OPTIMAL NONPARAMETRIC IDENTIFICATION FROM ARBITRARY CORRUPT FINITE-TIME SERIES

In this paper we formulate and solve a worst-case system identificatio n problem for single-input, single-output, linear, shift-invariant, di stributed parameter plants. The available a prior 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 poste riori information consists of a corrupt finite output time series obta ined in response to a known, nonzero, but otherwise arbitrary, input s ignal. 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 comprised of a nominal p lant model, a bounded additive output noise, and a bounded additive mo del uncertainty. The upper bound on the model uncertainty is explicit and expressed in terms of both the l1 and Hinfinity system norms. The identification method and the nominal model possess certain well-defin ed optimality properties and are computationally simple, requiring onl y the solution of a single linear programming problem.