solve a system with control input

[ga72kud]

I am new to reachability analysis.jl package and wondering why there are only autonomous systems without control input

\dot{x}=Ax+Bu
or
\dot{x}=Ax+u

I am looking how I would write following example from here:
https://juliareach.github.io/LazySets.jl/dev/man/reach_zonotopes/

with tools from reachabilityAnalysis.jl

[mforets]

For the first example,

using ReachabilityAnalysis, Plots

A = [-1 -4; 4 -1.0]
X0 = Zonotope([1.0, 0.0], Matrix(0.1*I, 2, 2))
μ = 0.05
δ = 0.02
T = 2.
U = BallInf(zeros(2), μ)

prob = @ivp(x' = A*x + u, x(0) ∈ X0, u ∈ U, x ∈ Universe(2))
sol = solve(prob, alg=GLGM06(δ=δ), T=T);

plot(sol, vars=(1, 2), fillalpha=0.1)

The second example can be defined similarly. Moreover, note that the projection is handled automatically by the plot command, i.e. plot(sol, vars=(1, 5)) should work.

[ga72kud]

I have tested the program with two examples. It worked thank you a lot.

using ReachabilityAnalysis, Plots
#example 1
A = [-1 -4; 4 -1.0]
X0 = Zonotope([1.0, 0.0], Matrix(0.1*I, 2, 2))
μ = 0.05
δ = 0.02
T = 2.
U = BallInf(zeros(2), μ)

prob = @ivp(x' = A*x + u, x(0) ∈ X0, u ∈ U, x ∈ Universe(2))
sol = solve(prob, alg=GLGM06(δ=δ), T=T);

plot(sol, vars=(1, 2), fillalpha=0.1)

#example 2
A = Matrix{Float64}([-1 -4 0 0 0;
                      4 -1 0 0 0;
                      0 0 -3 1 0;
                      0 0 -1 -3 0;
                      0 0 0 0 -2])
X0 = Zonotope([1.0, 0.0, 0.0, 0.0, 0.0], Matrix(0.1*I, 5, 5))
μ = 0.01
δ = 0.005
T = 1.
U = BallInf(zeros(5), μ)

prob = @ivp(x' = A*x + u, x(0) ∈ X0, u ∈ U, x ∈ Universe(5))
sol = solve(prob, alg=GLGM06(δ=δ), T=T);
plot(sol, vars=(1, 3))


#double integrator with ẋ=Ax+Bu
A = [0 0 1.0 0; 0 0 1.0 0; 0 0 0 0; 0 0 0 0]
B = [1.0 0; 1.0 0; 0 1.0; 0 1.0]
X0 = Zonotope([1.0, 0.0, 0.0, 0.0], Matrix(0.1*I, 4, 4))
μ = 0.05
δ = 0.02
T = 2.
U = BallInf(zeros(2), μ)
prob = @ivp(x' = A*x + B*u, x(0) ∈ X0, u ∈ U, x ∈ Universe(4))
sol = solve(prob, alg=GLGM06(δ=δ), T=T);
plot(sol, vars=(1, 2), fillalpha=0.1)