Tackling high-dimensional uncertainties in nonlinear MPC: monotonicity and randomization

• Applicant: Professor Dr.-Ing. Sergio Lucia Gil
• Subject Area: Automation, Mechatronics, Control Systems, Intelligent Technical Systems, Robotics
• Term: since 2025
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 559922123

Model predictive control (MPC) has become a standard advanced control strategy, primarily due to its ability to effectively address the complexities of multiple-input, multiple-output systems with constraints and general objective functions. However, one significant challenge impeding the widespread adoption of MPC is its inherent reliance on the accuracy of the underlying model. If the model is not perfectly calibrated, it can lead to undesirable outcomes such as constraint violations, reduced performance, or even closed-loop instabilities. This underscores the necessity for the development of robust MPC schemes. In the first phase of the project, three different strategies were employed to alleviate the curse of dimensionality of robust nonlinear MPC. These strategies were: exploiting system properties such as monotonicity, relaxing constraints to achieve probabilistic guarantees, and moving the computational effort offline by approximating the robust MPC policy. Monotonicity of dynamic systems allows the simple computation of reachable sets, enabling scalable robust nonlinear MPC. However, monotonicity is a strong assumption. Initial steps to the generalization to non-monotonous nonlinear systems were given in the first phase of project based on ideas of mixed-monotonicity. In the second phase, we will further develop these approaches by allowing non-smooth over-approximations of the reachable set and by developing a procedure to learn and validate the approximation of reachable sets. Furthermore, we will study the stability properties of the resulting approach. For very large or very fast systems, resorting to some approximations of the robust nonlinear MPC controller might be the only computationally tractable option. In that case, probabilistic validation techniques can provide performance guarantees. In the second phase of this project, we will extend the probabilistic guarantees for the validation of approximate robust nonlinear MPC to consider an ambiguity in the underlying distribution of the uncertainty. We will base our results on an ambiguity metric that enables computationally tractable results also for very low risk levels, as they are typically required in control applications, and we will develop methods to compute ambiguity sets based on data. The two approaches, following ideas on monotonicity and randomization, will facilitate the design of scalable and robust nonlinear MPC with guarantees and a framework for probabilistically validating and designing robust nonlinear MPC controllers when approximations are necessary. As it was the case in the initial funding phase, scientific collaborations with the University of Freiburg and benchmarking of different methods on joint case studies will further enrich the results of the project.

• DFG Programme: Research Grants