Computing mode invariant sets

Last week Jan worked on the enclosure interpreter, mainly focusing on additions that support more complex benchmarks. A modified version of the bouncing ball model, which tracks the energy of the ball as well as its position and velocity, has been the guiding example. The most demanding of the required additions is the computation of the support set of mode invariant predicates which comprise nontrivial numeric expressions. It is this set that allows the interpreter to use the mode invariant to reduce the over-approximation of the computed enclosures. Jan's idea was to enclosure-evaluate the expressions in the invariant and then use a simple interval constraint solving technique to compute a conservative approximation of the support. While this approach works well for linear expressions and for nonlinear expressions in one variable, mixed-variable nonlinear expressions lead to excessive over-approximation of the support. Jan suspects that this over-approximation may be one of the reasons why the benefits of adding the energy to the bouncing ball model could not be observed. Jan also spent some time experimenting with an alternative strategy for subdivision of the simulation time. In the coming week Jan will continue to work on the invariant support computation algorithm.