arXiv subjects

Johannes Köhler

Publications and source records attributed to Johannes Köhler.

At least 37 records · Page 2Linked to original sources

arXiv2026

Model Predictive Control with Reference Learning for Soft Robotic Intracranial Pressure Waveform Modulation

This paper introduces a learning-based control framework for a soft robotic actuator system designed to modulate intracranial pressure (ICP) waveforms, which is essential for studying cerebrospinal fluid dynamics and pathological processes underlying neurological disorders. A two-layer framework is proposed to safely achieve a desired ICP waveform modulation. First, a model predictive controller (MPC) with a disturbance observer is used for offset-free tracking of the system's motor position reference trajectory under safety constraints. Second, to address the unknown nonlinear dependence of ICP on the motor position, we employ a Bayesian optimization (BO) algorithm used for online learning of a motor position reference trajectory that yields the desired ICP modulation. The framework is experimentally validated using a test bench with a brain phantom that replicates realistic ICP dynamics in vitro. Compared to a previously employed proportional-integral-derivative controller, the MPC reduces mean and maximum motor position reference tracking errors by 83 % and 73 %, respectively. In less than 20 iterations, the BO algorithm learns a motor position reference trajectory that yields an ICP waveform with the desired mean and amplitude.

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arXiv2026

Safe and Near-Optimal Control with Online Dynamics Learning

Achieving both optimality and safety under unknown system dynamics is a central challenge in real-world deployment of agents. To address this, we introduce a notion of maximum safe dynamics learning, where sufficient exploration is performed within the space of safe policies. Our method executes $\textit{pessimistically}$ safe policies while $\textit{optimistically}$ exploring informative states and, despite not reaching them due to model uncertainty, ensures continuous online learning of dynamics. The framework achieves first-of-its-kind results: learning the dynamics model sufficiently $-$ up to an arbitrary small tolerance (subject to noise) $-$ in a finite time, while ensuring provably safe operation throughout with high probability and without requiring resets. Building on this, we propose an algorithm to maximize rewards while learning the dynamics $\textit{only to the extent needed}$ to achieve close-to-optimal performance. Unlike typical reinforcement learning (RL) methods, our approach operates online in a non-episodic setting and ensures safety throughout the learning process. We demonstrate the effectiveness of our approach in challenging domains such as autonomous car racing and drone navigation under aerodynamic effects $-$ scenarios where safety is critical and accurate modeling is difficult.

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arXiv2026

A model predictive control framework with robust stability guarantees under unbounded disturbances

To address feasibility issues in model predictive control (MPC), most implementations relax state constraints by using slack variables and adding a penalty to the cost. We propose an alternative strategy: relaxing the initial state constraint with a penalty. Compared to state-of-the-art soft constrained MPC formulations, the proposed formulation has two key features: (i) input-to-state stability and bounds on the cumulative constraint violation for unbounded disturbances; (ii) close-to-optimal performance under nominal operating conditions. The idea is initially presented for open-loop asymptotically stable nonlinear systems by designing the penalty as a Lyapunov function, but we also show how to relax this condition to: i) Lyapunov stable systems; ii) stabilizable systems; and iii) utilizing an implicit characterization of the Lyapunov function. In the special case of linear systems, the proposed MPC formulation reduces to a quadratic program, and the offline design and online computational complexity are only marginally increased compared to a nominal design. Numerical examples demonstrate benefits compared to state-of-the-art soft-constrained MPC formulations.

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arXiv2026

Adaptive Economic Model Predictive Control: Performance Guarantees for Nonlinear Systems

We consider the problem of optimizing the economic performance of nonlinear constrained systems subject to uncertain time-varying parameters and bounded disturbances. In particular, we propose an adaptive economic model predictive control (MPC) framework that: (i) directly minimizes transient economic costs, (ii) addresses parametric uncertainty through online model adaptation, (iii) determines optimal setpoints online, and (iv) ensures robustness by using a tube-based approach. The proposed design ensures recursive feasibility, robust constraint satisfaction, and a transient performance bound. In case the disturbances have a finite energy and the parameter variations have a finite path length, the asymptotic average performance is (approximately) not worse than the performance obtained when operating at the best reachable steady-state. We highlight performance benefits in a numerical example involving a chemical reactor with unknown time-invariant and time-varying parameters.

