A method of estimating the rate of convergence of an adaptive observer

Currently there is no exact formula or algorithm for calculating the rate of convergence of the adaptive observer described in 1. and 2. below. In this paper, an algebraic numerical technique is described for producing such rates of convergence when the inputs and outputs of the system to be identified can be approximated by almost periodic functions. Results of simulation studies will be presented to show that this method can produce accurate estimates. The examples studied indicate that the rate of convergence of the observer is very sensitive to initial conditions and that the rate of convergence can be very slow even in simple cases. 1. J.S.C. Yuan and W. M. Wonhmn, Probing signals for model reference identification, IEEE Trans. Automatic Control, AC-22(1977), pp. 530-538. 2. K.S. Narendra and P. Kudva, Stable adaptive schemes for system identification and control, IEEE Trans. Systems, Man, and Cybernetics, SMC-4 (1974), pp. 542-560.