A cyber-physical system (CPS) has cyber (or computational) components and physical components that communicate. The Kopernic team deals with the problem of studying time properties (execution time of a program or the schedulability of communicating programs, etc.) of the cyber components of a CPS. The cyber components may have functions with different criticalities with respect to time and a solution should come with associated proofs of its appropriateness for each criticality. A solution is appropriate for a criticality level if all functions fulfill the expectations of that criticality level.

Based on their mathematical foundations, the solutions are: either non-probabilistic when all time properties are estimated and/or bounded by numerical values or probabilistic when at least one time property is estimated and/or bounded by probability distributions.

The Kopernic team proposes a system-oriented solution to the problem of studying time properties of the cyber components of a CPS. The solution is expected to be obtained by composing probabilistic and non-probabilistic approaches for these systems.

Research directions

  • Proposing a classification of variability factors of execution times for a program with respect to the processor features.
  • Defining a compositional rule of statistical models based on Bayesian approaches for bounds on the execution times of programs.
  • Building scheduling algorithms taking into account the interaction between different variability factors.
  • Proving schedulability analyses for the proposed scheduling algorithms.
  • Deciding the schedulability of programs communicating through predictable and non predictable networks.


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