PhD Candidate in Mechanical and Process Engineering
Institute for Dynamic Systems and Control
ETH Zürich
Amon Lahr was born in Berlin, Germany, in 1996. He completed his Bachelor’s studies in Engineering
Science in 2018, with two semester-long stays at New York University and the German Aerospace
Center in Stuttgart, Germany, respectively. Redirecting his study focus towards numerical mathematics, control theory and model reduction, Amon later received a Master’s degree in Scientific Computing from TU Berlin in 2021, with his thesis on “ℋ-∞ Control for Large-Scale Linear Systems”. During his studies, Amon has worked as a Linux and web developer for IoT devices in the automotive industry, shaping his interests in embedded systems and data-driven control methods.
Project description
While the performance and potential of learning-based control has been recently demonstrated, the associated computational challenges remain a key limiting factor for moving these techniques into industrial applications. On embedded hardware in particular, the feasible model complexity and sampling times are restricted by the limited storage and computational power. The aim of this PhD project is to develop new controllers and computational methods for embedded control systems. Possible research directions include the development of tailored real-time optimization routines, controller approximation using learning-based function approximation schemes, as well as efficient data selection and reduction.
Publications
1.
Lahr, Amon; Köhler, Johannes; Scampicchio, Anna; Zeilinger, Melanie N.
Optimal Kernel Regression Bounds under Energy-Bounded Noise Working paper
2025.
@workingpaper{lahr_optimal_2025,
title = {Optimal Kernel Regression Bounds under Energy-Bounded Noise},
author = {Amon Lahr and Johannes Köhler and Anna Scampicchio and Melanie N. Zeilinger},
doi = {10.48550/arXiv.2505.22235},
year = {2025},
date = {2025-05-28},
abstract = {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.},
keywords = {},
pubstate = {published},
tppubtype = {workingpaper}
}
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.
2.
Prajapat, Manish; Köhler, Johannes; Lahr, Amon; Krause, Andreas; Zeilinger, Melanie N.
Finite-Sample-Based Reachability for Safe Control with Gaussian Process Dynamics Working paper
2025.
@workingpaper{prajapat_finite_sample_based_2025,
title = {Finite-Sample-Based Reachability for Safe Control with Gaussian Process Dynamics},
author = {Manish Prajapat and Johannes Köhler and Amon Lahr and Andreas Krause and Melanie N. Zeilinger},
doi = {10.48550/arXiv.2505.07594},
year = {2025},
date = {2025-05-12},
abstract = {Gaussian Process (GP) regression is shown to be effective for learning unknown dynamics, enabling efficient and safetyaware control strategies across diverse applications. However, existing GP-based model predictive control (GP-MPC) methods either rely on approximations, thus lacking guarantees, or are overly conservative, which limits their practical utility. To close this gap, we present a sampling-based framework that efficiently propagates the model’s epistemic uncertainty while avoiding conservatism. We establish a novel sample complexity result that enables the construction of a reachable set using a finite number of dynamics functions sampled from the GP posterior. Building on this, we design a sampling-based GP-MPC scheme that is recursively feasible and guarantees closed-loop safety and stability with high probability. Finally, we showcase the effectiveness of our method on two numerical examples, highlighting accurate reachable set over-approximation and safe closed-loop performance.},
keywords = {},
pubstate = {published},
tppubtype = {workingpaper}
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Gaussian Process (GP) regression is shown to be effective for learning unknown dynamics, enabling efficient and safetyaware control strategies across diverse applications. However, existing GP-based model predictive control (GP-MPC) methods either rely on approximations, thus lacking guarantees, or are overly conservative, which limits their practical utility. To close this gap, we present a sampling-based framework that efficiently propagates the model’s epistemic uncertainty while avoiding conservatism. We establish a novel sample complexity result that enables the construction of a reachable set using a finite number of dynamics functions sampled from the GP posterior. Building on this, we design a sampling-based GP-MPC scheme that is recursively feasible and guarantees closed-loop safety and stability with high probability. Finally, we showcase the effectiveness of our method on two numerical examples, highlighting accurate reachable set over-approximation and safe closed-loop performance.
3.
Scampicchio, Anna; Arcari, Elena; Lahr, Amon; Zeilinger, Melanie N.
Gaussian Processes for Dynamics Learning in Model Predictive Control Working paper
2025.
