@article{53101,
  abstract     = {{In this work, we consider optimal control problems for mechanical systems with fixed initial and free final state and a quadratic Lagrange term. Specifically, the dynamics is described by a second order ODE containing an affine control term. Classically, Pontryagin's maximum principle gives necessary optimality conditions for the optimal control problem. For smooth problems, alternatively, a variational approach based on an augmented objective can be followed. Here, we propose a new Lagrangian approach leading to equivalent necessary optimality conditions in the form of Euler-Lagrange equations. Thus, the differential geometric structure (similar to classical Lagrangian dynamics) can be exploited in the framework of optimal control problems. In particular, the formulation enables the symplectic discretisation of the optimal control problem via variational integrators in a straightforward way.}},
  author       = {{Leyendecker, Sigrid and Maslovskaya, Sofya and Ober-Blöbaum, Sina and Almagro, Rodrigo T. Sato Martín de and Szemenyei, Flóra Orsolya}},
  issn         = {{2158-2491}},
  journal      = {{Journal of Computational Dynamics}},
  keywords     = {{Optimal control problem, Lagrangian system, Hamiltonian system, Variations, Pontryagin's maximum principle.}},
  pages        = {{0--0}},
  publisher    = {{American Institute of Mathematical Sciences (AIMS)}},
  title        = {{{A new Lagrangian approach to control affine systems with a quadratic Lagrange term}}},
  doi          = {{10.3934/jcd.2024017}},
  year         = {{2024}},
}

@inproceedings{22894,
  abstract     = {{The first order optimality conditions of optimal control problems (OCPs) can
be regarded as boundary value problems for Hamiltonian systems. Variational or
symplectic discretisation methods are classically known for their excellent
long term behaviour. As boundary value problems are posed on intervals of
fixed, moderate length, it is not immediately clear whether methods can profit
from structure preservation in this context. When parameters are present,
solutions can undergo bifurcations, for instance, two solutions can merge and
annihilate one another as parameters are varied. We will show that generic
bifurcations of an OCP are preserved under discretisation when the OCP is
either directly discretised to a discrete OCP (direct method) or translated
into a Hamiltonian boundary value problem using first order necessary
conditions of optimality which is then solved using a symplectic integrator
(indirect method). Moreover, certain bifurcations break when a non-symplectic
scheme is used. The general phenomenon is illustrated on the example of a cut
locus of an ellipsoid.}},
  author       = {{Offen, Christian and Ober-Blöbaum, Sina}},
  issn         = {{2405-8963}},
  keywords     = {{optimal control, catastrophe theory, bifurcations, variational methods, symplectic integrators}},
  location     = {{Berlin, Germany}},
  pages        = {{334--339}},
  title        = {{{Bifurcation preserving discretisations of optimal control problems}}},
  doi          = {{https://doi.org/10.1016/j.ifacol.2021.11.099}},
  volume       = {{54(19)}},
  year         = {{2021}},
}

@phdthesis{9994,
  abstract     = {{Reliability-adaptive systems allow an adaptation of system behavior based on current system reliability. They can extend their lifetime at the cost of lowered performance or vice versa. This can be used to adapt failure behavior according to a maintenance plan, thus increasing availability while using up system capability fully. To facilitate setup, a control algorithm independent of a degradation model is desired. A closed loop control technique for reliability based on a health index, a measure for system degradation, is introduced. It uses self-optimization as means to implement behavior adaptation. This is based on selecting the priorities of objectives that the system pursues. Possible working points are computed beforehand using model-based multiobjective optimization techniques. The controller selects the priorities of objectives and this way balances reliability and performance. As exemplary application, an automatically actuated single plate dry clutch is introduced. The entire reliability control is setup and lifetime experiments are conducted. Results show that the variance of time to failure is reduced greatly, making the failure behavior more predictable. At the same time, the desired usable lifetime can be extended at the cost of system performance to allow for changed maintenance intervals. Together, these possibilities allow for greater system usage and better planning of maintenance.}},
  author       = {{Meyer, Tobias}},
  keywords     = {{dependability, reliability, behavior adaptation, self-optimization, multiobjective optimization, optimal control, automotive drivetrain, clutch system, reliability-adaptive system}},
  publisher    = {{Shaker}},
  title        = {{{Optimization-based reliability control of mechatronic systems}}},
  year         = {{2018}},
}

@inproceedings{9763,
  abstract     = {{Recent advances in information processing enable new kinds of technical systems, called self-optimizing systems. These systems are able to adapt their objectives and their behavior according to the current situation and influences autonomously. This behavior adaptation is non-deterministic and hence self-optimization is a risk to the system, e.g. if the result of the self-optimization process does not match the suddenly changed situation. In contrary, self-optimization could be used to increase the dependability by pursuing objectives like reliability and availability. In our preceding publications we introduced the so called multi-level dependability concept to cope with this new kind of systems (cf. [6]). This concept comprises the monitoring of the system behavior, the classification of the current situation, and the selection of the appropriate measure, if reliability limits are exceeded. In this paper we present for the first time experimental results. The dependability concept is implemented in the self-optimizing active guidance system of a railway vehicle. The test drives illustrate clearly that the proposed concept is able to cope with, e.g., sensor failures, and is able to increase the reliability and availability of the active guidance module.}},
  author       = {{Sondermann-Wölke, Christoph and Geisler, Jens and Sextro, Walter}},
  booktitle    = {{Reliability and Maintainability Symposium (RAMS), 2010 Proceedings - Annual}},
  issn         = {{0149-144X}},
  keywords     = {{availability, dependability concept, multilevel dependability concept, railway vehicle, reliability, self optimizing active guidance system, self optimizing railway guidance system, situation classification, system behavior monitoring, optimal control, railways, reliability theory, self-adjusting systems}},
  pages        = {{1 --6}},
  title        = {{{Increasing the reliability of a self-optimizing railway guidance system}}},
  doi          = {{10.1109/RAMS.2010.5448080}},
  year         = {{2010}},
}