@workingpaper{messerer2024fourthorder,

title = {Fourth-order suboptimality of nominal model predictive control in the presence of uncertainty},

author = {Florian Messerer and Katrin Baumgärtner and Sergio Lucia and Moritz Diehl},

url = {https://arxiv.org/abs/2403.04559},

year  = {2024},

date = {2024-03-08},

abstract = {We investigate the suboptimality resulting from the application of nominal model predictive control (MPC) to a nonlinear discrete time stochastic system. The suboptimality is defined with respect to the corresponding stochastic optimal control problem (OCP) that minimizes the expected cost of the closed loop system. In this context, nominal MPC corresponds to a form of certainty-equivalent control (CEC). We prove that, in a smooth and unconstrained setting, the suboptimality growth is of fourth order with respect to the level of uncertainty, a parameter which we can think of as a standard deviation. This implies that the suboptimality does not grow very quickly as the level of uncertainty is increased, providing further insight into the practical success of nominal MPC. Similarly, the difference between the optimal and suboptimal control inputs is of second order. We illustrate the result on a simple numerical example, which we also use to show how the proven relationship may cease to hold in the presence of state constraints.},

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}

}

@workingpaper{messerer2023approximate,

title = {Approximate propagation of normal distributions for stochastic optimal control of nonsmooth systems},

author = {Florian Messerer and Katrin Baumgärtner and Armin Nurkanovic and Moritz Diehl},

url = {https://arxiv.org/abs/2308.03431},

doi = {https://doi.org/10.48550/arXiv.2308.03431},

year  = {2023},

date = {2023-08-14},

abstract = {We present a method for the approximate propagation of mean and covariance of a probability distribution through ordinary differential equations (ODE) with discontinous right-hand side. For piecewise affine systems, a normalization of the propagated probability distribution at every time step allows us to analytically compute the expectation integrals of the mean and covariance dynamics while explicitly taking into account the discontinuity. This leads to a natural smoothing of the discontinuity such that for relevant levels of uncertainty the resulting ODE can be integrated directly with standard schemes and it is neither necessary to prespecify the switching sequence nor to use a switch detection method. We then show how this result can be employed in the more general case of piecewise smooth functions based on a structure preserving linearization scheme. The resulting dynamics can be straightforwardly used within standard formulations of stochastic optimal control problems with chance constraints.},

keywords = {},

pubstate = {published},

tppubtype = {workingpaper}

}