Experiment design using prior knowledge on controllability and stabilizability

Abstract: In this paper, we consider the problem of designing input signals for an unknown linear time-invariant system in such a way that the resulting input-state data is suitable for identification or stabilization. We will take into account prior knowledge on system-theoretic properties of the system, in particular, controllability and stabilizability. For this, we extend the notion of universal inputs to incorporate prior knowledge on the system. An input is called universal for identification (resp., stabilization) if, when applied to any system complying with the prior knowledge, it results in data suitable for identification (resp., stabilization) regardless of the initial condition. We provide a full characterization of such universal inputs. In addition, we discuss online experiment design using prior knowledge, and we study cases where this approach results in the shortest possible experiment for identification and stabilization.