Analysis of deterministic affine dynamics

[schillic]

Is this really not supported?

julia> b = [1.0]
1-element Array{Float64,1}:
 1.0

julia> prob = @ivp(x' = x + b, x(0) ∈ Singleton([1.0]))
InitialValueProblem{LinearControlContinuousSystem{Float64,IdentityMultiple{Float64},IdentityMultiple{Float64}},Singleton{Float64,Array{Float64,1}}}(LinearControlContinuousSystem{Float64,IdentityMultiple{Float64},IdentityMultiple{Float64}}([1.0], [1.0]), Singleton{Float64,Array{Float64,1}}([1.0]))

julia> sol = solve(prob, T=4.0)
ERROR: ArgumentError: the system type LinearControlContinuousSystem{Float64,IdentityMultiple{Float64},IdentityMultiple{Float64}} is currently not supported

---

Side note (probably an issue with MathematicalSystems):

julia> prob = @ivp(x' = -x + b, x(0) ∈ Singleton([1.0]))
ERROR: LoadError: Base.Meta.ParseError("\"*\" is not a unary operator")
Stacktrace:
 [1] @ivp(::LineNumberNode, ::Module, ::Vararg{Any,N} where N) at .julia/dev/MathematicalSystems/src/macros.jl:970
in expression starting at REPL[19]:1
caused by [exception 1]
Base.Meta.ParseError("\"*\" is not a unary operator")

[mforets]

true, that kind of system was not supported. we always specified state and input constraints, which in this case should be set by default as univesal set, i added this in #379

there is a new error now,

julia> sol = solve(prob, T=4.0)
ERROR: AssertionError: radius must not be negative
Stacktrace:
 [1] macro expansion at /home/mforets/.julia/dev/LazySets/src/Assertions/Assertions.jl:23 [inlined]
 [2] Hyperrectangle(::Array{Float64,1}, ::Array{Float64,1}; check_bounds::Bool) at /home/mforets/.julia/dev/LazySets/src/Sets/Hyperrectangle.jl:91
 [3] Hyperrectangle at /home/mforets/.julia/dev/LazySets/src/Sets/Hyperrectangle.jl:88 [inlined]
 [4] _symmetric_interval_hull(::LinearMap{Float64,Universe{Float64},Float64,IdentityMultiple{Float64}}) at /home/mforets/.julia/dev/ReachabilityAnalysis/src/Flowpipes/setops.jl:387
 [5] sih(::LinearMap{Float64,Universe{Float64},Float64,IdentityMultiple{Float64}}, ::Val{:concrete}) at /home/mforets/.julia/dev/ReachabilityAnalysis/src/Continuous/discretization.jl:250
 [6] discretize(::InitialValueProblem{ConstrainedLinearControlContinuousSystem{Float64,IdentityMultiple{Float64},IdentityMultiple{Float64},Universe{Float64},ConstantInput{Universe{Float64}}},Singleton{Float64,Array{Float64,1}}}, ::Float64, ::Forward{Val{:base},Val{:interval},Val{:concrete},Val{false}}) at /home/mforets/.julia/dev/ReachabilityAnalysis/src/Continuous/discretization.jl:316
 [7] post(::INT{Float64,Forward{Val{:base},Val{:interval},Val{:concrete},Val{false}}}, ::InitialValueProblem{LinearControlContinuousSystem{Float64,IdentityMultiple{Float64},IdentityMultiple{Float64}},Singleton{Float64,Array{Float64,1}}}, ::IntervalArithmetic.Interval{Float64}; Δt0::IntervalArithmetic.Interval{Float64}, kwargs::Base.Iterators.Pairs{Symbol,Float64,Tuple{Symbol},NamedTuple{(:T,),Tuple{Float64}}}) at /home/mforets/.julia/dev/ReachabilityAnalysis/src/Algorithms/INT/post.jl:29
 [8] solve(::InitialValueProblem{LinearControlContinuousSystem{Float64,IdentityMultiple{Float64},IdentityMultiple{Float64}},Singleton{Float64,Array{Float64,1}}}; kwargs::Base.Iterators.Pairs{Symbol,Float64,Tuple{Symbol},NamedTuple{(:T,),Tuple{Float64}}}) at /home/mforets/.julia/dev/ReachabilityAnalysis/src/Continuous/solve.jl:61
 [9] top-level scope at REPL[13]:1

[mforets]

Side note (probably an issue with MathematicalSystems):

yes, i think this one is reported JuliaReach/MathematicalSystems.jl#194

[mforets]

i take back JuliaReach/MathematicalSystems.jl#221 , that normalization does not apply (because U is the universal set, so discretization fails). on the other hand i think that the proper fix is to make the @ivp macro be more precise, as proposed in JuliaReach/MathematicalSystems.jl#221

[mforets]

this is an alternative for the OP:

julia> A = hcat(1.0); b = [1.0];

julia> prob = @ivp(AffineContinuousSystem(A, b), x(0) ∈ [1.0]);

julia> sol = solve(prob, T=4.0);

[schillic]

So it is not a problem of this package, sorry. From my side this can be closed.

[mforets]

The OP is now fixed on the MathematicalSystems.jl side, and we can do

prob = @ivp(x' = x + [1.0], x(0) ∈ Singleton([1.0]))
sol = solve(prob, T=4.0)
plot(sol, vars=(0, 1))

i'll add this example as a test before closing the issue.