arXiv subjects

Lukas Ecker

Publications and source records attributed to Lukas Ecker.

4 recordsLinked to original sources

arXiv2026

Analytic Optimal Control for a Class of Driftless x-Flat Systems

This paper studies optimal trajectory-tracking for driftless, x-flat nonlinear systems with three states and two inputs. The tracking problem is formulated in Bolza form with a quadratic cost of the tracking error and its derivative. Applying Pontryagin's maximum principle yields a mixed regular-singular optimal control problem. By exploiting geometric properties and a specific relation between the weighting matrices, a closed-form expression for the costate and an explicit feedback law for both inputs is derived. Thereby, the numerical solution of a two-point boundary-value problem is avoided. The singular input leads to a bang-singular-bang optimal control structure, while on the singular arc, the tracking error dynamics reduces to a linear dynamics of order two. The approach is illustrated for the kinematic model of a steerable axle, demonstrating accurate trajectory-tracking.

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arXiv2023

Data-driven control and transfer learning using neural canonical control structures*

An indirect data-driven control and transfer learning approach based on a data-driven feedback linearization with neural canonical control structures is proposed. An artificial neural network auto-encoder structure trained on recorded sensor data is used to approximate state and input transformations for the identification of the sampled-data system in Brunovsky canonical form. The identified transformations, together with a designed trajectory controller, can be transferred to a system with varied parameters, where the neural network weights are adapted using newly collected recordings. The proposed approach is demonstrated using an academic and an industrially motivated example.

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arXiv2022

An approximation of the Bayesian state observer with Markov chain Monte Carlo propagation stage

The state estimation problem for nonlinear systems with stochastic uncertainties can be formulated in the Bayesian framework, where the objective is to replace the state completely by its probability density function. Without the restriction to selected system classes and disturbance properties, the Bayesian estimator is particularly interesting for highly nonlinear systems with non-Gaussian noise. The main limitations of Bayesian filters are the significant computational costs and the implementation problems for higher dimensional systems. The present paper introduces a piecewise linear approximation of the Bayesian state observer with Markov chain Monte Carlo propagation stage and kernel density estimation. These methods are suitable for the prediction of multivariate probability density functions. The piecewise linear approximation and the proposed algorithms can increase the estimation performance at reasonable computational cost. The estimation performance is demonstrated in a benchmark comparing the Bayesian state observer with an extended Kalman filter and a particle filter.

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arXiv2021

Energy-based Control and Observer Design for higher-order infinite-dimensional Port-Hamiltonian Systems

In this paper, we present a control-design method based on the energy-Casimir method for infinite-dimensional, boundary-actuated port-Hamiltonian systems with two-dimensional spatial domain and second-order Hamiltonian. The resulting control law depends on distributed system states that cannot be measured, and therefore, we additionally design an infinite-dimensional observer by exploiting the port-Hamiltonian system representation. A Kirchhoff-Love plate serves as an example in order to demonstrate the proposed approaches.

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