A Computationally Efficient Robust Model Predictive Control Framework for Uncertain Nonlinear Systems
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In this article, we present a nonlinear robust model predictive control (MPC) framework for general (state and input dependent) disturbances. This approach uses an online constructed tube in order to tighten the nominal (state and input) constraints. To facilitate an efficient online implementation, the shape of the tube is based on an offline computed incremental Lyapunov function with a corresponding (nonlinear) incrementally stabilizing feedback. Crucially, the online optimization only implicitly includes these nonlinear functions in terms of scalar bounds, which enables an efficient implementation. Furthermore, to account for an efficient evaluation of the worst case disturbance, a simple function is constructed offline that upper bounds the possible disturbance realizations in a neighborhood of a given point of the open-loop trajectory. The resulting MPC scheme ensures robust constraint satisfaction and practical asymptotic stability with a moderate increase in the online computational demand compared to a nominal MPC. We demonstrate the applicability of the proposed framework in comparison to state-of-the-art robust MPC approaches with a nonlinear benchmark example.
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For MPC, the constrained optimal control problem is solved using state predictions generated by the nominal mathematical model in a horizon, where the difference between nominal and real models due to uncertainties and disturbances may degrade tracking performance.
“For MPC, the constrained optimal control problem (OCP) is solved using the state predictions generated by the nominal mathematical model in a horizon [14]-[18], where the difference between the nominal and real mathematical models due to uncertainties and disturbances may degrade tracking performance [19].”
From Incremental Model Predictive Control Exploiting Time-Delay Estimation for a Robot Manipulator (2022) · cites this paper as [19]
Cites
Using SeDuMi 1.02, A Matlab toolbox for optimization over symmetric cones
Sturm, J. F. (1999) · Optimization methods & software · doi:10.1080/10556789908805766 · Cited by 7,320 · see citing works
CasADi: a software framework for nonlinear optimization and optimal control
Andersson, J. A. E., Gillis, J., Horn, G., Rawlings, J. B., & Diehl, M. (2018) · Mathematical Programming Computation · doi:10.1007/s12532-018-0139-4 · Cited by 3,890 · see citing works
Chen, H., & Allgöwer, F. (1998) · Automatica · doi:10.1016/s0005-1098(98)00073-9 · Cited by 1,559 · see citing works
Input-to-state stability for discrete-time nonlinear systems
Jiang, Z., & Wang, Y. (2001) · Automatica · doi:10.1016/s0005-1098(01)00028-0 · Cited by 1,436 · see citing works
A Lyapunov approach to incremental stability properties
Angeli, D. (2002) · IEEE Transactions on Automatic Control · doi:10.1109/9.989067 · Cited by 782 · see citing works
Systems with persistent disturbances: predictive control with restricted constraints
Chisci, L., Rossiter, J. A., & Zappa, G. (2001) · Automatica · doi:10.1016/s0005-1098(01)00051-6 · Cited by 679 · see citing works
Cautious Model Predictive Control Using Gaussian Process Regression
Hewing, L., Kabzan, J., & Zeilinger, M. N. (2019) · IEEE Transactions on Control Systems Technology · doi:10.1109/tcst.2019.2949757 · Cited by 576 · see citing works
Kouvaritakis, B., & Cannon, M. (2016) · Advanced Textbooks in Control and Signal Processing · doi:10.1007/978-3-319-24853-0 · Cited by 515 · see citing works
Tube‐based robust nonlinear model predictive control
Mayne, D. Q., Kerrigan, E. C., van Wyk, E. J., & Falugi, P. (2011) · International Journal of Robust and Nonlinear Control · doi:10.1002/rnc.1758 · Cited by 464 · see citing works
Marruedo, D. L., Alamo, T., & Camacho, E. F. (2004) · Proceedings of the 41st IEEE Conference on Decision and Control, 2002. · doi:10.1109/cdc.2002.1185106 · Cited by 340 · see citing works
Robust Model Predictive Control via Scenario Optimization
Calafiore, G. C., & Fagiano, L. (2012) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2012.2203054 · Cited by 240 · see citing works
Min-max Model Predictive Control of Nonlinear Systems: A Unifying Overview on Stability
Raimondo, D. M., Limón, D., Lazar, M., Magni, L., & Camacho, E. F. (2009) · European Journal of Control · doi:10.3166/ejc.15.5-21 · Cited by 238 · see citing works
Yu, S., Maier, C., Chen, H., & Allgöwer, F. (2013) · Systems & Control Letters · doi:10.1016/j.sysconle.2012.11.004 · Cited by 236 · see citing works
Control Contraction Metrics: Convex and Intrinsic Criteria for Nonlinear Feedback Design
Manchester, I. R., & Slotine, J.-J. E. (2017) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2017.2668380 · Cited by 229 · see citing works
Safe and Fast Tracking on a Robot Manipulator: Robust MPC and Neural Network Control
Nubert, J., Köhler, J., Berenz, V., Allgöwer, F., & Trimpe, S. (2020) · IEEE Robotics and Automation Letters · doi:10.1109/lra.2020.2975727 · Cited by 227 · see citing works
Robust online motion planning via contraction theory and convex optimization
Singh, S., Majumdar, A., Slotine, J.-J. E., & Pavone, M. (2017) · Proceedings - IEEE International Conference on Robotics and Automation/Proceedings · doi:10.1109/icra.2017.7989693 · Cited by 183 · see citing works
