Recursive parameter estimation methods and convergence analysis for a special class of nonlinear systems

Abstract

Summary This paper is concerned with the joint estimation of states and parameters of a special class of nonlinear systems, ie, bilinear systems. The key is to investigate new estimation methods for interactive state and parameter estimation of the considered system based on the interactive estimation theory. Because the system states are unknown, a bilinear state observer is established based on the Kalman filtering principle. Then, the unavailable states are updated by the state observer outputs recursively. Once the state estimates are obtained, the bilinear state observer–based hierarchical stochastic gradient algorithm is developed by using the gradient search. For the purpose of improving the convergence rate and the parameter estimation accuracy, a bilinear state observer–based hierarchical multi‐innovation stochastic gradient algorithm is proposed by expanding a scalar innovation to an innovation vector. The convergence analysis indicates that the parameter estimates can converge to their true values. The numerical example illustrates the effectiveness of the proposed algorithms.

Fuzzy Boost Classifier of Decision Experts for Multicriteria Group Decision-Making

“…en the multicriteria group decision-making method will be efficient and intelligent. e proposed method in this paper can combine other estimation algorithms [62][63][64][65] to study the multicriteria decisionmaking problems.…”

Fault Detection and Identification Method for Quadcopter Based on Airframe Vibration Signals

“…Additionally, more fault modes, such as sensor fault, are expected to be incorporated into the established model. The proposed method in this paper can combine the iterative schemes [ 48 , 49 , 50 , 51 , 52 , 53 ] and recursive schemes [ 54 , 55 , 56 , 57 , 58 , 59 , 60 , 61 , 62 ] to study the parameter identification problems of linear and nonlinear stochastic systems with colored noises [ 63 , 64 , 65 , 66 , 67 , 68 , 69 , 70 , 71 ] and to present highly efficient fault detection methods that can also be applied to the literature.…”

Variational Bayesian identification for bilinear state space models with Markov‐switching time delays

“…35,36 In this article, we adopt the state observer to estimate system states, which is simpler in structure but can also achieve good performance. According to the considered bilinear state space model, the following bilinear state observer is designed to generate the states: [37][38][39] x t+1 = Ax t + Bx t u t + gu t .…”

“…A random binary signal with amplitude of 1 is added on q c (t) to generate the input sequence. Using the differential equation in (38) and (39) to generate the output C A (t), which is manually added with a Markov-switching time delay at Thousand sets of input data, output data and time delay data are displayed in Figure 5. The purpose of the simulation is to establish a bilinear state space model to describe the dynamic relationship between the input q c and output C A by using the proposed algorithm.…”