Coping with High-Dimensional Uncertainties in Nonlinear MPC: Monotonicity and Randomization

Model predictive control (MPC) has become a standard advanced control strategy, mainly because of its ability to handle multivariable systems with constraints and general cost functions. A major obstacle to its broader adoption, however, is its inherent dependence on the accuracy of the underlying model: if the model is not perfectly calibrated, the result can be constraint violations, performance degradation or even closed-loop instability. This motivates the development of robust MPC methods.

In the first phase of the project, three different strategies were explored to mitigate the curse of dimensionality of robust nonlinear MPC: exploiting system properties such as monotonicity, relaxing constraints to obtain probabilistic guarantees, and shifting the computational effort to an offline phase by approximating the robust MPC policy. Monotonicity of dynamic systems enables a simple computation of reachable sets and therefore a scalable robust nonlinear MPC, but it is a strong assumption. The first phase already took initial steps towards generalising the approach to non-monotone nonlinear systems based on ideas from mixed monotonicity.

In its second phase, the project develops these directions further. The reachable-set approach is extended to allow non-smooth overapproximations of the reachable set, together with a method to learn and validate such approximations and an analysis of the stability properties of the resulting controller. For very large or very fast systems, where relying on approximations of the robust nonlinear MPC controller may be the only feasible option, probabilistic validation techniques can provide performance guarantees. The project extends these probabilistic guarantees to account for errors in the assumed distribution of the uncertainty, building on an ambiguity metric that remains computable even at very low risk levels, and develops data-driven methods to construct ambiguity sets from samples.

Together, the two strands, based on monotonicity and on randomization, aim to deliver scalable robust nonlinear MPC schemes with guarantees, as well as a framework for the probabilistic validation and design of robust nonlinear MPC controllers. As in the first phase, scientific collaboration with the University of Freiburg and benchmarking of different methods on shared case studies will further enrich the project's results.

This project is the second phase of the previous "Robust MPC with High-Dimensional Uncertainty" project and is funded by the DFG (Sachbeihilfen/Individual Research Grants).