Johannes Köhler

Johannes Köhler, Daniel Zhang, Raffaele Soloperto et al.

We present a model predictive control (MPC) framework for efficient navigation of mobile robots in cluttered environments. The proposed approach integrates a finite-segment shortest path planner into the finite-horizon trajectory optimization of the MPC. This formulation ensures convergence to dynamically selected targets and guarantees collision avoidance, even under general nonlinear dynamics and cluttered environments. The approach is validated through hardware experiments on a small ground robot, where a human operator dynamically assigns target locations that a robot should reach while avoiding obstacles. The robot reached new targets within 2-3 seconds and responded to new commands within 50 ms to 100 ms, immediately adjusting its motion even while still moving at high speeds toward a previous target.

Amon Lahr, Anna Scampicchio, Johannes Köhler et al.

Non-conservative uncertainty bounds are essential for making reliable predictions about latent functions from noisy data--and thus, a key enabler for safe learning-based control. In this domain, kernel methods such as Gaussian process regression are established techniques, thanks to their inherent uncertainty quantification mechanism. Still, existing bounds either pose strong assumptions on the underlying noise distribution, are conservative, do not scale well in the multi-output case, or are difficult to integrate into downstream tasks. This paper addresses these limitations by presenting a tight, distribution-free bound for multi-output kernel-based estimates. It is obtained through an unconstrained, duality-based formulation, which shares the same structure of classic Gaussian process confidence bounds and can thus be straightforwardly integrated into downstream optimization pipelines. We show that the proposed bound generalizes many existing results and illustrate its application using an example inspired by quadrotor dynamics learning.

Johannes Köhler, Carlo Scholz, Melanie Zeilinger

We address the design of a model predictive control (MPC) scheme for large-scale linear systems using reduced-order models (ROMs). Our approach uses a ROM, leverages tools from robust control, and integrates them into an MPC framework to achieve computational tractability with robust constraint satisfaction. Our key contribution is a method to obtain guaranteed bounds on the predicted outputs of the full-order system by predicting a (scalar) error-bounding system alongside the ROM. This bound is then used to formulate a robust ROM-based MPC that guarantees constraint satisfaction and robust performance. Our method is developed step-by-step by (i) analysing the error, (ii) bounding the peak-to-peak gain, an (iii) using filtered signals. We demonstrate our method on a 100-dimensional mass-spring-damper system, achieving over four orders of magnitude reduction in conservatism relative to existing approaches.

Irene Schimperna, Lea Bold, Johannes Köhler et al.

This paper derives conditions under which Model Predictive Control (MPC) with terminal conditions, using a data-driven surrogate model as a prediction model, asymptotically stabilizes the plant despite approximation errors. In particular, we prove recursive feasibility and asymptotic stability if a proportional error bound holds, where proportional means that the bound is linear in the norm of the state and the input. For a broad class of nonlinear systems, this condition can be satisfied using data-driven surrogate models generated by kernel Extended Dynamic Mode Decomposition (kEDMD) using the Koopman operator. Last, the applicability of the proposed framework is demonstrated in a numerical case study.

Lea Bold, Irene Schimperna, Karl Worthmann et al.

We consider nonlinear model predictive control (MPC) schemes using surrogate models in the optimization step based on input-output data only. We establish exponential stability for sufficiently long prediction horizons assuming exponential stabilizability and a proportional error bound. Moreover, we verify the imposed condition on the approximation using kernel interpolation and demonstrate the practical applicability to nonlinear systems with a numerical example.

Johannes Köhler

We provide a method to design adaptive controllers for nonlinear systems using model predictive control (MPC). By combining a certainty-equivalent MPC formulation with least-mean-square parameter adaptation, we obtain an adaptive controller with strong robust performance guarantees: The cumulative tracking error and violation of state constraints scale linearly with noise energy, disturbance energy, and path length of parameter variation. A key technical contribution is developing the underlying certainty-equivalent MPC that tracks output references, accounts for actuator limitations and desired state constraints, requires no system-specific offline design, and provides strong inherent robustness properties. This is achieved by leveraging finite-horizon rollouts, artificial references, recent analysis techniques for optimization-based controllers, and soft state constraints. For open-loop stable systems, we derive a semi-global result that applies to arbitrarily large measurement noise, disturbances, and parametric uncertainty. For stabilizable systems, we derive a regional result that is valid within a given region of attraction and for sufficiently small uncertainty. Applicability and benefits are demonstrated with numerical simulations involving systems with large parametric uncertainty: a linear stable chain of mass-spring-dampers and a nonlinear unstable quadrotor navigating obstacles.