Variable time support in create_objective_function.

[moorepants]

No description provided.

[Peter230655]

Does this mean, that create_objective_function will soon be able to handle variable h? :-)

[moorepants]

Only if I can figure it out.

[Peter230655]

Only if I can figure it out.

I feel like you know it already! Surely will avoid these ugly expressions like in my ball/disc simulation.
If you want to minimize h, the only sensible expression to minimize would be weight * h, weight > 0.0 ?

[moorepants]

A general solution to this needs to support this cost function:

(general optimal control cost function)

Creating the discrete version of that and the discrete gradient from a general SymPy expression is not so simple.

There are past open issues about this: #30 #31

[Peter230655]

Just to make sure I understand it correctly:

• E and F are functions, differentiable in all their arguments.
• x is the state vector of the system.
• u is the control (input) vector.
• J[x(.), u(.), t_0, t_f] is to be minimized.

A necessary condition for a minimum is that grad_(x, u, t_f)(J) = 0.

[tjstienstra]

There are past open issues about this: #30 #31

See also #190

[moorepants]

Yes, I was starting to implement your suggestion but I think it was missing taking the derivative wrt to h and I started getting hung up on the solution. I basically copied your code and started trying to make it work, but haven't gotten it to yet.

[tjstienstra]

but I think it was missing taking the derivative wrt to h

I would expect that you can just add it to the objective_grad computation, the list of symbols w.r.t. which the jacobian is computed. However, I don't remember testing the solution (in depth), but it is nice to see that you have already written some tests.

[tjstienstra]

You should take into account that this is backward Euler, so the first term falls out, see test_backward_single_input.
If free is [x(t), v(t), f1(t), f2(t), c, k, m, h] then the objective should be (f1_vals[1:]**2 + f2_vals[1:]**2).sum() * h_val.
Similarly, the gradient should be a stack of zeros(2*N+1), 2*h_val*f1_vals[1:], [0] 2*h_val*f2_vals[1:], [0, 0, 0, (f1_vals[1:]**2 + f2_vals[1:]**2).sum()]

P.S. quickly wrote out the equations on my phone so would advise checking them.

[moorepants]

I don't think I assumed any specific integration routine in the manually created objective functions.