@inproceedings{Baumgaertner2023,

title = {Local Convergence Analysis of Damping for Zero-Order Optimization-Based Iterative Learning Control},

author = {Katrin Baumgärtner and Moritz Diehl},

url = {https://ieeexplore.ieee.org/document/10178225},

doi = {https://doi.org/10.23919/ECC57647.2023.10178225},

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

year  = {2023},

date = {2023-07-17},

urldate = {2023-07-17},

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

pages = {1-6},

publisher = {IEEE},

address = {Bucharest, Romania},

abstract = {Within the Iterative Learning Control (ILC) framework, damping is often introduced as a heuristic to facilitate convergence of the ILC iterates. We analyze how two simple damping approaches affect the local convergence behaviour of a zero-order optimization-based ILC method introduced in [1] and prove that the condition for local convergence, which is given in terms of the eigenvalues of an iteration matrix, can be relaxed if damping is introduced. Leveraging a simple example, we illustrate the effects of damping, which might be (1) convergence of an initially diverging iteration or (2) acceleration or deceleration of a converging iteration.},

keywords = {},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{Baumgaertner2023a,

title = {A Unified Local Convergence Analysis of Differential Dynamic Programming, Direct Single Shooting, and Direct Multiple Shooting},

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

url = {https://ieeexplore.ieee.org/document/10178367},

doi = {https://doi.org/10.23919/ECC57647.2023.10178367},

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 revisit three classical numerical methods for solving unconstrained optimal control problems - differential dynamic programming, direct single shooting, and direct multiple shooting - and examine their local convergence behaviour. In particular, we show that all three methods converge with the same linear rate if a Gauss-Newton (GN) - or Generalized Gauss-Newton (GGN) - Hessian approximation is used, which is the case in widely used implementations such as iLQR.},

keywords = {},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{Baumgaertner2022a,

title = {Fast Nonlinear Model Predictive Control using Barrier Formulations and Squashing with a Generalized Gauss-Newton Hessian},

author = {Katrin Baumgärtner and Yizhen Wang and Andrea Zanelli and Moritz Diehl},

url = {https://ieeexplore.ieee.org/document/9992869},

doi = {https://doi.org/10.1109/CDC51059.2022.9992869},

isbn = {978-1-6654-6761-2},

year  = {2023},

date = {2023-01-10},

urldate = {2023-01-10},

booktitle = {2022 IEEE 61st Conference on Decision and Control (CDC)},

pages = {558-563},

publisher = {IEEE},

abstract = {We propose an approximate algorithm for Nonlinear Model Predictive Control (NMPC) which is based on a reformulation of the inequality constrained optimal control problem using barrier terms and squashing functions. Within an SQP framework, the particular structure of the reformulated problem can be leveraged by using a Generalized Gauss-Newton Hessian approximation. Moreover, the quadratic subproblems can be efficiently solved using a single backward and forward sweep of the Riccati recursion. We show local linear convergence of the proposed algorithm, as well as local quadratic convergence in the case of linear system dynamics. The computational speed-up, which can be achieved with the proposed method, is illustrated in a simulation study.},

keywords = {},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{Baumgärtner2022MHE,

title = {Moving Horizon Estimation with Adaptive Regularization for Ill-Posed State and Parameter Estimation Problems},

author = {Katrin Baumgärtner and Rudolf Reiter and Moritz Diehl},

doi = {10.1109/CDC51059.2022.9993416},

isbn = {978-1-6654-6761-2},

year  = {2023},

date = {2023-01-10},

urldate = {2023-01-10},

booktitle = {2022 IEEE 61st Conference on Decision and Control (CDC)},

pages = {2165-2171},

publisher = {IEEE},

address = {Cancun, Mexico},

abstract = {We investigate the usage of Moving Horizon Estimation (MHE) for state and parameter estimation for partially non-detectable systems with measurements corrupted by outliers. We propose an arrival cost update formula based on the Generalized Gauss-Newton method and illustrate how it can be generalized to nonconvex loss functions that can be effectively used for outlier rejection. Moreover, we propose an adaptive regularization scheme for the arrival cost which introduces forgetting as well as additional pseudo-measurements to the arrival cost update. We illustrate the performance of the proposed algorithms on a longitudinal vehicle state and parameter estimation problem.},

keywords = {},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{cecchin2023locally,

title = {Locally Weighted Regression with Approximate Derivatives for Data-based optimization},

author = { Leonardo Cecchin and Katrin Baumgärtner and Stefan Gering and Moritz Diehl},

year  = {2023},

date = {2023-01-01},

urldate = {2023-01-01},

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

pages = {1–6},

organization = {IEEE},

abstract = {Interpolation and approximation of data provided in terms of a Look-Up Table (LUT) is a common and well-known task, and is especially relevant for industrial applications. When using the function for point-wise evaluation, the method choice only affects the accuracy of the function value itself. However, when the LUT is used as part of an optimization problem formulation, a bad method choice can prevent convergence or alter significantly the outcome of the solver. Moreover, computational efficiency becomes critical due to the much higher number of evaluations required. This work focuses on a variation of Locally Weighted Regression, with approximate derivatives computation. The result is a method that allows one to obtain the function value together with the first n derivatives, at a reduced computational cost. Theoretical properties of the approach are analyzed, and the results of a minimization problem using the proposed method are compared with more traditional ones. The new approach shows promising performance and results, both for computational efficiency and effectiveness when used in optimization.},

keywords = {},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{Baumgaertner2022,

title = {The Extended Gauss-Newton Method for Nonconvex Loss Functions and its Application to Time-Optimal Model Predictive Control},

author = {Katrin Baumgärtner and Moritz Diehl},

url = {https://ieeexplore.ieee.org/document/9867372},

doi = {https://doi.org/10.23919/ACC53348.2022.9867372},

isbn = {978-1-6654-5196-3},

year  = {2022},

date = {2022-09-05},

urldate = {2022-09-05},

booktitle = {2022 American Control Conference (ACC)},

pages = {4973-4978},

publisher = {IEEE},

abstract = {We introduce the eXtended Gauss-Newton (XGN) method, which extends the Generalized Gauss-Newton (GGN) method to a class of nonconvex loss functions with a well-behaved global minimum. We show linear local convergence of the XGN method to a stationary point, as well as global convergence in case of a linear residual function and linear constraints. As one possible application, we illustrate how the considered class of nonconvex loss functions can be used to approximate time-optimal behaviour within a Model Predictive Control (MPC) framework.},

keywords = {},

pubstate = {published},

tppubtype = {inproceedings}

}