Stochastic Gradient Algorithm for Multi-input Systems Based on the Auxiliary Model

—This paper presents an auxiliary model based stochastic gradient parameter estimation algorithm for multiinput output-error systems by minimizing a quadratic cost function. The basic idea is to replace the unknown variables in the information vector with the outputs of an auxiliary model or estimated outputs and the analysis and simulation results indicate that the parameter estimates converge to their true values for persistent excitation input signals. The algorithm proposed has significant computational advantage over existing least squares identification algorithms. A simulation example is given. I. PROBLEM FORMULATION Consider a multi-input, single-output (MISO) system described by the output-error model [1], [2], as depicted in Figure 1, y(t) = 1 A(z) r i=1 Bi(z)ui(t) + v(t), (1) where u(t) = [u1(t), u2(t), · · ·, ur(t)]T ∈ Rr the system input vector, y(t) ∈ R1 the system output, v(t) ∈ R1 the observation white noise with zero mean, z−1 represents a unit delay ope...

• Type: Conference
• Year: 2008
• Where: CSSE
• Authors: Yuwu Liao, Xianfang Wang, Rui Feng Ding
• Keywords: Auxiliary Model, CSSE 2008, Parameter Estimates Converge, Parameter Estimation Algorithm, Software Engineering