Level Set Method Based on Interval Analysis
Elwin de Weerdt, Eddy van Oort, Erik-Jan Van Kampen, Ping Chu, Jan Albert Mulder · 2011
Level set methods are used to determine the reachable set for a given time domain. In the aerospace industry level set methods are used to determine for example flight envelopes. A new level set method is presented which uses interval analysis to give guaranteed bounds on the solution. Unlike the current grid-based methods the new method does not use a grid and has a lower computation complexity. The guaranteed bounds are a product of using interval analysis. Both an inner and outer bound can be derived. The time step and accuracy are easily controlled by the user and can be automatically adapted during processing. Initial tests show that the new method provides accurate solutions and does so using lower computational loads. The new method is tested on a one-dimensional and a two-dimensional test bed, showing that correct outer bounds of the reachable sets can be computed.