-1078.pdf10.1016/j.automatica.2015.07.013Zhang Xiaojing, Sergio Grammatico, Gerorg Schildbach (2015). On the sample size of random convex programs with structured dependences on the uncertainty. Automatica 60(10), 182–188. 10.1016/j.automatica.2016.09.016Zhang Xiaojing, Maryam Kamgarpour, Angeios Georghial (2017). Robust optimal control with adjustable uncertainty sets. Automatica 75(1), 249–259. 10.1109/tac.2009.2031207T Alamo, R Tempo, E F Camacho (2009). Randomized strategy for probabilistic solution of uncertain feasiblity and optimization problems. IEEE Transactions on Automatic Control 54(11), 2545–2559. 10.1109/tac.2019.2896049D P Bertsekas (2019). Affine monotonic and risk sensitive models in dynamic programming. IEEE Transactions on Automatic Control 64(8), 3117–3128. 10.1007/s10107-011-0444-4D P Bertsekas, V Goyal (2012). On the power and limitations of affine policies in two stage adaptive optimization. Mathematical Programming 134(2), 491–531. 10.1109/tro.2011.2161160L Blackmore, M Ono, B C Williams (2011).Chance constrained optimal path planning with obstacles. IEEE Transactions on Robotics 27(6), 1080–1094. 10.1137/090773490G C Calafiore (2010). Random convex programs. SIAM Journal on Optimizaitons 20(6), 3427-3464. M C Campi, S Garatti (2016). Wait and judge scenario optimization. Automatica 50(12), 3019–3029 10.1016/j.arcontrol.2009.07.001M C Campi, S Garatti, M Prandini (2009).The scenario approach for systems and control design. Annual Reviews in Control 33(2), 149-157. D Callawy, I Hiskens (2011). Achieving controllability of electric loads. Proceedings of the IEEE 99(1), 184–199. 10.1016/j.jprocont.2016.03.005M Farina, L Giulioni(2016). Stochastic linear model predictive control with chance constraints- a review. Journal of Process Control 44(2), 53–67. S Garatti,M C Campi (2013). Modulating robustness in control design: principles and algorithm. IEEE Control Systems magazine 33(2), 36–51.