On-line Learning of Linear Systems

We consider the problem of learning/identification of a linear system by sampling its frequency response. A cumulative prediction error type criterion is used to describe the learnability of classes of (continuous- or discrete-time) linear systems with may have discontinuous frequency responses but of bounded variation. Upper and lower bounds are obtained for three input frequency sampling schemes: worst-case, random, and worst-case with small noise on the input frequency. Bounds are also obtained for the random sampling scheme with l
1
noise or i.i.d. noise corrupting the frequency response samples.