Estimation of parameters in linear control systems

1. There is now a wealth of literature on the problem of optimal control of linear systems under a variety of conditions, constraints, and performance indexes. Whatever the criterion or performance index, however, the optimal control law invariably depends on the physical and statistical parameters of the system. These parameters are at best only partially known to the controller, so the problem of statistical estimation of the parameters, consistent with the over-all performance index, is a natural and significant problem for study. 2. Since modern control theory provides the motivation for this paper, let us quickly review some of its aspects for the unversed reader.