SparseDynamicSystem computes outer approximations for maximum positively invariant set (MPI), region of attraction (ROA), global attractor (GA) of polynomial dynamic systems via the sparsity-adapted moment-SOS hierarchy. To use SparseDynamicSystem in Julia, run
pkg> add https://github.com/wangjie212/SparseDynamicSystem- MOSEK
- JuMP
The following script computes the MPI set for the Van-der-Pol oscillator on [-1.1, 1.1]^2:
using SparseDynamicSystem
using DynamicPolynomials
@polyvar x[1:2]
f = [2*x[2], -0.8*x[1] - 10*(x[1]^2-0.21)*x[2]]
g = [1.1^2-x[1]^2, 1.1^2-x[2]^2]
d = 8 # the relaxation order
opt,w = MPI(f, g, x, d, -1.1*ones(2), 1.1*ones(2), TS=["block","block"], SO=[1;1], β=1)