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A comparison on robust MPC methods for nonlinear systems
Nonlinear model predictive control (MPC), an advanced control method, often faces performance and safety issues due to model mismatch. Addressing this requires designing robust MPC schemes, a complex task given the variety of approaches in existing literature. This project aims to compare these methods, focusing on aspects like conservatism, complexity, and implementation ease, to establish clear guidelines for their application, supported by numerical benchmarks and exploration of their intrinsic limitations.
Keywords: Model predictive control, robustness, nonlinear systems, autonomous, robotics
Model predictive control (MPC) is an advanced control strategy, which is suitable for general nonlinear systems, can ensured general performance criteria, and satisfaction of safety critical constraints. However, the performance and safety properties of MPC deteriorate in practice due to model mismatch.
This problem can be addressed by designing a robust MPC scheme. However, this design becomes non-trivial for nonlinear systems. As a result, formulations developed in the literature differ significantly in how they approach this problem [5], considering complex offline designs [1], online Taylor approximation [2-5], optimization over feedback policies [4], control invariant sets [3], tube over-approximations [1,2,3], exact linear reachability [4]….
The goal of this project is to provide comparisons between these existing formulations (or at least some of them). This includes aspects such as conservatism, online and offline numerical complexity, ease of implementation, generality, etc. Ideally, the result of this thesis is a deep understanding that provides clear guidelines when either method may be more advantageous. These findings should be supported by numerical comparisons on realistic nonlinear benchmark problems. Ideally, also qualitative edge cases are discovered where provably one method suffers from some intrinsic limitation and is consistently worse. Part of this project includes providing a unified exposition of these different methods in a common framework and problem setup and thus necessitates a solid background in MPC. The focus of this work, in terms of number of numerical examples, number of robust MPC methods, and depth of comparison will be flexibly determined during the thesis.
[1] Sasfi, A., Zeilinger, M. N., & Köhler, J. (2023). Robust adaptive MPC using control contraction metrics.
[2] Houska, B., Logist, F., Van Impe, J., & Diehl, M. (2012). Robust optimization of nonlinear dynamic systems with application to a jacketed tubular reactor.
[3] Villanueva, M. E., Quirynen, R., Diehl, M., Chachuat, B., & Houska, B. (2017). Robust MPC via min–max differential inequalities.
[4] Leeman, A. P., Köhler, J., Zanelli, A., Bennani, S., & Zeilinger, M. N. (2023). Robust nonlinear optimal control via system level synthesis.
[5] Houska, B., & Villanueva, M. E. (2019). Robust optimization for MPC.
Model predictive control (MPC) is an advanced control strategy, which is suitable for general nonlinear systems, can ensured general performance criteria, and satisfaction of safety critical constraints. However, the performance and safety properties of MPC deteriorate in practice due to model mismatch. This problem can be addressed by designing a robust MPC scheme. However, this design becomes non-trivial for nonlinear systems. As a result, formulations developed in the literature differ significantly in how they approach this problem [5], considering complex offline designs [1], online Taylor approximation [2-5], optimization over feedback policies [4], control invariant sets [3], tube over-approximations [1,2,3], exact linear reachability [4]…. The goal of this project is to provide comparisons between these existing formulations (or at least some of them). This includes aspects such as conservatism, online and offline numerical complexity, ease of implementation, generality, etc. Ideally, the result of this thesis is a deep understanding that provides clear guidelines when either method may be more advantageous. These findings should be supported by numerical comparisons on realistic nonlinear benchmark problems. Ideally, also qualitative edge cases are discovered where provably one method suffers from some intrinsic limitation and is consistently worse. Part of this project includes providing a unified exposition of these different methods in a common framework and problem setup and thus necessitates a solid background in MPC. The focus of this work, in terms of number of numerical examples, number of robust MPC methods, and depth of comparison will be flexibly determined during the thesis.
[1] Sasfi, A., Zeilinger, M. N., & Köhler, J. (2023). Robust adaptive MPC using control contraction metrics.
[2] Houska, B., Logist, F., Van Impe, J., & Diehl, M. (2012). Robust optimization of nonlinear dynamic systems with application to a jacketed tubular reactor.
[3] Villanueva, M. E., Quirynen, R., Diehl, M., Chachuat, B., & Houska, B. (2017). Robust MPC via min–max differential inequalities.
[4] Leeman, A. P., Köhler, J., Zanelli, A., Bennani, S., & Zeilinger, M. N. (2023). Robust nonlinear optimal control via system level synthesis.
[5] Houska, B., & Villanueva, M. E. (2019). Robust optimization for MPC.
The project's goal is to conduct a comparison of various robust model predictive control (MPC) methods, assessing factors such as conservatism, computational complexity, ease of implementation, and overall performance. This includes performing numerical analyses on realistic nonlinear benchmark problems. The depth and scope of the comparisons will be determined during the course of the project.
The project's goal is to conduct a comparison of various robust model predictive control (MPC) methods, assessing factors such as conservatism, computational complexity, ease of implementation, and overall performance. This includes performing numerical analyses on realistic nonlinear benchmark problems. The depth and scope of the comparisons will be determined during the course of the project.
Johannes Köhler, jkoehle@ethz.ch, Antoine Leeman, aleeman@ethz.ch
Johannes Köhler, jkoehle@ethz.ch, Antoine Leeman, aleeman@ethz.ch