Experiment design for data-driven simulation and control: online computation and robustness

Henk van Waarde

Any data-driven method, whether it aims at simulation, modelling or control, requires sufficiently informative data. Experiment design concerns the question of how to obtain such informative data. In the field of systems and control, experiment design has enormous potential because the dynamical systems of interest are mostly input-output systems, where the input can be chosen freely. In this setting, experiment design problems thus boil down to the question of how to choose the input in such a way that the resulting input-output data are informative, the latter often being formalised in terms of rank conditions on Hankel matrices. An experiment design result that has recently received a lot of attention is the fundamental lemma by Willems and coauthors. It asserts that a persistently exciting input, applied to a controllable linear system, results in input-output data that fully describe the behaviour of the system. As a consequence, such data are suitable to identify a model of the system, or, more directly, to simulate future trajectories of the system and design controllers without the intermediate modelling step. Although the fundamental lemma has been applied successfully to a number of problems, the result suffers from a large sample 
complexity and a lack of robustness to noise. In this talk, we will thus discuss a new experiment design method that circumvents the use of persistently exciting inputs. The idea is instead to design the input in an online fashion, by making use of past data. It will be shown that this approach is fully sample efficient, meaning that the desirable rank conditions on the data are achieved by using the smallest possible number of samples. Finally, a robust version of the fundamental lemma will be presented that is applicable in the case of noisy data.

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