@workingpaper{lahr_probabilistic_2024,

title = {Probabilistic ODE Solvers for Integration Error-Aware Model Predictive Control},

author = {Amon Lahr and Filip Tronarp and Nathanael Bosch Jonathan Schmidt and Philipp Hennig and Melanie N. Zeilinger},

url = {https://doi.org/10.48550/arXiv.2401.17731},

year  = {2024},

date = {2024-02-07},

urldate = {2024-02-07},

abstract = {Appropriate time discretization is crucial for nonlinear model predictive control. However, in situations where 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.},

note = {Submitted to the 6th Annual Learning for Dynamics & Control Conference (L4DC 2024)},

keywords = {},

pubstate = {published},

tppubtype = {workingpaper}

}

@workingpaper{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},

year  = {2024},

date = {2024-02-07},

urldate = {2024-02-07},

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.

},

note = {Submitted to the 2024 IFAC Conference on Nonlinear Model Predictive Control (NMPC)},

keywords = {},

pubstate = {published},

tppubtype = {workingpaper}

}

@workingpaper{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 = {10.48550/arXiv.2311.04557},

year  = {2023},

date = {2023-12-18},

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 outside of the MPC problem. 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 = {workingpaper}

}