Result: Optimal nonparametric identification from arbitrary corrupt finite time series

Summary: We formulate and solve a worst-case system identification problem for single-input, single-output, linear, shift-invariant, distributed parameter plants. The available a priori information in this problem consists of time-dependent upper and lower bounds on the plant impulse response and the additive output noise. The available a posteriori information consists of a corrupt finite output time series obtained in response to a known, nonzero, but otherwise arbitrary, input signal. We present a novel identification method for this problem. This method maps the available a priori and a posteriori information into an ``uncertain model'' of the plant, which is composed of a nominal plant model, a bounded additive output noise, and a bounded additive model uncertainty. The upper bound on the model uncertainty is explicit and expressed in terms of both the \(l_1\) and \(H_\infty\) system norms. The identification method and the nominal model possess certain well-defined optimality properties and are computationally simple, requiring only the solution of a single linear programming problem.