Reachable sets of differential inclusions: New DI solver, parallel version, interdisciplinary applications
1Universidad Panamericana, Facultad de Ingeniería, Augusto Rodin 498, Ciudad de México, 03920, México.
Methodsx
|August 25, 2021
Summary
This study introduces an advanced differential inclusion solver for calculating reachable sets. The new parallel algorithm enhances computational efficiency and introduces functional sensitivity analysis for control systems.
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.
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