same betts 10 1 simulation but new branch #308
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I'll merge this one as the demonstration of how to handle inequalities (until we have native support). |
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| This is example 10.1 from Betts' book "Practical Methods for Optimal Control | ||
| Using NonlinearProgramming", 3rd edition, Chapter 10: Test Problems. | ||
| More details are in sectionn 4.11.7 of the book. |
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Can you cite Bett's book using RST citation notation, i.e. [Betts2010]_.
examples-gallery/plot_betts_10_1.py
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| :math:`y_1^2 + y_2^2 + y_3^2 + y_4^2 \\geq function(time, parameters)` | ||
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| As presently *opty* does not support inequality constraints, I introduced a new | ||
| state variable `fact` to take care of the inequality. The inequality is then |
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| state variable `fact` to take care of the inequality. The inequality is then | |
| state variable ``fact`` to take care of the inequality. The inequality is then |
double back ticks give monspace font
| - :math:`u_1, u_2` : control variables | ||
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| Note: I simply copied the equations of motion, the bounds and the constants | ||
| from the book. I do not know their meaning. |
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The why is the name of the problem "Alp Rider"? what does that mean? Please clarify.
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I simply took the name give to this problem by Dr. Betts.
Below it says:
Stiff ODE, terrain following [Betts2010] Sect. 4.7.6
But my 3rd edition does not seem to have this section.
I will send an email to Dr. Betts and will ask ihm.
In chapter 4.11.7 are more details about this problem.
I will correct the issues and push.
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We should just name it something that has a meaning to the reader of opty documentation, as they may not have the book.
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In chapter 4.11.7 it is described what the system does:
It must follow steep peaks as closely as possible, see fig 4.6 there.
Maybe: System following uneven terrain ?
examples-gallery/plot_betts_10_1.py
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| integration_method=integration_method, | ||
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| #prob.add_option('nlp_scaling_method', 'gradient-based') |
examples-gallery/plot_betts_10_1.py
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| print(f'minimum value of fact = {np.min(solution[4*num_nodes: 5*num_nodes]):.4e}') | ||
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| # %% | ||
| # sphinx_gallery_thumbnail_number = 2 |
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This is displaying in the rendered notebook, so I guess it not correctly specified. It should not show up in the rendered version.
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This is displaying in the rendered notebook, so I guess it not correctly specified. It should not show up in the rendered version.
corrected.
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These are the peaks the system (whatever it is, I do not know) has to follow. |
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I am not so concerned with what Bett's has, but I just would like the examples to be understandable without having his book. Can you make sure to provide enough information so that is the case. The name "Alp Rider" was no where else in your text so I don't know what it means. |
As I understand it from section 4.11.7, this was designed to be a stiff system, without apparent physical meaning. It was proposed to check optimization routines. The inequality constraint forces the norm of the state vector has to be larger than a wildly fluctuating function (the function in the picture), and the objective forces it to be close to this function. More I cannot find out about it. |
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Yes, perfect! |
Thanks! |
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NB: |
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We're probably not comparing apples to apples though. Opty does not do many of the fancy things (like mesh refinement, variable node spacing, higher order integrators, etc.) |
Fair enough, but if opty's minimum is lower and all the constraints are met very closely, does this not mean it works very well? |
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I think it still depends on the integrator and steps you use, as the constraints are a function of those choices. |
I think you are right: If I understand opty correctly, the results are "correct" only at the points in time given by num_nodes, and by continuity one hopes they are about right in between, too. And this is a tricky system as I now remember again. It took me a while to get it to converge. |
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Yes, this suffers from the same effects that any integration routine faces and the accuracy is effected by truncation error and floating point error. opty uses very simple integration algorithms relative to what Bett's recommends. Maybe one day I'll have time to include better integrators, but we could also move to pycollo and build that out instead. |
I just looked around a bit. It seems, pycollo has been kinda dormant for more than a year? |
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Sam wrote pycollo for his 2021 dissertation. He worked on it some when he was a post doc with me (we used it for the skateboard ollie) and then he moved on to other things. So, yes, it is dormant but it has all of the more advanced collocation methods and it works with SymPy. |
This is the same betts 10 1 as before. As I could not fix the branch, I put it into a new one and made a new PR. I will close the old PR.