Optimality of simulation-based nonlinear model reduction: Pathwise stochastic controllability

In previous work, it was showed that nonlinear model reduction by model-based method considering the controllability and data-driven method are equivalent when the input port is open to a noisy environment. The controllability considered only the input energy to regulate around the goal state. In view of this, we consider a generalized controllability taking account of the state transition cost. In this paper, we show a similar equivalence of model-based method considering the generalized controllability and data-driven method under the same noisy environment.