@workingpaper{scampicchio_gaussian_2025,
title = {Gaussian Processes for Dynamics Learning in Model Predictive Control},
author = {Anna Scampicchio and Elena Arcari and Amon Lahr and Melanie N. Zeilinger},
doi = {10.48550/arXiv.2502.02310},
year = {2025},
date = {2025-02-04},
abstract = {Due to its state-of-the-art estimation performance complemented by rigorous and non-conservative uncertainty bounds, Gaussian process regression is a popular tool for enhancing dynamical system models and coping with their inaccuracies. This has enabled a plethora of successful implementations of Gaussian process-based model predictive control in a variety of applications over the last years. However, despite its evident practical effectiveness, there are still many open questions when attempting to analyze the associated optimal control problem theoretically and to exploit the full potential of Gaussian process regression in view of safe learning-based control.},
keywords = {},
pubstate = {published},
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Due to its state-of-the-art estimation performance complemented by rigorous and non-conservative uncertainty bounds, Gaussian process regression is a popular tool for enhancing dynamical system models and coping with their inaccuracies. This has enabled a plethora of successful implementations of Gaussian process-based model predictive control in a variety of applications over the last years. However, despite its evident practical effectiveness, there are still many open questions when attempting to analyze the associated optimal control problem theoretically and to exploit the full potential of Gaussian process regression in view of safe learning-based control.
4.
Prajapat, Manish; Lahr, Amon; Köhler, Johannes; Krause, Andreas; Zeilinger, Melanie N.
Towards Safe and Tractable Gaussian Process-Based MPC: Efficient Sampling within a Sequential Quadratic Programming Framework Proceedings Article
In: 2024 IEEE 63rd Conference on Decision and Control CDC, pp. 7458-7465, IEEE, Milan, Italy, 2024, ISBN: 9798350316339.
@inproceedings{prajapat_towards_2024,
title = {Towards Safe and Tractable Gaussian Process-Based MPC: Efficient Sampling within a Sequential Quadratic Programming Framework},
author = {Manish Prajapat and Amon Lahr and Johannes Köhler and Andreas Krause and Melanie N. Zeilinger},
doi = {10.1109/CDC56724.2024.10886350},
isbn = {9798350316339},
year = {2024},
date = {2024-12-16},
urldate = {2024-09-13},
booktitle = {2024 IEEE 63rd Conference on Decision and Control CDC},
pages = {7458-7465},
publisher = {IEEE},
address = {Milan, Italy},
abstract = {Learning uncertain dynamics models using Gaussian process (GP) regression has been demonstrated to enable high-performance and safety-aware control strategies for challenging real-world applications. Yet, for computational tractability, most approaches for Gaussian process-based model predictive control (GP-MPC) are based on approximations of the reachable set that are either overly conservative or impede the controller’s safety guarantees. To address these challenges, we propose a robust GP-MPC formulation that guarantees constraint satisfaction with high probability. For its tractable implementation, we propose a sampling-based GPMPC approach that iteratively generates consistent dynamics samples from the GP within a sequential quadratic programming framework. We highlight the improved reachable set approximation compared to existing methods, as well as realtime feasible computation times, using two numerical examples.},
keywords = {},
pubstate = {published},
tppubtype = {inproceedings}
}
Learning uncertain dynamics models using Gaussian process (GP) regression has been demonstrated to enable high-performance and safety-aware control strategies for challenging real-world applications. Yet, for computational tractability, most approaches for Gaussian process-based model predictive control (GP-MPC) are based on approximations of the reachable set that are either overly conservative or impede the controller’s safety guarantees. To address these challenges, we propose a robust GP-MPC formulation that guarantees constraint satisfaction with high probability. For its tractable implementation, we propose a sampling-based GPMPC approach that iteratively generates consistent dynamics samples from the GP within a sequential quadratic programming framework. We highlight the improved reachable set approximation compared to existing methods, as well as realtime feasible computation times, using two numerical examples.
5.
Lahr, Amon; Näf, Joshua; Wabersich, Kim P.; Frey, Jonathan; Siehl, Pascal; Carron, Andrea; Diehl, Moritz; Zeilinger, Melanie N.
L4acados: Learning-based Models for Acados, Applied to Gaussian Process-Based Predictive Control Working paper
2024.
