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Area of Science:

  • Control Systems Engineering
  • Computational Mathematics

Background:

  • Differential inclusions model systems with uncertainty, crucial in control theory.
  • Previous solvers, like the 2002 version, had limitations in computational speed and analysis capabilities.

Purpose of the Study:

  • To present a new, parallel version of a differential inclusion solver.
  • To enhance the calculation of reachable sets for differential inclusions.
  • To introduce the concept of functional sensitivity analysis.

Main Methods:

  • Development of a parallel algorithm for reachable set computation.
  • Integration of uncertainty treatment using differential inclusions.
  • Formulation of functional sensitivity analysis.

Main Results:

  • The new solver efficiently calculates reachable sets using a parallel algorithm.
  • The study details advancements over the original 2002 solver.
  • A novel approach to functional sensitivity is proposed and discussed.

Conclusions:

  • The enhanced differential inclusion solver offers improved performance for reachable set calculations.
  • The inclusion of functional sensitivity analysis expands the solver's applicability in control systems.
  • This work provides a more robust tool for analyzing uncertain dynamical systems.