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

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 the achieved control performance? In this work, we provide a quantitative answer to these questions. We formulate a Behavioral version of the Input-Output Parametrization (BIOP) for the 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 recent suboptimality results for the Linear Quadratic Gaussian (LQG) control problem, 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 a behavioral model. We conclude the paper with numerical experiments to validate our results.