Sparse decompositions of nonlinear dynamical systems and applications to moment-sum-of-squares relaxations

Understand

In this paper, we propose a general sparse decomposition of dynamical systems provided that the vector field and constraint set possess certain sparse structures, which we call subsystems.

• This notion is based on causal dependence in the dynamics between the different states.
• This results in sparse descriptions for fundamental problems from nonlinear dynamical systems: region of attraction, maximum positively invariant set, and global attractor.
• The decompositions can be paired with any method for computing (outer) approximations of these sets to reduce the computation to lower dimensional systems.