Variational identification methods for linear dynamic systems and the local extrema problem

The problem of a large number of local extrema is considered. This problem arises when using “direct” methods to identify parameters of linear dynamical systems with finite-sample observations. A new class of variational (“indirect”) parameter estimators is defined by the projectivity property of matrix kernels in the objective function. The variational objective functions are constructed having the number of local extrema not greater than the number of elements in system matrices. We obtain conditions for consistency of variational estimates in the limit of large number of observations of independent finite-length trajectories.