Recursive Parameter And State Estimation For Bilinear State-Space Systems

Bilinear systems widely exist in the industrial processes,such as fluid heat exchange and nuclear fission can be modeled by the bilinear state-space system.Considering some practical factors such as the unmeasurable states and the delay of the output measurement,this thesis focuses on the joint recursive parameter and state estimation methods,which has important theoretical and practical significance.The main research contents are as follows.1.For the state estimation of bilinear state-space systems,because of the special system structure,the considered system can be transformed into linear parameter varying models.Then based on the Kalman filter,the state estimator of the bilinear statespace system is derived.Moreover,a bilinear state estimation algorithm based on the delta operator is proposed by minimizing the covariance matrix of the state estimation errors.The theoretical analysis and numerical simulation show the effectiveness of the presented algorithm.2.For the bilinear state-space systems with white noise,the identification difficulty is that the system contains unknown parameters,unknown states and the product relation of the unknown parameters,unknown states and control variables(bilinear term).Faced with the problem,this thesis uses the interactive estimation theory to compute the joint estimation of parameters and states.When computing the unknown parameters,the unknown states in the identification model are replaced with their estimates.Based on the estimated parameters,the bilinear state observer can be constructed.Then this thesis presents the bilinear state observer based multiinnovation stochastic gradient identification algorithm to realize the joint recursive parameter and state estimation.3.For the bilinear state-space systems with colored noise,in order to reduce the effect of the noise on the parameter and state estimation,the data filtering method is used to filter the input and output.Then this thesis proposes the bilinear state observer based multi-innovation extended stochastic gradient identification algorithm to improve the parameter estimation accuracy.The effectiveness of the algorithm is verified by the numerical simulation.4.For the large-scale bilinear state-space systems with high dimension and many parameters,which lead to the large amount of computation in the identification procedure.In order to solve this problem,the hierarchical identification principle is used to decompose the original system into several sub-systems with low dimension.Then by using the bilinear state observer to estimate the unknown states,this thesis presents the bilinear state observer based multi-stage generalized extended least squares identification algorithm to improve the computational efficiency.Based on the stochastic martingale convergence theorem,the convergence performance of the proposed algorithm is analyzed under the persistent excitation condition.5.For the bilinear state-space systems with time-delay,considering the unknown timedelay,the original identification model is transformed into the augmented identification model.Then the bilinear state observer based recursive least squares algorithm and hierarchical least squares algorithm are presented for the state and parameter estimation.Once the augmented parameter estimate is computed,the time-delay can be determined through setting a threshold,so as to realize the joint parameter,state and delay estimation.Finally,the effectiveness of the algorithm is verified by the Monte Carlo simulation.In this thesis,the numerical simulation of the proposed joint parameter and state estimation is given to verify the effectiveness.The computational complexity of some presented algorithms is compared to show the computational efficiency.The convergence performance for some presented algorithms is analyzed based on the martingale convergence theorem.