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EMbrake

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Marcelo Forets edited this page Apr 28, 2020 · 65 revisions

Notes

Results

Flowpipe computation

Alg. Jitter Run(s) Alloc
nopv GLGM06(δ=1e-8, max_order=3) no 7.21 4.16GB
nopv GLGM06(δ=1e-8, max_order=3) ζ=1e-7 7.23 s 4.27GB
pv1 ASB07(δ=1e-8, max_order=3) no 152.25 s 46.14GB
ASB07(δ=1e-8, max_order=3) ζ=1e-7 153.66 s 46.24GB
pv2, χ=5.0% ASB07(δ=1e-8, max_order=3) no 151.84 s 46.14GB
ASB07(δ=1e-8, max_order=3) ζ=1e-7 153.30 s 46.24GB
pv2, χ=0.5% ASB07(δ=1e-8, max_order=3) no 140.54 s 46.14GB
ASB07(δ=1e-8, max_order=3) ζ=1e-7 143.26 s 46.24GB
  • In all cases, Tsample = 1e-4 and max_jumps = 1_000 (1_001) without (with) jitter.
  • Final width: defined as the width of the final set projected to variable I (current).
  • p.v. 1: parameter variation changing 1 constant, Flow* setting
  • p.v. 2: parameter variation changing all constants associated to physical variables by +-χ% w.r.t. their nominal values
  • G means GLGM06
  • A means ASB07
  • n°s: number of sets

Other data:

Alg. Jitter w(I[end]) w(x[end]) n°s
nopv GLGM06(δ=1e-8, max_order=3) no 1.369 7.34e-5 10010000
nopv GLGM06(δ=1e-8, max_order=3) ζ=1e-7 28.6 1.5e-3 9999990
pv1 ASB07(δ=1e-8, max_order=3) no 137.24 7.31e-3 10010000
ASB07(δ=1e-8, max_order=3) ζ=1e-7 165.10 8.79e-3 9999990
pv2, χ=5.0% ASB07(δ=1e-8, max_order=3) no 30948.66 1.402 10010000
ASB07(δ=1e-8, max_order=3) ζ=1e-7 31131.96 1.411 9999990
pv2, χ=0.5% ASB07(δ=1e-8, max_order=3) no 921.62 4.85e-2 10010000
ASB07(δ=1e-8, max_order=3) ζ=1e-7 952.91 5.02e-2 9999990

Experiments were performed on a computer with 3.2G Hz Intel Core i7-8700 processor and 16 GiB RAM running 64-Bit Windows 10 Pro Version 1909.

Property verification

Past commit of RA for ASB07 with parameter variation

https://github.com/JuliaReach/ReachabilityAnalysis.jl/commit/8978e8e0064b960c74c71dbe5c3c5200fffeb90e

$ git checkout 8978e8e0064b960c74c71dbe5c3c520

Code:

using ReachabilityAnalysis
using ReachabilityAnalysis: solve_hybrid
using SparseArrays
# model's constants
L = 1.e-3
KP = 10000.
KI = 1000.
R = 0.5
K = 0.02
drot = 0.1
i = 113.1167
Tsample = 1.E-4
p = 504. + (-3. .. +3.)

# state variables: [I, x, xe, xc]
A = IntervalMatrix([-p            0      KP/L   KI/L; 
                    K/i/drot      0      0      0;
                    0             0      0      0;
                    0             0      0      0])

EMbrake = @system(x' = Ax)

# initial conditions
I₀  = Singleton([0.0]) #+ Interval(0., 10.0)
x₀  = Singleton([0.0]) #+ Interval(-0.001, 0.001)
xe₀ = Singleton([0.0])
xc₀ = Singleton([0.0])

X₀ = I₀ × x₀ × xe₀ × xc₀;

x0 = 0.05
Ar = sparse([1, 2, 3, 4, 4], [1, 2, 2, 2, 4], [1., 1., -1., -Tsample, 1.], 4, 4)
br = sparsevec([3, 4], [x0, Tsample*x0], 4)

reset_map(X) = Ar * X + br
δ = 3e-7
@time sol_flow_7 = solve_hybrid(EMbrake, X₀, reset_map; Tsample=Tsample, max_jumps=1001, ζ=1e-7, alg=ASB07(δ=δ));

Introduce modifications to use reduce_order in ASB07

(Refs: <: remove; >: add)

1.- LazySets: branch mforets/EMbrake

  • Approximations/overapproximate.jl -- function overapproximate
< row = @view Ms[i, :] 
> row = Ms[i, :]

2.- ReachabilityAnalysis: branch master, commit 8978e8e0064b960c74c71dbe5c3c520

$ git checkout 8978e8e0064b960c74c71dbe5c3c520
  • Algorithms/ASB07/reach.jl -- function reach_homog_ASB07!
  while k <= NSTEPS
      Rₖ = overapproximate(Φ * set(F[k-1]), Zonotope)
>     Rₖ = reduce_order(Rₖ, max_order)
      Δt += δ

OUT OF MEMORY:

δ = 1e-8
@time sol_flow_7 = solve_hybrid(EMbrake, X₀, reset_map; Tsample=Tsample, max_jumps=6, ζ=1e-7, alg=ASB07(δ=δ));

(Note that max_jumps=6)

TO-DO

  • Use the same discretization method.
  • Run with shifted flowpipes again, see mforets/shifted_flowpipe.
  • Consider different overapproximation strategies for the convexification operation.

function LazySets.diameter(R::ReachabilityAnalysis.AbstractLazyReachSet; vars::Int) overapproximate(project(R, vars=vars), Interval) |> set |> diameter end

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