@workingpaper{lahr_l4acados_2024,
title = {L4acados: Learning-based Models for Acados, Applied to Gaussian Process-Based Predictive Control},
author = {Amon Lahr and Joshua Näf and Kim P. Wabersich and Jonathan Frey and Pascal Siehl and Andrea Carron and Moritz Diehl and Melanie N. Zeilinger},
doi = {10.48550/arXiv.2411.19258},
year = {2024},
date = {2024-11-28},
urldate = {2024-11-28},
abstract = {Incorporating learning-based models, such as artificial neural networks or Gaussian processes, into model predictive control (MPC) strategies can significantly improve control performance and online adaptation capabilities for real-world applications. Still, enabling state-of-the-art implementations of learning-based models for MPC is complicated by the challenge of interfacing machine learning frameworks with real-time optimal control software. This work aims at filling this gap by incorporating external sensitivities in sequential quadratic programming solvers for nonlinear optimal control. To this end, we provide L4acados, a general framework for incorporating Python-based residual models in the real-time optimal control software acados. By computing external sensitivities via a user-defined Python module, L4acados enables the implementation of MPC controllers with learning-based residual models in acados, while supporting parallelization of sensitivity computations when preparing the quadratic subproblems. We demonstrate significant speed-ups and superior scaling properties of L4acados compared to available software using a neural-network-based control example. Last, we provide an efficient and modular real-time implementation of Gaussian process-based MPC using L4acados, which is applied to two hardware examples: autonomous miniature racing, as well as motion control of a full-scale autonomous vehicle for an ISO lane change maneuver.},
keywords = {},
pubstate = {published},
tppubtype = {workingpaper}
}
Incorporating learning-based models, such as artificial neural networks or Gaussian processes, into model predictive control (MPC) strategies can significantly improve control performance and online adaptation capabilities for real-world applications. Still, enabling state-of-the-art implementations of learning-based models for MPC is complicated by the challenge of interfacing machine learning frameworks with real-time optimal control software. This work aims at filling this gap by incorporating external sensitivities in sequential quadratic programming solvers for nonlinear optimal control. To this end, we provide L4acados, a general framework for incorporating Python-based residual models in the real-time optimal control software acados. By computing external sensitivities via a user-defined Python module, L4acados enables the implementation of MPC controllers with learning-based residual models in acados, while supporting parallelization of sensitivity computations when preparing the quadratic subproblems. We demonstrate significant speed-ups and superior scaling properties of L4acados compared to available software using a neural-network-based control example. Last, we provide an efficient and modular real-time implementation of Gaussian process-based MPC using L4acados, which is applied to two hardware examples: autonomous miniature racing, as well as motion control of a full-scale autonomous vehicle for an ISO lane change maneuver.
6.
Leeman, Antoine P.; Köhler, Johannes; Messerer, Florian; Lahr, Amon; Diehl, Moritz; Zeilinger, Melanie N.
Fast System Level Synthesis: Robust Model Predictive Control Using Riccati Recursions Proceedings Article
In: 8th IFAC Conference on Nonlinear Model Predictive Control NMPC 2024, IFAC-PapersOnLine, 2024.
@inproceedings{leeman_fast_2024,
title = {Fast System Level Synthesis: Robust Model Predictive Control Using Riccati Recursions},
author = {Antoine P. Leeman and Johannes Köhler and Florian Messerer and Amon Lahr and Moritz Diehl and Melanie N. Zeilinger},
url = {https://doi.org/10.48550/arXiv.2401.13762},
doi = {10.1016/j.ifacol.2024.09.027},
year = {2024},
date = {2024-09-01},
urldate = {2024-02-07},
booktitle = {8th IFAC Conference on Nonlinear Model Predictive Control NMPC 2024},
volume = {58},
number = {18},
publisher = {IFAC-PapersOnLine},
abstract = {System Level Synthesis (SLS) enables improved robust MPC formulations by allowing for joint optimization of the nominal trajectory and controller. This paper introduces a tailored algorithm for solving the corresponding disturbance feedback optimization problem. The proposed algorithm builds on a recently proposed joint optimization scheme and iterates between optimizing the controller and the nominal trajectory while converging q-linearly to an optimal solution. We show that the controller optimization can be solved through Riccati recursions leading to a horizon-length, state, and input scalability of O(N2(n3x+n3u)) for each iterate. On a numerical example, the proposed algorithm exhibits computational speedups of order 10 to 10^3 compared to general-purpose commercial solvers.
},
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System Level Synthesis (SLS) enables improved robust MPC formulations by allowing for joint optimization of the nominal trajectory and controller. This paper introduces a tailored algorithm for solving the corresponding disturbance feedback optimization problem. The proposed algorithm builds on a recently proposed joint optimization scheme and iterates between optimizing the controller and the nominal trajectory while converging q-linearly to an optimal solution. We show that the controller optimization can be solved through Riccati recursions leading to a horizon-length, state, and input scalability of O(N2(n3x+n3u)) for each iterate. On a numerical example, the proposed algorithm exhibits computational speedups of order 10 to 10^3 compared to general-purpose commercial solvers.
