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Overapproximate TaylorModelReachSet by mincing in time

Open mforets opened this issue 3 years ago • 0 comments

example:

@taylorize function _vanderpol!(du, u, params, t)
  local μ = 1.0
  du[1] = u[2]
  du[2] = (μ * u[2]) * (1 - u[1]^2) - u[1]
  nothing
end

u0 = [1.4, 2.4]
X0 = Singleton(u0)
#X0 = BallInf(u0, 0.000001)
prob = @ivp(x' = _vanderpol!(x), dim=2, x(0) ∈ X0)
sol_reach = RA.solve(prob, T=7.0, alg=TMJets());

R2 = sol_reach[10]; X = set(R2)

2-element Array{TaylorModels.TaylorModel1{TaylorN{Float64},Float64},1}:
    1.7584019718866175 + ( 1.576769151568127) t + ( - 2.528483775679568) t² + ( 0.043135304283992516) t³ + ( 3.3666964995718303) t⁴ + ( - 2.4497160637433772) t⁵ + ( - 4.003646265251382) t⁶ + ( 7.094860114694345) t⁷ + ( 2.2866621267912666) t⁸ + [-1.10586e-13, 2.9598e-14]
 1.576769151568127 + ( - 5.056967551359136) t + ( 0.12940591285197756) t² + ( 13.466785998287321) t³ + ( - 12.248580318716886) t⁴ + ( - 24.021877591508293) t⁵ + ( 49.66402080286042) t⁶ + ( 18.293297014330133) t⁷ + ( - 131.72991923602365) t⁸ + [-7.02493e-13, 2.64356e-13]

we should add something like overapproximate(R2, Hyperrectangle, length_time=10)

mforets avatar Jan 28 '21 14:01 mforets