Title data
Riedl, Wolfgang ; Baier, Robert ; Gerdts, Matthias:
Optimizationbased subdivision algorithm for reachable sets.
Mathematisches Institut, Universität Bayreuth; Institut für Mathematik und Rechneranwendung, Universität der Bundeswehr in Neubiberg/München
Bayreuth
,
2020
.  38 p.
DOI: https://doi.org/10.15495/EPub_UBT_00005054
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Project information
Project title: 
Project's official title  Project's id 

European Union's Seventh Framework Programme  338508 

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Abstract in another language
Reachable sets for nonlinear control systems can be computed via the use of solvers for optimal control problems. The paper presents a new improved variant which applies adaptive concepts similar to the framework of known subdivision techniques by Dellnitz/Hohmann. Using set properties of the nearest point projection, the convergence and rigorousness of the algorithm can be proved without the assumption of diffeomorphism on a nonlinear mapping. The adaptive method is demonstrated by two nonlinear academic examples and for a more complex robot model with box constraints for four states, two controls and five boundary conditions. In these examples adaptive and nonadaptive techniques as well as various discretization methods and optimization solvers are compared. The method also offers interesting features, like zooming into details of the reachable set, selfdetermination of the needed bounding box, easy parallelization and the use of different grid geometries. With the calculation of a 3d funnel in one of the examples, it is shown that the algorithm can also be used to approximate higher dimensional reachable sets and the resulting box collection may serve as a starting point for more sophisticated visualizations or algorithms.
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