7.
Lahr, Amon; Tronarp, Filip; Schmidt, Nathanael Bosch Jonathan; Hennig, Philipp; Zeilinger, Melanie N.
Probabilistic ODE Solvers for Integration Error-Aware Numerical Optimal Control Proceedings Article
In: Proceedings of the 6th Annual Learning for Dynamics & Control Conference (L4DC), pp. 1018–1032, PMLR, 2024.
@inproceedings{lahr_probabilistic_2024,
title = {Probabilistic ODE Solvers for Integration Error-Aware Numerical Optimal Control},
author = {Amon Lahr and Filip Tronarp and Nathanael Bosch Jonathan Schmidt and Philipp Hennig and Melanie N. Zeilinger},
url = {https://proceedings.mlr.press/v242/lahr24a.html
https://proceedings.mlr.press/v242/lahr24a/lahr24a.pdf},
year = {2024},
date = {2024-07-15},
urldate = {2024-02-07},
booktitle = {Proceedings of the 6th Annual Learning for Dynamics & Control Conference (L4DC)},
volume = {242},
pages = {1018--1032},
publisher = {PMLR},
series = {Proceedings of Machine Learning Research},
abstract = {Appropriate time discretization is crucial for real-time applications of numerical optimal control, such as nonlinear model predictive control. However, if the discretization error strongly depends on the applied control input, meeting accuracy and sampling time requirements simultaneously can be challenging using classical discretization methods. In particular, neither fixed-grid nor adaptive-grid discretizations may be suitable, when they suffer from large integration error or exceed the prescribed sampling time, respectively. In this work, we take a first step at closing this gap by utilizing probabilistic numerical integrators to approximate the solution of the initial value problem, as well as the computational uncertainty associated with it, inside the optimal control problem (OCP). By taking the viewpoint of probabilistic numerics and propagating the numerical uncertainty in the cost, the OCP is reformulated such that the optimal input reduces the computational uncertainty insofar as it is beneficial for the control objective. The proposed approach is illustrated using a numerical example, and potential benefits and limitations are discussed.},
keywords = {},
pubstate = {published},
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}
Appropriate time discretization is crucial for real-time applications of numerical optimal control, such as nonlinear model predictive control. However, if the discretization error strongly depends on the applied control input, meeting accuracy and sampling time requirements simultaneously can be challenging using classical discretization methods. In particular, neither fixed-grid nor adaptive-grid discretizations may be suitable, when they suffer from large integration error or exceed the prescribed sampling time, respectively. In this work, we take a first step at closing this gap by utilizing probabilistic numerical integrators to approximate the solution of the initial value problem, as well as the computational uncertainty associated with it, inside the optimal control problem (OCP). By taking the viewpoint of probabilistic numerics and propagating the numerical uncertainty in the cost, the OCP is reformulated such that the optimal input reduces the computational uncertainty insofar as it is beneficial for the control objective. The proposed approach is illustrated using a numerical example, and potential benefits and limitations are discussed.
8.
Frey, Jonathan; Gao, Yunfan; Messerer, Florian; Lahr, Amon; Zeilinger, Melanie N.; Diehl, Moritz
Efficient Zero-Order Robust Optimization for Real-Time Model Predictive Control with Acados Proceedings Article
In: 2024 European Control Conference (ECC), IEEE, Stockholm, Sweden, 2024, ISBN: 978-3-9071-4410-7.