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arXiv2026

Optimal kernel regression bounds under energy-bounded noise

Non-conservative uncertainty bounds are key for both assessing an estimation algorithm's accuracy and in view of downstream tasks, such as its deployment in safety-critical contexts. In this paper, we derive a tight, non-asymptotic uncertainty bound for kernel-based estimation, which can also handle correlated noise sequences. Its computation relies on a mild norm-boundedness assumption on the unknown function and the noise, returning the worst-case function realization within the hypothesis class at an arbitrary query input location. The value of this function is shown to be given in terms of the posterior mean and covariance of a Gaussian process for an optimal choice of the measurement noise covariance. By rigorously analyzing the proposed approach and comparing it with other results in the literature, we show its effectiveness in returning tight and easy-to-compute bounds for kernel-based estimates.

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arXiv2025

MHE under parametric uncertainty -- Robust state estimation without informative data

In this paper, we study joint state and parameter estimation for general nonlinear systems with uncertain parameters and persistent process and measurement noise. In particular, we are interested in stability properties of the resulting state estimate in the absence of persistency of excitation (PE). With a simple academic example, we show that existing moving horizon estimation (MHE) approaches for joint state and parameter estimation as well as classical adaptive observers can result in diverging state estimates in the absence of PE, even if the noise is small. We propose an MHE formulation involving a regularization based on a constant prior estimate of the unknown system parameters. Only assuming the existence of a stable state estimator, we prove that the proposed MHE approach results in practically robustly stable state estimates irrespective of PE. We discuss the relation of the proposed MHE formulation to state-of-the-art results from MHE and adaptive estimation. The properties of the proposed MHE approach are illustrated with a numerical example of a car with unknown tire friction parameters.

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arXiv2025

Approximate non-linear model predictive control with safety-augmented neural networks

Model predictive control (MPC) achieves stability and constraint satisfaction for general nonlinear systems, but requires computationally expensive online optimization. This paper studies approximations of such MPC controllers via neural networks (NNs) to achieve fast online evaluation. We propose safety augmentation that yields deterministic guarantees for convergence and constraint satisfaction despite approximation inaccuracies. We approximate the entire input sequence of the MPC with NNs, which allows us to verify online if it is a feasible solution to the MPC problem. We replace the NN solution by a safe candidate based on standard MPC techniques whenever it is infeasible or has worse cost. Our method requires a single evaluation of the NN and forward integration of the input sequence online, which is fast to compute on resource-constrained systems. The proposed control framework is illustrated using two numerical non-linear MPC benchmarks of different complexity, demonstrating computational speedups that are orders of magnitude higher than online optimization. In the examples, we achieve deterministic safety through the safety-augmented NNs, where a naive NN implementation fails.

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arXiv2025

Stochastic Model Predictive Control for Sub-Gaussian Noise

We propose a stochastic Model Predictive Control (MPC) framework that ensures closed-loop chance constraint satisfaction for linear systems with general sub-Gaussian process and measurement noise. By considering sub-Gaussian noise, we can provide guarantees for a large class of distributions, including time-varying distributions. Specifically, we first provide a new characterization of sub-Gaussian random vectors using matrix variance proxy, which can more accurately represent the predicted state distribution. We then derive tail bounds under linear propagation for the new characterization, enabling tractable computation of probabilistic reachable sets of linear systems. Lastly, we utilize these probabilistic reachable sets to formulate a stochastic MPC scheme that provides closed-loop guarantees for general sub-Gaussian noise. We further demonstrate our approach in simulations, including a challenging task of surgical planning from image observations.

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arXiv2025

Guaranteed Robust Nonlinear MPC via Disturbance Feedback

Robots must satisfy safety-critical state and input constraints despite disturbances and model mismatch. We introduce a robust model predictive control (RMPC) formulation that is fast, scalable, and compatible with real-time implementation. Our formulation guarantees robust constraint satisfaction, input-to-state stability (ISS) and recursive feasibility. The key idea is to decompose the uncertain nonlinear system into (i) a nominal nonlinear dynamic model, (ii) disturbance-feedback controllers, and (iii) bounds on the model error. These components are optimized jointly using sequential convex programming. The resulting convex subproblems are solved efficiently using a recent disturbance-feedback MPC solver. The approach is validated across multiple dynamics, including a rocket-landing problem with steerable thrust. An open-source implementation is available at https://github.com/antoineleeman/robust-nonlinear-mpc.

