A Unified Approach to Recursive System Identification

A unified approach to recursively identifying ARMAX systems, Hammerstein systems, Wiener systems, and nonlinear ARX systems is presented, by which the problem is solved by two steps. First, the task of identification is transformed to a root-seeking problem by selecting a regression function, whose roots coincide with the estimated parameters, and by forming an available value called \observation” at each time. However, the resulting root-seeking problem is hardly to be solved by the classical Robbins-Monro (RM) algorithm. Instead, the stochastic approximation (SA) algorithm with expanding truncations (SAAWET) and its general convergence theorem (GCT) serve as the main tool. The second step of the unified approach is to verify conditions required by GCT. Reasonable conditions are respectively given for each system mentioned above, under which the estimates given by the recursive algorithms are strongly consistent.