Instrumental variable‐based multi‐innovation gradient estimation for nonlinear systems with scarce measurements

Abstract

Summary This article considers the identification problems of nonlinear systems with scarce measurements by using the instrumental variable technique. When the product of the instrumental matrix and the information matrix is a nonsingular matrix and the weak persistent excitation condition about the instrumental vector is true, the obtained parameter estimates can be unbiased consistent estimates. The key is how to choose the instrumental variables. Difficulty arises in that the system outputs are unavailable. By applying the negative gradient search, a recursive instrumental variable‐based gradient algorithm is derived to estimate the parameters of the nonlinear systems with missing observed data. Moreover, the multi‐innovation identification theory is introduced to further improve the parameter estimation accuracy. The simulation results illustrate that the proposed methods are effective.

Auxiliary model‐based interval‐varying maximum likelihood estimation for nonlinear systems with missing data

“…Firstly, the parameter estimation errors of the ML-IV-RLS algorithm are shown in Figure 1 with 𝜎 2 = 0.05 2 , n * s = 1 and n * s = 2, respectively. Secondly, the parameter estimation errors of the ML-IV-RLS algorithm and the IV-RLS algorithm are shown in Figure 2 with 𝜎 2 = 0.05 2 .…”

“…Thirdly, applying the ML-IV-RLS algorithm in ( 9)-( 20) and the IV-RLS algorithm to estimate the example system, the parameter estimates and their errors 𝛿 ∶= || θ(n s ) − 𝜽||∕||𝜽|| are shown in Tables 1-3 with 𝜎 2 = 0.05 2 and 𝜎 2 = 0.11 2 , respectively, and their parameter tracking curves s are shown in Figures 3 and 4. The ML-IV-RLS algorithm prediction values versus n s are shown in Figure 5.…”

“…Model parameter estimation plays a crucial role in the analysis and design of control systems. 1,2 In practice, due to the limitations of hardware equipment, economic conditions and environmental factors, it is difficult to obtain observation data from some sampling points, which means data is missing. 3,4 The identification of missing data systems has attracted much attention.…”

“…Accurate modeling is very important for timely monitoring and effective control of industrial processes. Model parameter estimation plays a crucial role in the analysis and design of control systems 1,2 . In practice, due to the limitations of hardware equipment, economic conditions and environmental factors, it is difficult to obtain observation data from some sampling points, which means data is missing 3,4 .…”

“…The ML-IV-RLS estimate θ versus s with 𝜎 2 = 0.112 . The prediction values versus n s of the ML-IV-RLS algorithm with 𝜎 2 = 0.05 2 .…”