@inproceedings{frey_efficient_2023,
title = {Efficient Zero-Order Robust Optimization for Real-Time Model Predictive Control with Acados},
author = {Jonathan Frey and Yunfan Gao and Florian Messerer and Amon Lahr and Melanie N. Zeilinger and Moritz Diehl},
doi = {10.23919/ECC64448.2024.10591148},
isbn = {978-3-9071-4410-7},
year = {2024},
date = {2024-06-03},
urldate = {2023-12-18},
booktitle = {2024 European Control Conference (ECC)},
publisher = {IEEE},
address = {Stockholm, Sweden},
abstract = {Robust and stochastic optimal control problem (OCP) formulations allow a systematic treatment of uncertainty, but are typically associated with a high computational cost. The recently proposed zero-order robust optimization (zoRO) algorithm mitigates the computational cost of uncertainty-aware MPC by propagating the uncertainties separately from the nominal dynamics. This paper details the combination of zoRO with the real-time iteration (RTI) scheme and presents an efficient open-source implementation in acados, utilizing BLASFEO for the linear algebra operations. In addition to the scaling advantages posed by the zoRO algorithm, the efficient implementation drastically reduces the computational overhead, and, combined with an RTI scheme, enables the use of tube-based MPC for a wider range of applications. The flexibility, usability and effectiveness of the proposed implementation is demonstrated on two examples. On the practical example of a differential drive robot, the proposed implementation results in a tenfold reduction of computation time with respect to the previously available zoRO implementation.},
keywords = {},
pubstate = {published},
tppubtype = {inproceedings}
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Robust and stochastic optimal control problem (OCP) formulations allow a systematic treatment of uncertainty, but are typically associated with a high computational cost. The recently proposed zero-order robust optimization (zoRO) algorithm mitigates the computational cost of uncertainty-aware MPC by propagating the uncertainties separately from the nominal dynamics. This paper details the combination of zoRO with the real-time iteration (RTI) scheme and presents an efficient open-source implementation in acados, utilizing BLASFEO for the linear algebra operations. In addition to the scaling advantages posed by the zoRO algorithm, the efficient implementation drastically reduces the computational overhead, and, combined with an RTI scheme, enables the use of tube-based MPC for a wider range of applications. The flexibility, usability and effectiveness of the proposed implementation is demonstrated on two examples. On the practical example of a differential drive robot, the proposed implementation results in a tenfold reduction of computation time with respect to the previously available zoRO implementation.
9.
Lahr, Amon; Zanelli, Andrea; Carron, Andrea; Zeilinger, Melanie N.
Zero-Order Optimization for Gaussian Process-based Model Predictive Control Journal Article
In: European Journal of Control, pp. 100862, 2023, ISSN: 0947-3580.
@article{lahrZeroOrderOptimizationGaussian2023,
title = {Zero-Order Optimization for Gaussian Process-based Model Predictive Control},
author = {Amon Lahr and Andrea Zanelli and Andrea Carron and Melanie N. Zeilinger},
url = {https://www.sciencedirect.com/science/article/pii/S0947358023000912},
doi = {10.1016/j.ejcon.2023.100862},
issn = {0947-3580},
year = {2023},
date = {2023-06-15},
urldate = {2023-07-18},
journal = {European Journal of Control},
pages = {100862},
abstract = {By enabling constraint-aware online model adaptation, model predictive control using Gaussian process (GP) regression has exhibited impressive performance in real-world applications and received considerable attention in the learning-based control community. Yet, solving the resulting optimal control problem in real-time generally remains a major challenge, due to (i) the increased number of augmented states in the optimization problem, as well as (ii) computationally expensive evaluations of the posterior mean and covariance and their respective derivatives. To tackle these challenges, we employ (i) a tailored Jacobian approximation in a sequential quadratic programming (SQP) approach and combine it with (ii) a parallelizable GP inference and automatic differentiation framework. Reducing the numerical complexity with respect to the state dimension nx for each SQP iteration from O(nx6) to O(nx3), and accelerating GP evaluations on a graphical processing unit, the proposed algorithm computes suboptimal, yet feasible, solutions at drastically reduced computation times and exhibits favorable local convergence properties. Numerical experiments verify the scaling properties and investigate the runtime distribution across different parts of the algorithm.
},
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pubstate = {published},
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By enabling constraint-aware online model adaptation, model predictive control using Gaussian process (GP) regression has exhibited impressive performance in real-world applications and received considerable attention in the learning-based control community. Yet, solving the resulting optimal control problem in real-time generally remains a major challenge, due to (i) the increased number of augmented states in the optimization problem, as well as (ii) computationally expensive evaluations of the posterior mean and covariance and their respective derivatives. To tackle these challenges, we employ (i) a tailored Jacobian approximation in a sequential quadratic programming (SQP) approach and combine it with (ii) a parallelizable GP inference and automatic differentiation framework. Reducing the numerical complexity with respect to the state dimension nx for each SQP iteration from O(nx6) to O(nx3), and accelerating GP evaluations on a graphical processing unit, the proposed algorithm computes suboptimal, yet feasible, solutions at drastically reduced computation times and exhibits favorable local convergence properties. Numerical experiments verify the scaling properties and investigate the runtime distribution across different parts of the algorithm.