Hi,

I am having trouble with a problem, in the field of Optimal Control and the generation of optimal time-series.

Let's consider a system, whose dynamics are represented by dx/dt = f(t,x(t),u(t),p(t)), x and u being respectively the state and control vectors for the system. p is a vector of parameters which have a direct influence on a system's dynamics.

An example illustrating this would be considering a drone, going from point A to point B, in minimum time, but subject to a windy environment (the wind being represented by the time-dependent variable p(t)).

I have generated, by solving an Optimal Control Problem, optimal time-series for x(t) and u(t), for several values of p=p(t)=constant.

I would now like to interpolate, for any given value of p(t) at time t, the "nearly-optimal" control u(t) to be applied to the system between time t and time t+1, based on the OCP results previously computed.

The idea behing this would be, based on the solving of the OCP problem in constant wind p(t)=p=constant, to predict the nearly-optimal time-series u(t) to apply to the drone to control it in random wind p(t) (the random wind being in the range of the constant winds which were used to generate the OCP database).

Would you know if this is even possible ? I have not really been able to find published work on this topic, if you had any suggestions I would be grateful.

Thanks,