Recursive Least Squares With Variable-Direction Forgetting: Compensating for the Loss of Persistency [Lecture Notes]

The ability to estimate parameters depends on two things: identifiability [1] (which is the ability to distinguish distinct parameters) and persistent excitation (which refers to the spectral content of the signals needed to ensure convergence of the parameter estimates to the true parameter values) [2]-[4]. Roughly speaking, the level of persistency must be commensurate with the number of unknown parameters. For example, a harmonic input has 2D persistency and thus can be used to identify two parameters, whereas white noise is sufficiently persistent for identifying an arbitrary number of parameters. Within the context of adaptive control, persistent excitation is needed to avoid bursting [5]; recent research has focused on relaxing these requirements [6]-[8].