Model free probabilistic design with uncertain Markov parameters identified in closed loop

In this paper, we present a new probabilistic design approach based on Markov parameters identified via subspace methods from a finite batch of input and output data. This approach not only links closed-loop subspace identification with optimal control; but also directly evaluates parametric uncertainties on the identified Markov parameters. Neither a state-space model nor its stochastic uncertainty has to be realized in this approach. The effects of the parametric uncertainties on the output predictor are analyzed explicitly. Analytic solution to the probabilistic design is derived in a closed form, which avoids computing the empirical mean of a cost function as required by randomized algorithms. The solution hence leads to an easily implementable cautious optimal design, robust to the uncertainties in the identified Markov parameters from a closed-loop plant.