Complex Dynamics Constraints #278
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tpresser570
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Can you please provide a minimum working example (i.e., the full script to reproduce this)? |
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First off, welcome to the forum! With respect to the formulation a few observations:
To address the above concerns, I would recommend the following:
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transfer_example.txt
Hello,
I am trying to solve the optimal control problem for a spacecraft with thrust in a two-body problem. This should closely follow the hovercraft examples but the optimizer fails. My objective function is to minimize the energy (full script below):
@objective(model, Min, ∫(u[1]^2 + u[2]^2 + u[3]^2, t))
My variables are:
@variables(model, begin # state variables x[1:3], Infinite(t) v[1:3], Infinite(t) # control variables u[1:3], Infinite(t) end)
I provide two waypoints, the start and end positions
@constraint(model, [i = 1:3, j = eachindex(tw)], x[i](tw[j]) == xw[i, j])
as well as use the two body dynamics as the constraints on the derivative:
#compute radius ^ 3/2 @expression(model, expr, ((x[1]^2+x[2]^2+x[3]^2)^(3/2))) #ODE equations @constraint(model, [i = 1:3], ∂(x[i], t) == v[i]) @constraint(model, [i = 1:3], ∂(v[i], t) == -μ*x[i]/expr + u[i])
But this results in IPOPT with a 0 Jacobian.
Number of nonzeros in equality constraint Jacobian...: 384
Number of nonzeros in inequality constraint Jacobian.: 0
Number of nonzeros in Lagrangian Hessian.............: 210
The Jacobian for the equality constraints contains an invalid number
Has anyone encountered this problem before??
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