@inproceedings{Ghezzi2023b,

title = {Imitation Learning from Nonlinear MPC via the Exact Q-Loss and its Gauss-Newton Approximation},

author = {Andrea Ghezzi and Jasper Hoffman and Jonathan Frey and Joschka Boedecker and Moritz Diehl},

doi = {https://doi.org/10.48550/arXiv.2304.01782},

year  = {2023},

date = {2023-08-17},

booktitle = {2023 Conference on Decision and Control (CDC)},

abstract = {This work presents a novel loss function for learning nonlinear Model Predictive Control policies via Imitation Learning. Standard approaches to Imitation Learning neglect information about the expert and generally adopt a loss function based on the distance between expert and learned controls. In this work, we present a loss based on the Q-function directly embedding the performance objectives and constraint satisfaction of the associated Optimal Control Problem (OCP). However, training a Neural Network with the Q-loss requires solving the associated OCP for each new sample. To alleviate the computational burden, we derive a second Q-loss based on the Gauss-Newton approximation of the OCP resulting in a faster training time. We validate our losses against Behavioral Cloning, the standard approach to Imitation Learning, on the control of a nonlinear system with constraints. The final results show that the Q-function-based losses significantly reduce the amount of constraint violations while achieving comparable or better closed-loop costs.},

keywords = {},

pubstate = {forthcoming},

tppubtype = {inproceedings}

}

@inproceedings{Ghezzi2023a,

title = { A Voronoi-Based Mixed-Integer Gauss-Newton Algorithm for MINLP Arising in Optimal Control},

author = {Andrea Ghezzi and Léo Simpson and Adrian Bürger and Clemens Zeile and Sebastian Sager and Moritz Diehl},

doi = {https://doi.org/10.23919/ECC57647.2023.10178130},

isbn = {978-3-907144-08-4},

year  = {2023},

date = {2023-07-17},

urldate = {2023-07-17},

booktitle = {2023 European Control Conference (ECC)},

pages = {1-7},

publisher = {IEEE},

address = {Bucharest, Romania},

abstract = {We present a new algorithm for addressing nonconvex Mixed-Integer Nonlinear Programs (MINLPs) where the cost function is of nonlinear least squares form. We exploit this structure by leveraging a Gauss-Newton quadratic approximation of the original MINLP, leading to the formulation of a Mixed-Integer Quadratic Program (MIQP), which can be solved efficiently. The integer solution of the MIQP is used to fix the integer variables of the original MINLP, resulting in a standard Nonlinear Program. We introduce an iterative procedure to repeat the optimization of the two programs in order to improve the solution. To guide the iterations towards unexplored regions, we devise a strategy to partition the integer solution space based on Voronoi diagrams. Finally, we first illustrate the algorithm on a simple example of MINLP and then test it on an example of real-world complexity concerning the optimal control of an energy system. Here, the new algorithm outperforms state-of-the-art methods, finding a solution with a lower objective value, at the cost of requiring an increased runtime compared to other approximate methods.},

keywords = {},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{Simpson2023EMJE,

title = {An Efficient Method for the Joint Estimation of System Parameters and Noise Covariances for Linear Time-Variant Systems },

author = {Léo Simpson and Andrea Ghezzi and Jonas Asprion and Moritz Diehl},

url = {https://arxiv.org/abs/2211.12302},

year  = {2023},

date = {2023-03-20},

booktitle = {2023 Conference of Decision and Control (CDC) },

abstract = {We present an optimization-based method for the joint estimation of system parameters and noise covariances of linear time-variant systems. Given measured data, this method maximizes the likelihood of the parameters. We solve the optimization problem of interest via a novel structure-exploiting solver. We present the advantages of the proposed approach over commonly used methods in the framework of Moving Horizon Estimation. Finally, we show the performance of the method through numerical simulations on a realistic example of a thermal system. In this example, the method can successfully estimate the model parameters in a short computational time.},

keywords = {},

pubstate = {forthcoming},

tppubtype = {inproceedings}

}