Direct data‐driven design of switching controllers

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Deciding Stability of a Switched System Without Identifying It

We address the problem of deciding stability of a “black-box” dynamical system (i.e., a system whose model is not known) from a set of observations. The only assumption we make on the black-box system is that it can be described by a switched linear system. We show that, for a given (randomly generated) set of observations, one can give a stability guarantee, for some level of confidence, with a trade-off between the quality of the guarantee and the level of confidence. We provide an explicit way of computing the best stability guarantee, as a function of both the number of observations and the required level of confidence. Our results rely on geometrical analysis and combine chance-constrained optimization theory with stability analysis techniques for switched systems 1