delay_constraint

[Peter230655]

This shows how to use numerical trajectories for a bound of the form $\int_{t - time_{\textrm{delay}}}^{t} P(\tau) d\tau \leq E_{max}$.
The basic idea is Neville's only! I simply changed W_delay.diff(t) to W_dalay.diff(P).
I placed it in intermediate, because I think, this using of numerical trajectories for a bound is not so trivial - at least it took me a good while to get it (hopefully) right.
NOTE: Convergence is still a bit tricky, even though the eoms look simple.

[Peter230655]

Better not to merge, yet anyway: Other than this simplest of mechanical systems I have been unable to get convergence on any more complicated system.

[Peter230655]

@moorepants:
Neville wants to achieve this. $E(P) = \int_{t - time_{\textrm{delay}}}^{t} P(\tau) d\tau \leq E_{max}$.
(e.g. a battery can only give $E_{max}$ energy within an interval of $time\textrm{delay}$ without overheating.
He found a differentiable function $f(P) \approx max(0, P)$. so $\dfrac{d}{dt}E(P(t)) = f(P(t)$

Now, for the numerical trajcetory we need $\dfrac{d}{dP}E(P)$

[Peter230655]

In the simulation, it is better to give all zeros for the derivative of the numerical trajectory than what I tried to give. Obviously what I thought was the right derivate is not correct.