{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,7,18]],"date-time":"2024-07-18T00:13:26Z","timestamp":1721261606818},"reference-count":40,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2024,6,23]],"date-time":"2024-06-23T00:00:00Z","timestamp":1719100800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Information"],"abstract":"In this paper, we present a data-driven model predictive control (DDMPC) framework specifically designed for constrained single-input single-output (SISO) nonlinear systems. Our approach involves customizing a set-theoretic receding horizon controller within a data-driven context. To achieve this, we translate model-based conditions into data series of available input and output signals. This translation process leverages recent advances in data-driven control theory, enabling the controller to operate effectively without relying on explicit system models. The proposed framework incorporates a robust methodology for managing system constraints, ensuring that the control actions remain within predefined bounds. By means of time sequences, the controller learns the underlying system dynamics and adapts to changes in real time, providing enhanced performance and reliability. The integration of set-theoretic methods allows for the systematic handling of uncertainties and disturbances, which are common when the trajectory of a nonlinear system is embedded inside a linear trajectory state tube. To validate the effectiveness of our DDMPC framework, we conduct extensive simulations on a nonlinear DC motor system. The results demonstrate significant improvements in control performance, highlighting the robustness and adaptability of our approach compared to traditional model-based MPC techniques.<\/jats:p>","DOI":"10.3390\/info15070369","type":"journal-article","created":{"date-parts":[[2024,6,24]],"date-time":"2024-06-24T10:59:58Z","timestamp":1719226798000},"page":"369","source":"Crossref","is-referenced-by-count":0,"title":["A Data-Driven Approach to Set-Theoretic Model Predictive Control for Nonlinear Systems"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"http:\/\/orcid.org\/0000-0001-5892-2049","authenticated-orcid":false,"given":"Francesco","family":"Giannini","sequence":"first","affiliation":[{"name":"Department of Computer Engineering, Modeling, Electronics and Systems (DIMES), Universit\u00e0 della Calabria, Via P. Bucci, 42-C, 87036 Rende, Italy"}]},{"ORCID":"http:\/\/orcid.org\/0000-0003-0185-2611","authenticated-orcid":false,"given":"Domenico","family":"Famularo","sequence":"additional","affiliation":[{"name":"Department of Computer Engineering, Modeling, Electronics and Systems (DIMES), Universit\u00e0 della Calabria, Via P. Bucci, 42-C, 87036 Rende, Italy"}]}],"member":"1968","published-online":{"date-parts":[[2024,6,23]]},"reference":[{"key":"ref_1","unstructured":"Rawlings, J., Mayne, D., and Diehl, M. (2017). Model Predictive Control: Theory, Computation, and Design, Nob Hill Publishing."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/j.ins.2012.07.014","article-title":"From model-based control to data-driven control: Survey, classification and perspective","volume":"235","author":"Hou","year":"2013","journal-title":"Inf. Sci."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"4753","DOI":"10.1109\/TAC.2020.2966717","article-title":"Data Informativity: A New Perspective on Data-Driven Analysis and Control","volume":"65","author":"Eising","year":"2020","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"883","DOI":"10.1109\/TAC.2022.3148374","article-title":"Bridging Direct and Indirect Data-Driven Control Formulations via Regularizations and Relaxations","volume":"68","author":"Coulson","year":"2023","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Krishnan, V., and Pasqualetti, F. (2021, January 14\u201317). On Direct vs. Indirect Data-Driven Predictive Control. Proceedings of the 2021 60th IEEE Conference on Decision and Control (CDC), Austin, TX, USA.","DOI":"10.1109\/CDC45484.2021.9683187"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"100914","DOI":"10.1016\/j.arcontrol.2023.100914","article-title":"Handbook of linear data-driven predictive control: Theory, implementation and design","volume":"56","author":"Verheijen","year":"2023","journal-title":"Annu. Rev. Control"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Formentin, S., van Heusden, K., and Karimi, A. (2013, January 17\u201319). Model-based and data-driven model-reference control: A comparative analysis. Proceedings of the 2013 European Control Conference (ECC), Zurich, Switzerland.","DOI":"10.23919\/ECC.2013.6669388"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"50","DOI":"10.1016\/j.jprocont.2015.07.009","article-title":"Data-driven model reduction-based nonlinear MPC for large-scale distributed parameter systems","volume":"35","author":"Xie","year":"2015","journal-title":"J. Process. Control"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"4492","DOI":"10.1109\/TSMC.2019.2937002","article-title":"Knowledge-Data-Driven Model Predictive Control for a Class of Nonlinear Systems","volume":"51","author":"Han","year":"2021","journal-title":"IEEE Trans. Syst. Man, Cybern. Syst."