@article{MESSERER2024101499,

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://www.sciencedirect.com/science/article/pii/S1751570X24000360},

doi = {https://doi.org/10.1016/j.nahs.2024.101499},

issn = {1751-570X},

year  = {2024},

date = {2024-08-01},

urldate = {2023-08-14},

journal = {Nonlinear Analysis: Hybrid Systems},

volume = {53},

pages = {101499},

abstract = {We present a method for the approximate propagation of mean and covariance of a probability distribution through ordinary differential equations (ODE) with discontinuous 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 = {article}

}

@article{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},

doi = {10.1109/LCSYS.2024.3396611},

year  = {2024},

date = {2024-03-08},

urldate = {2024-03-08},

journal = {IEEE Control Systems Letters},

volume = {8},

pages = {508-513},

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 = {article}

}

@article{GHEZZI2023100841,

title = {An Implicit and Explicit Dual Model Predictive Control Formulation for a Steel Recycling Process},

author = {Andrea Ghezzi and Florian Messerer and Jacopo Balocco and Vincenzo Manzoni and Moritz Diehl},

url = {https://www.sciencedirect.com/science/article/pii/S0947358023000705},

doi = {https://doi.org/10.1016/j.ejcon.2023.100841},

issn = {0947-3580},

year  = {2023},

date = {2023-06-14},

urldate = {2023-06-14},

journal = {European Journal of Control},

pages = {100841},

abstract = {We present a formulation for both implicit and explicit dual model predictive control for a steel recycling process. The process consists in the production of new steel by choosing a combination of several different steel scraps with unknown pollutant content. The pollutant content can only be measured after a scrap combination is molten, allowing for inference on the pollutants in the different scrap heaps. The production cost should be minimized while ensuring high quality of the product through constraining the maximum amount of pollutant. The dual control formulation allows to achieve the optimal explore-exploit trade-off between uncertainty reduction and cost minimization for the examined problem. Specifically, the dual effect is obtained by considering the dependence of the future pollutant uncertainties on the scrap selection in the predictions. The implicit formulation promotes uncertainty reduction indirectly via the impact of active constraints on the objective, while the explicit formulation adds a heuristic cost on uncertainty to encourage active exploration. We compare the formulations by numerical simulations of a simplified but representative industrial steel recycling process. The results demonstrate the superiority of the two dual formulations with respect to a robustified but non-dual formulation.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{Messerer2023,

title = {A Dual-Control Effect Preserving Formulation for Nonlinear Output-Feedback Stochastic Model Predictive Control With Constraints},

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

url = {https://ieeexplore.ieee.org/document/9993720},

doi = {10.1109/LCSYS.2022.3230552},

year  = {2023},

date = {2023-01-01},

urldate = {2023-01-01},

journal = {IEEE Control Systems Letters},

volume = {7},

number = {1171--1176},

keywords = {},

pubstate = {published},

tppubtype = {article}

}