@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{Simpson2023DCSODE,

title = {Direct Collocation for Numerical Optimal Control of Second-Order ODE},

author = {Léo Simpson and Armin Nurkanovic and Moritz Diehl},

url = {https://ieeexplore.ieee.org/document/10178181},

doi = {https://doi.org/10.23919/ECC57647.2023.10178181},

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 = {Mechanical systems are usually modeled by second-order Ordinary Differential Equations (ODE) which take the form q¨=f(t, q, q˙). While simulation methods tailored to these equations have been studied, using them in direct optimal control methods is rare. Indeed, the standard approach is to perform a state augmentation, adding the velocities to the state. The main drawback of this approach is that the number of decision variables is doubled, which could harm the performance of the resulting optimization problem. In this paper, we present an approach tailored to second-order ODE. We compare it with the standard one, both on theoretical aspects and in a numerical example. Notably, we show that the tailored formulation is likely to improve the performance of a direct collocation method, for solving optimal control problems with second-order ODE of the more restrictive form q¨=f(t, q).},

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}

}