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"113895","DOI":"10.1016\/j.enbuild.2024.113895","article-title":"Real-life data-driven model predictive control for building energy systems comparing different machine learning models","volume":"305","author":"Stoffel","year":"2024","journal-title":"Energy Build."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Kim, H., Nair, S.H., and Borrelli, F. (2024). Scalable Multi-modal Model Predictive Control via Duality-based Interaction Predictions. arXiv.","DOI":"10.1109\/IV55156.2024.10588718"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"99589","DOI":"10.1109\/ACCESS.2023.3310887","article-title":"Data-Driven MPC for a Fog-Cloud Platform with AI-Inferencing in Mobile-Robotics","volume":"11","author":"Vinod","year":"2023","journal-title":"IEEE Access"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Shah, K., He, A., Wang, Z., Du, X., and Jin, X. (2022, January 19\u201320). Data-Driven Model Predictive Control for Roll-to-Roll Process Register Error. Proceedings of the 2022 International Additive Manufacturing Conference, International Manufacturing Science and Engineering Conference, Lisbon, Portugal.","DOI":"10.1115\/IAM2022-96840"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"633","DOI":"10.1016\/j.ifacol.2022.11.253","article-title":"Data-Driven Prediction and Predictive Control Methods for Eco-Driving in Production Vehicles","volume":"55","author":"Baby","year":"2022","journal-title":"IFAC-PapersOnLine"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"3932","DOI":"10.1073\/pnas.1517384113","article-title":"Discovering governing equations from data by sparse identification of nonlinear dynamical systems","volume":"113","author":"Brunton","year":"2016","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"32190","DOI":"10.1109\/ACCESS.2022.3160709","article-title":"Toward Data-Driven Optimal Control: A Systematic Review of the Landscape","volume":"10","author":"Prag","year":"2022","journal-title":"IEEE Access"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"617","DOI":"10.1016\/j.ifacol.2023.10.1636","article-title":"Data-driven nonlinear predictive control for feedback linearizable systems","volume":"56","author":"Alsalti","year":"2023","journal-title":"IFAC-PapersOnLine"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Sawant, S., Reinhardt, D., Kordabad, A.B., and Gros, S. (2023, January 13\u201315). Model-Free Data-Driven Predictive Control Using Reinforcement Learning. Proceedings of the 2023 62nd IEEE Conference on Decision and Control (CDC), Marina Bay Sands, Singapore.","DOI":"10.1109\/CDC49753.2023.10383431"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"189204","DOI":"10.1007\/s11432-018-9645-3","article-title":"Synthesis of model predictive control based on data-driven learning","volume":"63","author":"Zhou","year":"2019","journal-title":"Sci. China Inf. Sci."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1109\/TSMC.2020.3042898","article-title":"Internet of Things as System of Systems: A Review of Methodologies, Frameworks, Platforms, and Tools","volume":"51","author":"Fortino","year":"2021","journal-title":"IEEE Trans. Syst. Man, Cybern. Syst."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1016\/j.inffus.2020.08.003","article-title":"Deep learning for pedestrian collective behavior analysis in smart cities: A model of group trajectory outlier detection","volume":"65","author":"Belhadi","year":"2021","journal-title":"Inf. Fusion"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Coulson, J., Lygeros, J., and D\u00f6rfler, F. (2019, January 25\u201328). Data-Enabled Predictive Control: In the Shallows of the DeePC. Proceedings of the 2019 18th European Control Conference (ECC), Naples, Italy.","DOI":"10.23919\/ECC.2019.8795639"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"2625","DOI":"10.1109\/TAC.2022.3163110","article-title":"Robust Stability Analysis of a Simple Data-Driven Model Predictive Control Approach","volume":"68","author":"Bongard","year":"2023","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1016\/j.sysconle.2004.09.003","article-title":"A note on persistency of excitation","volume":"54","author":"Willems","year":"2005","journal-title":"Syst. Control Lett."