Johannes Köhler

ETH Zürich

Tuesday, March 18, 2025, 11:00 - 13:30

SR 01-012

I: Incremental system properties of nonlinear systems using contraction metrics

Time: 11:00-11:45

This tutorial covers basic concepts and recent advances in contraction metrics, an analysis and synthesis tools from nonlinear control theory. First, incremental system properties will be introduced and their usefulness for control of nonlinear systems will be highlighted, by showing their application to: reference tracking, robust/probabilistic reachability analysis, detectability and observer design, robustness, distributed methods, etc. Then, a more technical introduction will be given on the role of contraction metrics. Specifically, I will show that the Riemannian energy induced by a contraction metric yields an incremental Lyapunov function for the nonlinear system. As contraction metric pose conditions on the Jacobian of the nonlinear system, this allows us to seamlessly extend linear analysis and synthesis tools to (continuously differentiable) nonlinear systems. Computational tools will be discussed and some numerical example will illustrate the application of contraction metrics to control, estimation, and reachability problems.

II: MPC designs for nonlinear uncertain systems

Time: 12:30-13:15

In this talk, I introduce a framework to design MPC schemes for nonlinear uncertain systems that provide closed-loop guarantees. Specifically, contraction metrics are constructed offline to provide a computationally efficient evaluation of robust reachable sets for nonlinear systems subject to bounded disturbances and parametric error. A corresponding MPC formulation is provided that robustly ensures recursive feasibility, constraint satisfaction, and asymptotic convergence. Generality of this framework is demonstrated, by highlighting how the approach can be naturally particularized for:

 -more efficient constraint tightening formulations;

 -online model adaptation/learning (parametric and non-parametric);

 -stochastic noise.

Comparisons to existing nonlinear robust MPC formulations highlight benefits and limitations of different methods.