A Scenario Optimization Approach to System Identification with Reliability Guarantees

This paper proposes an optimization-based framework for the calibration of parametric models according to multi-variate, input-output data. We focus on continuous models whose outputs depend nonlinearly (and possibly implicitly) on the inputs and the parameters. Maximum likelihood and scenario optimization techniques are combined to generate stochastic predictor models having dependent parameters. Furthermore, the reliability of the predictor, as measured by the probability of future data falling outside the predicted output ranges, is formally bounded using non-convex scenario theory. This framework is illustrated by calibrating a linear time invariant model of a system having a non-colocated sensor-actuator pair according to modal analysis data.