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"909","DOI":"10.1109\/TAC.2019.2959924","article-title":"Formulas for Data-Driven Control: Stabilization, Optimality, and Robustness","volume":"65","author":"Tesi","year":"2020","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1101","DOI":"10.1109\/TAC.2022.3146726","article-title":"Data-Driven Simulation of Generalized Bilinear Systems via Linear Time-Invariant Embedding","volume":"68","author":"Markovsky","year":"2023","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Giannini, F., Franz\u00e8, G., Pupo, F., and Fortino, G. (2023, January 6\u20138). Set-theoretic receding horizon control for nonlinear systems: A data-driven approach. Proceedings of the IEEE EUROCON 2023\u201420th International Conference on Smart Technologies, Torino, Italy.","DOI":"10.1109\/EUROCON56442.2023.10198968"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"3113","DOI":"10.1016\/j.automatica.2008.04.027","article-title":"An ellipsoidal off-line MPC scheme for uncertain polytopic discrete-time systems","volume":"44","author":"Angeli","year":"2008","journal-title":"Automatica"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1091","DOI":"10.1002\/1099-1239(200011)10:13<1091::AID-RNC518>3.0.CO;2-W","article-title":"Constrained predictive control of nonlinear plants via polytopic linear system embedding","volume":"10","author":"Angeli","year":"2000","journal-title":"Int. J. Robust Nonlinear Control"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Boyd, S., El Ghaoui, L., Feron, E., and Balakrishnan, V. (1994). Linear Matrix Inequalities in System and Control Theory, SIAM Studies in Applied Mathematics.","DOI":"10.1137\/1.9781611970777"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1002\/rnc.815","article-title":"Robust model predictive control for nonlinear discrete-time systems","volume":"13","author":"Magni","year":"2003","journal-title":"Int. J. Robust Nonlinear Control"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Blanchini, F., and Miani, S. (2007). Set-Theoretic Methods in Control, Birkh\u00e4user. [1st ed.].","DOI":"10.1007\/978-0-8176-4606-6"},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Kurzhanski, A., and Valyi, I. (1996). Ellipsoidal Calculus for Estimation and Control, Birkh\u00e4user. Systems & Control: Foundations & Applications.","DOI":"10.1007\/978-1-4612-0277-6"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"317","DOI":"10.1080\/1055678031000098773","article-title":"PENNON: A code for convex nonlinear and semidefinite programming","volume":"18","author":"Stingl","year":"2003","journal-title":"Optim. Methods Softw."},{"key":"ref_35","unstructured":"Russell, S., and Norvig, P. (2009). Artificial Intelligence: A Modern Approach, Prentice Hall Press. [3rd ed.]."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Jampani, R., Xu, F., Wu, M., Perez, L.L., Jermaine, C., and Haas, P.J. (2008, January 9\u201312). MCDB: A monte carlo approach to managing uncertain data. Proceedings of the SIGMOD \u201908 2008 ACM SIGMOD International Conference on Management of Data, New York, NY, USA.","DOI":"10.1145\/1376616.1376686"},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Krause, P., Wasynczuk, O., Sudhoff, S., and Pekarek, S. (2013). Analysis of Electric Machinery and Drive Systems, Wiley.","DOI":"10.1002\/9781118524336"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"107195","DOI":"10.1016\/j.compchemeng.2020.107195","article-title":"Adaptive multi-model predictive control applied to continuous stirred tank reactor","volume":"145","author":"Pipino","year":"2021","journal-title":"Comput. Chem. Eng."},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Ben-Tal, A., and Nemirovski, A. (2001). Lectures on Modern Convex Optimization, Society for Industrial and Applied Mathematics.","DOI":"10.1137\/1.9780898718829"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1016\/j.arcontrol.2004.05.001","article-title":"Efficient nonlinear model predictive control algorithms","volume":"28","author":"Cannon","year":"2004","journal-title":"Annu. Rev. Control"}],"container-title":["Information"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2078-2489\/15\/7\/369\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,7,17]],"date-time":"2024-07-17T17:21:53Z","timestamp":1721236913000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2078-2489\/15\/7\/369"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,6,23]]},"references-count":40,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2024,7]]}},"alternative-id":["info15070369"],"URL":"https:\/\/doi.org\/10.3390\/info15070369","relation":{},"ISSN":["2078-2489"],"issn-type":[{"value":"2078-2489","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,6,23]]}}}