Optimizing a function in optimal control problem

Specific Domains Optimization (Mathematical)
, ,
15

Hi there; JuMP.jl and InfiniteOpt.jl will sure do.

@yhchang you can also have a look at OptimalControl.jl for a combination of direct (= JuMP like) and shooting method approaches. The Goddard example cited by @odow (with an additional state constraint) reads like that:

ocp = @def begin # definition of the optimal control problem

    tf ∈ R, variable
    t ∈ [t0, tf], time
    x = (r, v, m) ∈ R³, state
    u ∈ R, control

    x(t0) == [ r0, v0, m0 ]
    m(tf) == mf,         (1)
    0 ≤ u(t) ≤ 1
    r(t) ≥ r0
    0 ≤ v(t) ≤ vmax

    ẋ(t) == F0(x(t)) + u(t) * F1(x(t))

    r(tf) → max

end

F0(x) = begin
    r, v, m = x
    D = Cd * v^2 * exp(-β*(r - 1)) # Drag force
    return [ v, -D/m - 1/r^2, 0 ]
end

F1(x) = begin
    r, v, m = x
    return [ 0, Tmax/m, -b*Tmax ]
end

Check out below for the complete example:

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