Performance and safety guarantees from NOISY data! *New Preprint*
© 2021 EPFL
Solely using noisy historical data, we synthesize a robustly safe output-feedback policy, for which the suboptimality and safety gaps are explicitly and tightly upperbounded in terms of the level of corrupting noise. This is achieved by developing a new tractable optimal control method, the Behavioral Input-Output Parametrization (BIOP), which first exploits behavioral theory to identify a precise impulse response, and then sets up a quasi-convex optimal control procedure with guaranteed high performance.
Check out our preprint!
Abstract:
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, two key aspects remain unclear when the data are corrupted by noise: how can safety be guaranteed, and to what extent is the control performance affected? In this work, we provide a quantitative answer to these questions. In particular, we formulate a robustly safe version of the recently introduced Behavioral Input-Output Parametrization (BIOP) for the optimal predictive control of unknown constrained systems. The proposed framework has three main advantages: 1) it allows one to safely operate the system while explicitly quantifying, as a function of the noise level corrupting the data, how much the performance degrades, 2) it can be used in combination with state-of-the-art impulse response estimators, and finally, being a data-driven approach, 3) the state-space parameters and the initial state need not be specified for controller synthesis. We corroborate our results through numerical experiments.