  Recent work in data-driven control has revived behavioral theory to perform a
variety of complex control tasks, by directly plugging libraries of past
input-output trajectories into optimal control problems. Despite recent
advances, a key aspect remains unclear: how and to what extent do
noise-corrupted data impact control performance? In this work, we provide a
quantitative answer to this question. We formulate a Behavioral version of the
Input-Output Parametrization (BIOP) for the optimal predictive control of
unknown systems using output-feedback dynamic control policies. The main
advantages of the proposed framework are that 1) the state-space parameters and
the initial state need not be specified for controller synthesis, 2) it can be
used in combination with state-of-the-art impulse response estimators, and 3)
it allows to recover suboptimality results on learning the Linear Quadratic
Gaussian (LQG) controller, therefore revealing, in a quantitative way, how the
level of noise in the data affects the performance of behavioral methods.
Specifically, it is shown that the performance degrades linearly with the
prediction error of the behavioral model. We conclude the paper with numerical
experiments to validate our results.

Systems and Control;Systems and Control;Optimization and Control