Robust Tube MPC for Linear Systems With Multiplicative Uncertainty
Fleming, J. M., Kouvaritakis, B., & Cannon, M. (2014) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2014.2336358 · Cited by 142 · see citing works
Dynamic Tube MPC for Nonlinear Systems
Lopez, B. T., Slotine, J.-J. E., & How, J. P. (2019) · Proceedings of the ... American Control Conference/Proceedings of the American Control Conference · doi:10.23919/acc.2019.8814758 · Cited by 124 · see citing works
Robust Model Predictive Control of Nonlinear Systems With Bounded and State-Dependent Uncertainties
Pin, G., Raimondo, D. M., Magni, L., & Parisini, T. (2009) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2009.2020641 · Cited by 116 · see citing works
Köhler, J., Müller, M. A., & Allgöwer, F. (2019) · arXiv (Cornell University) · doi:10.1109/tac.2019.2949350 · Cited by 113 · see citing works
Robust MPC via min–max differential inequalities
Villanueva, M. E., Quirynen, R., Diehl, M., et al. (2017) · Automatica · doi:10.1016/j.automatica.2016.11.022 · Cited by 109 · see citing works
Robust MPC of constrained nonlinear systems based on interval arithmetic
Limón, D., Bravo, J. M., Álamo, T., & Camacho, E. F. (2005) · IEE Proceedings - Control Theory and Applications · doi:10.1049/ip-cta:20040480 · Cited by 89 · see citing works
A robust adaptive model predictive control framework for nonlinear uncertain systems
Köhler, J., Kötting, P., Soloperto, R., et al. (2020) · International Journal of Robust and Nonlinear Control · doi:10.1002/rnc.5147 · Cited by 89 · see citing works
Self-citationDiscrete-time Incremental ISS: A framework for Robust NMPC
Bayer, F. A., Bürger, M., & Allgöwer, F. (2013) · European Control Conference (ECC) · doi:10.23919/ecc.2013.6669322 · Cited by 80 · see citing works
A novel constraint tightening approach for nonlinear robust model predictive control
Köhler, J., Müller, M. A., & Allgöwer, F. (2018) · Proceedings of the ... American Control Conference/Proceedings of the American Control Conference · doi:10.23919/acc.2018.8431892 · Cited by 79 · see citing works
Getting Robustness Against Unstructured Uncertainty: A Tube-Based MPC Approach
Falugi, P., & Mayne, D. Q. (2013) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2013.2287727 · Cited by 76 · see citing works
Soloperto, R., Köhler, J., Allgöwer, F., & Müller, M. A. (2019) · European Control Conference (ECC) · doi:10.23919/ecc.2019.8796049 · Cited by 59 · see citing works
Self-citationLöhning, M., Reble, M., Hasenauer, J., et al. (2014) · Journal of Process Control · doi:10.1016/j.jprocont.2014.07.006 · Cited by 29 · see citing works
Real-Time Tube MPC Applied to a 10-State Quadrotor Model
Hu, H., Feng, X., Quirynen, R., et al. (2018) · Proceedings of the ... American Control Conference/Proceedings of the American Control Conference · doi:10.23919/acc.2018.8431112 · Cited by 22 · see citing works
DIRTREL: Robust Trajectory Optimization with Ellipsoidal Disturbances and LQR Feedback
Manchester, Z. R., & Kuindersma, S. (2017) · doi:10.15607/rss.2017.xiii.057 · Cited by 19 · see citing works
Bonzanini, A. D., Santos, T. L. M., & Mesbah, A. (2019) · IFAC-PapersOnLine · doi:10.1016/j.ifacol.2019.06.128 · Cited by 15 · see citing works
A Short Note on Constrained Linear Control Systems With Multiplicative Ellipsoidal Uncertainty
Houska, B., Mohammadi, A., & Diehl, M. (2016) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2016.2551682 · Cited by 14 · see citing works
A simple framework for nonlinear robust output-feedback MPC
Köhler, J., Allgöwer, F., & Müller, M. A. (2019) · European Control Conference (ECC) · doi:10.23919/ecc.2019.8795965 · Cited by 12 · see citing works
Schlüter, H., & Allgöwer, F. (2020) · IFAC-PapersOnLine · doi:10.1016/j.ifacol.2020.12.518 · Cited by 12 · see citing works
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Incremental Model Predictive Control Exploiting Time-Delay Estimation for a Robot Manipulator
Wang, Y., Leibold, M., Lee, J., Ye, W., Xie, J., & Buss, M. (2022) · IEEE Transactions on Control Systems Technology · doi:10.1109/tcst.2022.3142629 · Cited by 52 · see citing works
- Authors
- Kohler, J., Soloperto, R., Muller, M. A., & Allgower, F.
- Affiliations
- University of Stuttgart (DE)
- Venue
- IEEE Transactions on Automatic Control
- Published
- 2021-02
- Volume
- 66
- Issue
- 2
- Pages
- 794-801
- ISSN
- 0018-9286 (ISSN-L)
- 1558-2523
- 2334-3303
- OpenAlex
- W2981706805
- Cited by
- 19
- References
- 34
- Citations by year
- 2024: 1 · 2023: 2 · 2022: 3 · 2021: 3 · 2020: 7 · 2019: 3
- FWCI
- 1.85
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Licence
- Locations
- IEEE Transactions on Automatic Control (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Deutsche Forschungsgemeinschaft (GRK 2198/1-277536708, AL 316/12-2, MU 3929/1-2-279734922)
- International Max Planck Research School for Intelligent Systems
- Topics
- Physical Sciences › Engineering › Control and Systems Engineering › Advanced Control Systems Optimization
- Physical Sciences › Mathematics › Numerical Analysis › Advanced Optimization Algorithms Research
- Physical Sciences › Engineering › Control and Systems Engineering › Stability and Control of Uncertain Systems
- Keywords
- robust model predictive control, nonlinear systems, tube-based MPC, worst-case disturbance, constraint tightening, online optimization, computational efficiency, asymptotic stability, robust constraint satisfaction
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