Dymos constraint dependency on parameter

user_14068468 0
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I am wondering if it is possible to handle problems where a boundary constraint is dependent on a parameter that can be changed by the optimizer. I have model of a multistage rocket and I can optimize the trajectory and certain parameters like for example, thrust for a given stage. However, let's say I want to also make the actual stage masses parameters (subject to constraint that they all add up to a constant). I have certain boundary constraints in my model that depend on mass -- one phase representing one stage ends when propellant mass burned is equal to propellant load, and that's encoded as boundary constraint. So the actual constraint itself would vary based on how the parameter of that stages mass is changed by the optimizer. Also, the phase linking that happens between stages, phases representing rocket stages, requires me to add a linkage constraint in the form

traj.add_linkage_constraint('stage_1', 'stage_2', equals=stage_1_dry_mass)

in order to represent jettisoning the first stage empty mass. So that jettison mass is predetermined, and can't be changed as a parameter that gets optimized.

Is there a way to handle this in Dymos? I think I may be able to reformulate the problem in terms of fractions but haven't thought it through yet, and I have feeling the phase linkage would still be a problem.

openmdao
1 Answers

I am wondering if it is possible to handle problems where a boundary constraint is dependent on a parameter that can be changed by the optimizer.

Absolutely.

So the mass of your vehicle is:

Initial mass = Stage 1 Prop mass + Stage 1 Dry Mass + Stage 2 Prop Mass + Stage 2 Dry Mass

If you have a state or ODE output that tracks your current vehicle mass (m). Before the stage 1 drop, m_1 will include the stage 1 dry mass. Immediately after the drop, the total mass m_2 will not.

At that point, the equation which defines the relationship will be:

m_1 - m_2 = m_stage_1

As you said, you cannot specify an ODE variable as the bounds in a boundary or linkage constraint (they're just numeric values), but we can write the equation above as a linkage constraint.

If you make an output in your ODE that is "current total mass minus stage 1 dry mass" (m_minus_stage_1 for lack of a better name), then we can make that variable continuous with the current total mass at the start of the next phase after the drop.

traj.add_linkage_constraint(phase_a='phase1', phase_b='phase2',
                            loc_a='final', loc_b='initial',
                            var_a='m_minus_stage_1', var_b='m',
                            equals=0)

Also, there's nothing stopping you from using an openMDAO constraint to link them here. Something like this would work.

prob.add_subsystem('mass_linkage', om.ExecComp(m_error = m_1 - m_2 - m_stage_1))
prob.model.connect('traj.phase1.timeseries.states:m', 'mass_linkage.m_1', src_indices=[-1])
prob.model.connect('traj.phase2.timeseries.states:m', 'mass_linkage.m_2', src_indices=[0])
prob.model.promotes('traj', inputs=[('parameters:m_stage_1', 'm_stage_1')])
prob.model.promotes('mass_linkage', inputs=['m_stage_1'])
prob.model.add_constraint('mass_linkage.m_error', equals=0)

Note that parameters are treated as inputs in Dymos, and OpenMDAO doesn't allow an input to connect to another input. They both must be promoted to the same name. We're working on a 'statics' output component in Dymos that will let us output those parameters so they can be connected.

Now I fully admit that the manual way, while more efficient than calculating something in the ODE, is more confusing. That's the sort of complexity that dymos is intended to help users deal with.

Also, there's probably a way to handle this as a set of boundary constraints as well, but it seems like it's more naturally posed as a linkage constraint.

user_7545360
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