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arXiv2025

Robust MPC for Uncertain Linear Systems -- Combining Model Adaptation and Iterative Learning

This paper presents a robust adaptive learning Model Predictive Control (MPC) framework for linear systems with parametric uncertainties and additive disturbances performing iterative tasks. The approach refines the parameter estimates online using set-membership estimation. Performance enhancement over iterations is achieved by learning the terminal cost from data. Safety is enforced using a terminal set, which is also learned iteratively. The proposed method guarantees recursive feasibility, constraint satisfaction, and a robust bound on the closed-loop cost. Numerical simulations on a mass-spring-damper system demonstrate improved computational efficiency and control performance compared to a robust adaptive MPC scheme without iterative learning of the terminal ingredients.

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arXiv2025

Output-feedback model predictive control under dynamic uncertainties using integral quadratic constraints

In this work, we propose an output-feedback tube-based model predictive control (MPC) scheme for linear systems under dynamic uncertainties that are described via integral quadratic constraints (IQC). By leveraging IQCs, a large class of nonlinear and dynamic uncertainties can be addressed. We leverage recent IQC synthesis tools to design a dynamic controller and an estimator that are robust to these uncertainties and minimize the size of the resulting constraint tightening in the MPC. Thereby, we show that the robust estimation problem using IQCs with peak-to-peak performance can be convexified. We guarantee recursive feasibility, robust constraint satisfaction, and input-to-state stability of the resulting MPC scheme.

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arXiv2025

A Step-by-step Guide on Nonlinear Model Predictive Control for Safe Mobile Robot Navigation

Designing a model predictive control (MPC) scheme that enables a mobile robot to safely navigate through an obstacle-filled environment is a complicated yet essential task in robotics. In this technical report, safety refers to ensuring that the robot respects state and input constraints while avoiding collisions with obstacles despite the presence of disturbances and measurement noise. This report offers a step-by-step approach to implementing nonlinear model predictive control (NMPC) schemes addressing these safety requirements. Numerous books and survey papers provide comprehensive overviews of linear MPC (LMPC), NMPC, and their applications in various domains, including robotics. This report does not aim to replicate those exhaustive reviews. Instead, it focuses specifically on NMPC as a foundation for safe mobile robot navigation. The goal is to provide a practical and accessible path from theoretical concepts to mathematical proofs and implementation, emphasizing safety and performance guarantees. It is intended for researchers, robotics engineers, and practitioners seeking to bridge the gap between theoretical NMPC formulations and real-world robotic applications. This report is not necessarily meant to remain fixed over time. If someone finds an error in the presented theory, please reach out via the given email addresses. We are happy to update the document if necessary.

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arXiv2025

From Data to Safe Mobile Robot Navigation: An Efficient and Modular Robust MPC Design Pipeline

Model predictive control (MPC) is a powerful strategy for planning and control in autonomous mobile robot navigation. However, ensuring safety in real-world deployments remains challenging due to the presence of disturbances and measurement noise. Existing approaches often rely on idealized assumptions, neglect the impact of noisy measurements, and simply heuristically guess unrealistic bounds. In this work, we present an efficient and modular robust MPC design pipeline that systematically addresses these limitations. The pipeline consists of an iterative procedure that leverages closed-loop experimental data to estimate disturbance bounds and synthesize a robust output-feedback MPC scheme. We provide the pipeline in the form of deterministic and reproducible code to synthesize the robust output-feedback MPC from data. We empirically demonstrate robust constraint satisfaction and recursive feasibility in quadrotor simulations using Gazebo.

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arXiv2025

Robust Nonlinear Optimal Control via System Level Synthesis

This paper addresses the problem of finite horizon constrained robust optimal control for nonlinear systems subject to norm-bounded disturbances. To this end, the underlying uncertain nonlinear system is decomposed based on a first-order Taylor series expansion into a nominal system and an error (deviation) described as an uncertain linear time-varying system. This decomposition allows us to leverage system level synthesis to jointly optimize an affine error feedback, a nominal nonlinear trajectory, and, most importantly, a dynamic linearization error over-bound used to ensure robust constraint satisfaction for the nonlinear system. The proposed approach thereby results in less conservative planning compared with state-of-the-art techniques. We demonstrate the benefits of the proposed approach to control the rotational motion of a rigid body subject to state and input constraints.

