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Recent work in data-driven control has revived behavioral theory to perform avariety of complex control tasks, by directly plugging libraries of pastinput-output trajectories into optimal control problems. Despite recentadvances, a key aspect remains unclear: how and to what extent donoise-corrupted data impact control performance? In this work, we provide aquantitative answer to this question. We formulate a Behavioral version of theInput-Output Parametrization (BIOP) for the optimal predictive control ofunknown systems using output-feedback dynamic control policies. The mainadvantages of the proposed framework are that 1) the state-space parameters andthe initial state need not be specified for controller synthesis, 2) it can beused in combination with state-of-the-art impulse response estimators, and 3)it allows to recover suboptimality results on learning the Linear QuadraticGaussian (LQG) controller, therefore revealing, in a quantitative way, how thelevel of noise in the data affects the performance of behavioral methods.Specifically, it is shown that the performance degrades linearly with theprediction error of the behavioral model. We conclude the paper with numericalexperiments to validate our results.

A Behavioral Input-Output Parametrization of Control Policies with Suboptimality Guarantees