Multi-phase OCP constraints in transitions

User Questions
,
1

Hi, I am very excited to try the multi-phase OCP feature soon; But while implementing I got a few questions regearding the constraint handling between phases.

Lets say I have a MOCP with 2 phases and a non trivial transition. From your paper and the examples I understand that:

  • I am not able to set a terminal (non-linear or linear constraint) onto the “terminal” state of the first phase x_{1,N_1}
  • However, I am able to set an “initial” constraint onto the first state of the second phase (x_{2,0}), which is mapped from the terminal state of the previous phase (x_{2,0} = \Gamma(x_{1,N_1}) )
  • Also I am able to set a cost onto the ‘terminal’ state of the first phase ( x_{1,N_1} ) via the cost function of the transition-phase E_1.

Are these assumptions correct?

In my use case, I want to use different model fidelities over the prediction horizon, so the state dimension becomes smaller in phase 2. In other words, I “drop” some components of the state when mapping from x_{1,N_1} to x_{2,0}. For this, it would be important to impose constraints on those components of x_{1,N_1} that do not directly carry over into x_{2,0}.

Can I simply to impose these as path constraints in the transition stage (or on the last node of phase 1), or is there a different way to achieve this?

Thanks again for your great work and your help!
Franek

2

Hi Franek,

that’s great to hear!
A transition with different state representation has to be modeled with a separate phase with model transition from node x_{{N_1}+1} = x_{2,0} = \Gamma(x_{N_1}) = \phi_{N_1}(x_{N_1}) (mixing the notation of eq (2) and (11) of our paper.
On the transition phase, you can define extra constraints on x, which is the final state of your first phase.
So, it is the same as for the transition cost, which is also defined on the transition stage.
Note that the fields to define the path cost and constraints are relevant for the transition stages.

Best,
Jonathan

1 Like