Recursive Identification Of Bilinear State Space Systems

Determining the system mathematical model is the basis of the control problem,only to understand the motion model of the system,can we better analyze its behavioral characteristics,understand its law of motion,design its control strategy or estimate its motion states.As an experimental statistical method,system identification is very important to obtain the system model in the process of industry.After a lot of consulting literature,aimed at the bilinear system,this paper derives in detailed its identification model and some effective identification algorithms,the main work is summarized as follows:1.For the bilinear state space system with white noise,this paper obtaines the identification model of bilinear system by the equivalent transformation of the state vector and control vector.This model eliminates the bilinear terms in the system which add the difficulty to identification,and makes the information vector contain the observed data only,after transformation,the system can be approximated as an equation error(CAR)model.For this model,this paper adopts the recursive least squares algorithm and the stochastic gradient algorithm to identify this model,in the meantime,estimating the system real-time states.This paper also gets the forecast output by using the eatimated parameters,and comparing with the true output.In order to improve the convergence rate and accuracy of stochastic gradient identification algorithm,extending the innovation vector to derive multi-innovation identification algorithm is finished.2.This paper derives the identification methods of equation error bilinear system and output error bilinear system,and discusses the recursive least squares identification algorithm and the multi-innovation stochastic gradient identification algorithm.In order to further improve the identification accuracy,this paper decomposes the bilinear parameter system into several identification subsystems based on the hierarchical identification principle,and combines the decomposition ideas with the recursive least squares and multi-innovation stochastic gradient algorithms by adopting the interactive estimation method to identify the bilinear system.The simulation results show that the decomposition algorithm can decrease the cost of the computation and ensure the effectiveness of the algorithm.At the end of this paper,the summary and prospects are given.At the same time,this paper introduces some difficulties in the research of bilinear system identification and further valuable research fields.