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arXiv2025

Online convex optimization for constrained control of nonlinear systems

This paper proposes a modular approach that combines the online convex optimization framework and reference governors to solve a constrained control problem featuring time-varying and a priori unknown cost functions. Compared to existing results, the proposed framework is uniquely applicable to nonlinear dynamical systems subject to state and input constraints. Furthermore, our method is general in the sense that we do not limit our analysis to a specific choice of online convex optimization algorithm or reference governor. We show that the dynamic regret of the proposed framework is bounded linearly in both the dynamic regret and the path length of the chosen online convex optimization algorithm, even though the online convex optimization algorithm does not account for the underlying dynamics. We prove that a linear bound with respect to the online convex optimization algorithm's dynamic regret is optimal, i.e., cannot be improved upon. Furthermore, for a standard class of online convex optimization algorithms, our proposed framework attains a bound on its dynamic regret that is linear only in the variation of the cost functions, which is known to be an optimal bound. Finally, we demonstrate implementation and flexibility of the proposed framework by comparing different combinations of online convex optimization algorithms and reference governors to control a nonlinear chemical reactor in a numerical experiment.

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arXiv2025

Time-Varying Coverage Control: A Distributed Tracker-Planner MPC Framework

Time-varying coverage control addresses the challenge of coordinating multiple agents covering an environment where regions of interest change over time. This problem has broad applications, including the deployment of autonomous taxis and coordination in search and rescue operations. The achievement of effective coverage is complicated by the presence of time-varying density functions, nonlinear agent dynamics, and stringent system and safety constraints. In this paper, we present a distributed multi-agent control framework for time-varying coverage under nonlinear constrained dynamics. Our approach integrates a reference trajectory planner and a tracking model predictive control (MPC) scheme, which operate at different frequencies within a multi-rate framework. For periodic density functions, we demonstrate closed-loop convergence to an optimal configuration of trajectories and provide formal guarantees regarding constraint satisfaction, collision avoidance, and recursive feasibility. Additionally, we propose an efficient algorithm capable of handling nonperiodic density functions, making the approach suitable for practical applications. Finally, we validate our method through hardware experiments using a fleet of four miniature race cars.

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arXiv2025

Safe Guaranteed Exploration for Non-linear Systems

Safely exploring environments with a-priori unknown constraints is a fundamental challenge that restricts the autonomy of robots. While safety is paramount, guarantees on sufficient exploration are also crucial for ensuring autonomous task completion. To address these challenges, we propose a novel safe guaranteed exploration framework using optimal control, which achieves first-of-its-kind results: guaranteed exploration for non-linear systems with finite time sample complexity bounds, while being provably safe with arbitrarily high probability. The framework is general and applicable to many real-world scenarios with complex non-linear dynamics and unknown domains. We improve the efficiency of this general framework by proposing an algorithm, SageMPC, SAfe Guaranteed Exploration using Model Predictive Control. SageMPC leverages three key techniques: i) exploiting a Lipschitz bound, ii) goal-directed exploration, and iii) receding horizon style re-planning, all while maintaining the desired sample complexity, safety and exploration guarantees of the framework. Lastly, we demonstrate safe efficient exploration in challenging unknown environments using SageMPC with a car model.

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arXiv2025

A model-free approach to control barrier functions using funnel control

Control barrier functions (CBFs) are a popular approach to design feedback laws that achieve safety guarantees for nonlinear systems. The CBF-based controller design relies on the availability of a model to select feasible inputs from the set of CBF-based controls. In this paper, we develop a model-free approach to design CBF-based control laws, eliminating the need for knowledge of system dynamics or parameters. Specifically, we address safety requirements characterized by a time-varying distance to a reference trajectory in the output space and construct a CBF that depends only on the measured output. Utilizing this particular CBF, we determine a subset of CBF-based controls without relying on a model of the dynamics by using techniques from funnel control. The latter is a model-free high-gain adaptive control methodology, which achieves tracking guarantees via reactive feedback. In this paper, we discover and establish a connection between the modular controller synthesis via zeroing CBFs and model-free reactive feedback. The theoretical results are illustrated by a numerical simulation.

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