Strange MPC inverted pendulum problem. Please, help...

manuka

Hello.


The problem:
1. there is an inverted pendulum on a cart.( a 2D case)
2. we need to stabilize it in the upright position. So it's classical problem.
3. we NEED to use NMPC (non-linear model predictive control) for this.
4. the enviroment in which this pendulum operates is highly disturbed (winds blow on it, human kick it and so on, so basicly we just don't know what will happen and with what intensity)
5. we have a loooong history ( of time and position ) of cart doing it's job stabilizing the pendulum.
6. we know that during that history cart did everything absolutly optimal. (swinning pendulum upright, then resisting winds - failed (pendulum dropped), then swung it again and got it stabilized alright, then reacted on the human push and so on for very long time.)


now the Question:
1.I need (initial conditios) x0 to start iterating NMPC. How to obtain the initial position of a pendulum from the history?
Because it is not clear what angle pendulum has at x0.
2.how to incorporate this external disturbance in the prediction process? My guess i need to start not from x0 but from x0-200 for example. but question 1. (obtaining initial conditions for x0-200) stays unanswered.