Generation of worst-case input signals based on the guaranteed sampling of linear interval predictors with non-held uncertain inputs

This paper deals with the design of experiments for the validation of a class of interval dynamic models. Set-membership algorithms based on interval analysis often allow the computation of guaranteed bounds (e.g. reach tubes, bounds for some estimates) enclosing all the possible scenarios according to some model where uncertainties are specified in a bounded error context. The guarantee of inclusion is very useful to ensure a complete coverage of all the specified scenarios in verification problems (e.g. verification of safety properties). However, such a guarantee and, consequently, the verified properties hold in practice only up to the validity of the considered uncertain model. In addition, the practical validation of dynamic interval models involving bounded uncertain inputs is quite difficult since finding a relevant input excitation leading to some worst-case scenario (e.g. an output reaching its maximum or minimum admissible value at a given time instant) is not a trivial task in general. The current paper proposes a constructive method to generate such worst-case input signals based on the guaranteed sampling of linear interval predictors with non-held uncertain inputs. The results are then illustrated through the example of designing worst-case road profiles to validate the interval model of a quarter vehicle suspension.