Application Of QR Decomposition Techniques In Recursive System Identification

Modern control theory consists of system identification,state estimation and control theory.System identification,part of system modeling,includes identifying the structure of mathematical model and estimating parameters of mathematical model. It plays a key role in both reality and theory to identify the structure and parameters of systems.The Least Square Method(LS),as an important approach of system parameter identification,has been widely applied to numerous fields and occasions,Realization method of LS is improved to accelerate identification by means of QR decomposition in this paper.QR decomposition of the block Hankel matrix is obtained though GIVENS transformation,on the basis of which the recursive identification for system parameters is derived.In this paper,the following aspects are mainly studied:Firstly,the Least Square method of system parameters identification is studied,and by analyzing the output equation model,the Least Square estimation result can be got; then the QR decomposition is introduced to make up for its disadvantages such as low precision and efficiency besides its bad numerical stability.The QR decomposition can be implemented by several methods,by contrast of which the simplest 2×2 GIVENS transformation is chosen as the avenue of decomposing to fit for the algorithm.Based on this,the modified recursive identification algorithm for Single-Input-Single-Output (SISO)system is derived and applied to the case of containing forgetting factor.The data-driven problem is also dealt with in detail later.By analyzing the mathematical model of MIMO system and changing the form of the transform function,the Multi-Input-Multi-Output(MIMO)system can equivalently be replaced by several Multi-Input-Single-Output subsystems.Thus the parameters identification for MIMO system can be implemented by identifying the subsystems.The inputs are the same for all subsystems,so by dealing with the input data and citing the results,the recursive identification for subsystem parameters can be rapidly derived. Then the identification for MIMO system parameters can be obtained rapidly by the subsystem method,the data driven problem also solved effectively.Considering the reality of the industrial process,it is not suitable to identify MIMO system by the subsystem method,so parameters of the MIMO system are identified as a whole.The Least Square Methods of the MIMO system are studied,the structure of the lower triangle matrix also included.Thus the recursive identification for the MIMO system parameters is realized by decomposing the block Hankel matrix through Givens transformation,and the data driven problem is also dealt with at last.