System identification with binary-valued sensors

The problem of system identification is investigated for plants which are equipped only with binary-valued sensors. Optimal identification errors, time complexity, optimal input design, and impact of disturbances and unmodelled dynamics on identification accuracy and complexity are explored. It is revealed that switching sensors impose fundamental limitations on identification accuracy and time complexity, and carry distinct features beyond identification with regular sensors. Furthermore, it is shown that the time complexity of such identification problems is intimately related to the Kolmogorov E-entropy of parameter uncertainty sets.