ABSTRACT
CONTENTS 2.1 Parameter Estimation as Root-Seeking for Functions . . . . . . . . . . . . . . . . 44 2.2 Classical Stochastic Approximation Method: RM Algorithm . . . . . . . . 46 2.3 Stochastic Approximation Algorithm with Expanding Truncations . . . 51 2.4 SAAWET with Nonadditive Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 2.5 Linear Regression Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 2.6 Convergence Rate of SAAWET . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 2.7 Notes and References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
A practical systemmay be modeled as to belong to a certain class of dynamic systems with unknown parameters, for example, the class of linear stochastic systems with input uk and output yk. Then, the task of system identification is to determine the unknown system coefficients and systems orders. In the linear case, i.e., in the case where the system output linearly depends upon the unknown parameters, the leastsquares (LS) method is commonly used and often gives satisfactory results. This will be addressed in Chapter 3. However, in many cases a system from a class is defined by parameters nonlinearly entering the system, and the LS method may not be as convenient as for the linear case. Then the task of system identification is to estimate unknown parameters and the nonlinearity on the basis of the available system inputoutput data set Dn {uk, 0≤ k ≤ n−1, y j, 0≤ j ≤ n}.
