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Some future challenges in the validation of control systems

Starting with our work on the characterization of the imprecision error in programs using floating-point-numbers, by abstract interpretation, this paper shows that there are numerous perspectives, if one wants to fully qualify the numerical quality of control systems, as found in the aeronautical and automotive industry, for instance. Some very common functions (e.g. integrators) are hard to statically analyse, because their numerical correctness depend on a fine- grained specification of the classes of input signals they handle. This gets even more complex in the case of e.g. PID controllers, which interact in closed loop with an external environment, since their input signals are in part the consequence of their own computation, similarly for the imprecision errors. We show examples of non-trivial bad and good numerical behaviours, discuss the results of our methods, and present our current research directions, that should hopefully help characterize the imprecision error of such control systems.