Randomized Controls for Linear Plants and Confidence Regions for Parameters under External Arbitrary Noise

This paper considers the possibilities of randomized controls for designing confidence regions for unknown parameters. The assumptions about external noise that affect a linear plant are reduced to a minimum: external noise can virtually be arbitrary, but, independently of it, the user must be able to add test perturbations through the input channel. Based on a finite set of observations, we suggest a new procedure which can be used in adaptive control schemes. It has been developed in the general framework of "counting of leave-out sign-dominant correlation regions" (LSCR), which is mostly being promoted by M. Campi et al. for identification problems. The procedure returns confidence regions which are guaranteed to contain true parameters with a user-chosen probability. The theoretical results are illustrated by an example of a nonminimum-phase second-order plant.