Two papers and a library related to Acumen's enclosure semantics

During the past week Adam has been comparing the enclosure semantics of Acumen to three sets of algorithms that address the problem of reliability in simulations of hybrid systems. The first one, described in An asynchronous integration and event detection algorithm for simulating multi-agent hybrid systems by Esposito et. al. is an algorithm for simulating hierarchical, multi-rate, hybrid systems in which event detection is guaranteed and which makes it possible to simulate using a lower average integration rate. The second one, described in Robustness of Model-based Simulations by Fainekos et. al. is a method for statically analysing a concrete Simulink simulation in order to detect whether uncertainties in the inputs or parameters of the model, or computational errors, could have produced a result that differs from that of the given simulation. The analysis compares the sequence of Simulink blocks traversed by the simulation and warns the user if a different sequence is possible given the uncertainties present in the model, or due to floating point computation errors. The third set of algorithms is a MATLAB toolbox for validated numerical computation called INTLAB. It includes several data types and algorithms which are useful when building validated ODE IVP solvers like that of Acumen's enclosure semantics, including interval- and interval polynomial arithmetic, validated standard function approximations, integration of such functions as well as automatic differentiation. During the coming week Adam will focus on writing a survey of tools for virtual experimentation.