A bias-variance perspective of data-driven control
Résumé
Data-driven control, the task of designing a controller based process data, find application in a wide range of disciplines and the topic has been subject to intense research over more than half a decade. The main purpose of this contribution is to elucidate on the commonalities between data-driven control and parameter estimation. In particular, we discuss the bias-variance trade-off, i.e. rather than aiming for the optimal controller one should aim for a constrained version, that, for example, may be characterized by tunable parameters, corresponding to hyperparameters in parameter estimation. To keep technicalities at a minimum, still capturing the essential features of the problem, we consider a quadratic open loop control problem applied to a finite impulse response system. We consider the problem of minimizing the expected control cost and first show that, for our setting, model-based data-driven control outperforms other methods. We then make a systematic study of 3 different controller structures and two different (model-based) data-driven tuning techniques and illustrate their behaviours numerically.
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