obj_grad function

[Peter230655]

In the example of the pedalling with variable h you use this gradient function:

def obj_grad(free):
    T = free[laenge * num_nodes:]
    grad = np.zeros_like(free)
    grad[laenge * num_nodes:] = 2.0*free[-1]*free[laenge*num_nodes:]
    grad[-1] = np.sum(T**2)
    return grad

The second to last line: grad[-1] = np.sum(T**2) I do not understand.
What is the 'mathematical' background?

Thanks for any explanation!

[moorepants]

In #164 this is the objective and its gradient:

def obj(free):
    """Return h (always the last element in the free variables)."""
    return free[-1]


def gradient(free):
    """Return the gradient of the objective."""
    grad = np.zeros_like(free)
    grad[-1] = 1.0
    return grad

[moorepants]

The objective here is simply minimize h. h is the last value in free (always if variable duration problem). The gradient of h wrt to each variable in free is zero except for the last entry which is dhdh = 1.

[Peter230655]

The objective here is simply minimize h. h is the last value in free (always if variable duration problem). The gradient of h wrt to each variable in free is zero except for the last entry which is dhdh = 1.

The total 'amount of torque needed does not matter here, correct?
I must think about this some more, I think I mixed up mnimizing h and minimizimg 'total torque'.

[moorepants]

In the pedaling problem I am minimizing the "race time". I want the cyclist to pass the finish line in the minimal amount of time and they can use their muscles maximally. I'm not minimizing the inputs in this case, I'm simply minimizing time to travel a specific distance.

[Peter230655]

In the pedaling problem I am minimizing the "race time". I want the cyclist to pass the finish line in the minimal amount of time and they can use their muscles maximally. I'm not minimizing the inputs in this case, I'm simply minimizing time to travel a specific distance.

I simply have not given the objective much thought. This discussion helped!

[Peter230655]

Clear, thanks!
The example I copied has what you show, but multiplied by sum(T**2).
I will remove, and see if this helps.

[moorepants]

You can't just remove things. The gradient has to calculate the gradient of the objective wrt all values in free.

[Peter230655]

Now I simply bounded h: 1.e-5 < h < 1, and it finds a solution quickly!
(I am also optimizing h only, and bound the force like -250 < force < 250.)

[Peter230655]

my simulation is a double pendulum attached to a chart, which moves left / right on a horizontal line. The force pushes the chart.
In the solution, the force seems to jump from minimum to maximun and back.
I vaguely remember such a "min / max Theorem" from control theory 40+ years ago - or is my memory failing me?

[moorepants]

Bang bang control