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Abstract

Embedded controllers for cyber-physical systems are often parameterized by
look-up maps representing discretizations of continuous functions on metric
spaces. For example, a non-linear control action may be represented as a table
of pre-computed values, and the output action of the controller for a given
input is computed by using interpolation. For industrial-scale control systems,
several man-hours of effort is spent in tuning the values within the look-up
maps, and sub-optimal performance is often associated with inappropriate values
in look-up maps. Suppose that during testing, the controller code is found to
have sub-optimal performance. The parameter fault localization problem asks
which parameter values in the code are potential causes of the sub-optimal
behavior. We present a statistical parameter fault localization approach based
on binary similarity coefficients and set spectra methods. Our approach extends
previous work on software fault localization to a quantitative setting where
the parameters encode continuous functions over a metric space and the program
is reactive.
We have implemented our approach in a simulation workflow for automotive
control systems in Simulink. Given controller code with parameters (including
look-up maps), our framework bootstraps the simulation workflow to return a
ranked list of map entries which are deemed to have most impact on the
performance. On a suite of industrial case studies with seeded errors, our tool
was able to precisely identify the location of the errors.