Optimal Inputs for Approximate Linear Systems in Hilbert Spaces

The paper is a study of the problem of determining an optimal input given only an approximate linear model of an actual input-output system. The optimality criterion is the minimization of the maximal possible error in the output. Under the assumption that the input and the output spaces can be modeled as Hilbert spaces, complete results on the existence, uniqueness, and characterization of optimal inputs are obtained. The results culminate in an unconditionally convergent iterative algorithm for the optimal inputs.