Efficient robust nonlinear predictive control with stability and feasibility guarantees by parallel time-stage considerations
Final Report Abstract
Model Predictive Control (MPC) is a modern and versatile control approach that offers many benefits. It is naturally capable of dealing with multi-input multi-output systems and constraints on the input, state, and output. Its control performance furthermore often surpasses that of other control approaches because it uses a mathematical prediction model of the process, which enables it to take future information into account. Besides the performance, also theoretical properties, such as stability, depend on this prediction model. In the case of uncertainty however (e.g. model-plant mismatch or unknown disturbances), these properties deteriorate (e.g. the closed-loop performance) or can be lost completely (e.g. stability). To recover these properties, robust MPC formulations are necessary. The objective of this project was to further develop the field of robust MPC. To this end, we have developed different approaches in the course of this project. One contribution was the derivation of theoretical properties for multi-stage MPC, a robust and nonconservative MPC scheme developed by one of our project partners. We embedded multi-stage MPC in the framework of dual mode MPC and derived conditions under which the controller yields always feasible and stabilizing inputs to the system. In addition, a computational approach was provided to compute the necessary ingredients in the case of linear uncertain systems. Other works focused on achieving robust constraint satisfaction and recursive feasibility despite uncertain and bounded disturbances for MPC control of certain system classes. The proposed approach uses different model granularities, which allows using simplified models for predictions into the far future instead of detailed models. The approach provides efficient, suboptimal, but feasible solutions while allowing embedding different types of information into the controller via using models of different system classes. Furthermore, the computational cost of the involved optimal control problem of multistage MPC could be reduced. In addition to this, we derived methods to efficiently solve MPC problems using parallel computation. This led to a significant reduction of the time required to compute the solution of an MPC problem. Moreover, for large-scale problems, we proposed the concept of contract based MPC to increase the scalability of MPC and avoid the curse of dimensionality. For this approach we derived conditions to guarantee robust constraint satisfaction and robust stability. In another work, we investigated sampled data issues, i.e. problems arising from the fact that the continuous dynamics need to be approximated by discrete equations. In particular, we showed that one can derive conditions to guarantee constraint satisfaction in the continuous-time domain and other closed-loop properties such as robust stability. These results greatly extend the available methods both in theory and practice. Not only do they allow more thorough investigations and examinations of robust control setups, but they also make their application more feasible. While computational power has highly increased in the past years, only specifically tailored algorithms will be able to effectively use that power. For our approaches, we showed their applicability in benchmark examples that can be used as a starting point for realworld implementation. Furthermore, we developed new ideas for further research on these topics, like combinations and extensions of these methods with approaches from machine learning.
Publications
- Parallel solutions of model predictive control using the alternating direction method of multipliers. In Proc. 4th IFAC Conference on Nonlinear Model Predictive Control Conference (NMPC), 2012, p. 369-374
M. Kögel and R. Findeisen
(See online at https://doi.org/10.3182/20120823-5-NL-3013.00081) - Robust Nonlinear Model Predictive Control with Constraint Satisfaction: A Relaxation-based Approach. In Proc. 19th IFAC World Congress (IFAC WC), 2014, p. 11073-11079
S. Streif, M. Kögel, T. Bäthge and R. Findeisen
(See online at https://doi.org/10.3182/20140824-6-ZA-1003.02420) - Contract-based predictive control of distributed systems with plug and play capabilities. In Proc. 5th IFAC Conf. Nonlinear Model Predictive Control (NMPC), p. 205-211, 2015
S. Lucia, M. Kögel, and R. Findeisen
(See online at https://doi.org/10.1016/j.ifacol.2015.11.284) - Discrete-time robust model predictive control for continuous-time nonlinear systems. American Control Conference (ACC), 2015, p. 924- 930
M. Kögel and R. Findeisen
(See online at https://doi.org/10.1109/ACC.2015.7170852) - Scenario-based model predictive control: Recursive feasibility and stability. In Proc. 9th International Symposium on Advanced Control of Chemical Processes (ADCHEM), p. 50-56, 2015
M. Maiworm, T. Bäthge, and R. Findeisen
(See online at https://doi.org/10.1016/j.ifacol.2015.08.156) - Exploiting Models of Different Granularity in Robust Predictive Control. In Proc. 55th IEEE Conf. Decision and Control (CDC), p. 2763-2768. 2016
T. Bäthge, S. Lucia, and R. Findeisen
(See online at https://doi.org/10.1109/CDC.2016.7798680)
