Convergence rate analysis of a multivariable recursive least squares parameter estimator

Control design of complex systems offer many challenges, particularly under system uncertainty. System identification, and in particular, parameter estimation is one of the crucial steps for many control strategies requiring a reasonable system model. Then the issue becomes one of selecting the parameter identifier in such a way that convergence can be obtained within a relatively fast period while the control is compensating under uncertainty. In this paper, a convergence rate analysis procedure is developed for multivariable parameter identification. The method allows the designer to select the appropriate initial conditions in order to satisfy a desired convergence rate through an error weighting matrix. Further, this paper develops an exact continuous-time solution in the recursive least squares problem and relates the results to the classical discrete-time case; time-scaling and traditional discrete recursive approaches are shown to be appropriate approximations to this continuous-time result. Finally, the parameter identifier procedure is applied to an example to illustrate the effects of selecting the initial auxiliary matrix to satisfy convergence and the effects of time-scaling on discrete-time and continuous time recursive least squares estimation.