arXiv subjects

Kathrin Flaßkamp

Publications and source records attributed to Kathrin Flaßkamp.

23 records · Page 2Linked to original sources

arXiv2021

Manifold Turnpikes, Trims and Symmetries

Classical turnpikes correspond to optimal steady states which are attractors of optimal control problems. In this paper, motivated by mechanical systems with symmetries, we generalize this concept to manifold turnpikes. Specifically, the necessary optimality conditions on a symmetry-induced manifold coincide with those of a reduced-order problem under certain conditions. We also propose sufficient conditions for the existence of manifold turnpikes based on a tailored notion of dissipativity with respect to manifolds. We show how the classical Legendre transformation between Euler-Lagrange and Hamilton formalisms can be extended to the adjoint variables. Finally, we draw upon the Kepler problem to illustrate our findings.

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arXiv2020

A Dissipativity Characterization of Velocity Turnpikes in Optimal Control Problems for Mechanical Systems

Turnpikes have recently gained significant research interest in optimal control, since they allow for pivotal insights into the structure of solutions to optimal control problems. So far, mainly steady state solutions which serve as optimal operation points, are studied. This is in contrast to time-varying turnpikes, which are in the focus of this paper. More concretely, we analyze symmetry-induced velocity turnpikes, i.e. controlled relative equilibria, called trim primitives, which are optimal operation points regarding the given cost criterion. We characterize velocity turnpikes by means of dissipativity inequalities. Moreover, we study the equivalence between optimal control problems and steady-state problems via the corresponding necessary optimality conditions. An academic example is given for illustration.

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arXiv2019

Towards Velocity Turnpikes in Optimal Control of Mechanical Systems

The paper proposes first steps towards the formalization and characterization of time-varying turnpikes in optimal control of mechanical systems. We propose the concepts of velocity steady states, which can be considered as partial steady states, and hyperbolic velocity turnpike properties for analysis and control. We show for a specific example that, for all finite horizons, both the (essential part of the) optimal solution and the orbit of the time-varying turnpike correspond to (optimal) trim solutions. Hereby, the present paper appears to be the first to combine the concepts of trim primitives and time-varying turnpike properties.

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arXiv2019

Symmetry and Motion Primitives in Model Predictive Control

Symmetries, e.g. rotational and translational invariances for the class of mechanical systems, allow to characterize solution trajectories of nonlinear dynamical systems. Thus, the restriction to symmetry-induced dynamics, e.g. by using the concept of motion primitives, may be considered as a quantization of the system. Symmetry exploitation is well-established in both motion planning and control. However, the linkage between the respective techniques to optimal control is not yet fully explored. In this manuscript, we want to lay the foundation for the usage of symmetries in Model Predictive Control (MPC). To this end, we investigate a mobile robot example in detail where our contribution is twofold: Firstly, we establish asymptotic stability of a desired set point w.r.t. the MPC closed loop, which is also demonstrated numerically by using motion primitives applied to the parallel parking scenario. Secondly, if the optimization criterion is not consistent with the symmetry action, we provide guidelines to rigorously derive stability guarantees based on symmetry exploitation.

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arXiv2018

Optimization Strategies for Real-Time Control of an Autonomous Melting Probe

We present an optimization-based approach for trajectory planning and control of a maneuverable melting probe with a high number of binary control variables. The dynamics of the system are modeled by a set of ordinary differential equations with a priori knowledge of system parameters of the melting process. The original planning problem is handled as an optimal control problem. Then, optimal control is used for reference trajectory planning as well as in an MPC-like algorithm. Finally, to determine binary control variables, a MINLP fitting approach is presented. The proposed strategy has recently been tested during experiments on the Langenferner glacier. The data obtained is used for model improvement by means of automated parameter identification.

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