Probabilistic robust design of control systems for high-fidelity cyber–physical testing

Cyber–physical empirical methods consist in partitioning a dynamical system under study into a set of physical and numerical substructures that interact in real-time through a control system. In this paper, we define and investigate the fidelity of such methods, that is their capacity to generate systems whose outputs remain close to those of the original system under study. In practice, fidelity is jeopardized by uncertain and heterogeneous artefacts originating from the control system, such as actuator dynamics, time delays and measurement noise. We present a computationally efficient method, based on surrogate modelling and active learning techniques, to (1) verify that a cyber–physical empirical setup achieves probabilistic robust fidelity, and (2) to derive fidelity bounds, which translate to absolute requirements to the control system. For verification purposes, the method is first applied to the study of a simple mechanical system. Its efficiency is then demonstrated on a more complex problem, namely the active truncation of slender marine structures, in which the substructures’ dynamics cannot be described by an analytic solution