Safety Verification of Real-Time Control Systems with Flexible Timing

Description

The topic of this work is the analysis of control loops under the influence of input/output timing deviations. Such deviations from the ideal periodic timing can lead to increased control error or even to instability. To address this issue, methods are presented to determine a safe tolerance band for the timing deviation. Two alternatives are addressed: stability analysis at design time and timing adaptation at run time. In both cases, the methods support multiple inputs and outputs with individual timing uncertainties.
For the analysis at design time, the work presents methods to determine stability and maximal control error at design time for a given input/output time window. The linear case is analyzed using linear impulsive systems. Progress towards solving the nonlinear case is made by reachability analysis of hybrid automata in connection with the Continuization method.
For a flexible adaptation at run time, the framework of convergence rate abstractions is developed. By this, the decision about the permissible input/output timing can be made according to the current situation and with little computational overhead. Hence, larger temporal deviations can be permitted for a short time as long as the timing remains good enough in the long-term average to preserve stability.