System Identification Methods Based On Decomposition

With the development of modern industrial process is speeding up, the scale of theresearch object in the control science is becoming bigger and the variables are more andmore, the computational costs of the identifcation method are becoming large. Therefore,how to improve the computational efciency of identifcation methods and reduce thecalculation amount is a new research topic to system identifcation. In this paper, bythe decomposition technique, we study the least square iterative identifcation method oflinear systems, nonlinear systems and multivariable systems. It has theory signifcanceand the application value.The work of this thesis includes:1. For the linear fnite impulse response moving average system, we give the leastsquares iterative identifcation algorithm. In order to reduce the computational costs, wepropose the matrix decomposition based least squares iterative identifcation algorithm byblock matrix inversion formula and the information matrix to be decomposed to inverse.The proposed algorithm has less computation costs than the least squares iterative iden-tifcation algorithm. Then we extend the proposed identifcation algorithm to controlledautoregressive autoregressive moving systems and Box-Jenkins systems.2. For the fnite impulse response autoregressive system, we give the iterative leastsquares identifcation algorithm. And we develop the matrix decomposition based itera-tive least square identifcation algorithm and the model decomposition based least squareiterative identifcation algorithm. Analysis shows that the model decomposition basedleast square iterative identifcation algorithm has minimum computational costs, the ma-trix decomposition based least square iterative identifcation algorithm has the smallercomputational costs, the least square iterative algorithm has the maximum computationalcosts.3. For multivariable fnite impulse response moving average systems, accord to over-parameterization identifcation model, we deduce the least squares iterative identifcationalgorithm and the matrix decomposition based least squares iterative identifcation al-gorithm with the small computational costs. And we extend the method to the inputnonlinear output error systems and output nonlinear systems and propose correspondingmatrix decomposition based least squares identifcation algorithm.4. In order to reduce the computation amount of the identifcation algorithm based onthe overparametrization identifcation model based, we propose the matrix decompositionbased least squares iterative for Hammerstein controlled autoregressive systems by usingthe key variable separation technology, the proposed algorithm has the smaller calculation amount.5. For the multivariable fnite impulse response moving average system, we deducethe matrix parameters case iterative least squares algorithm based on matrix decompo-sition. For the multivariable output error moving average system, combined with theauxiliary model identifcation theory and model equivalence principle, we propose leastsquares iterative identifcation algorithm based on matrix decomposition. This algrithmis extended to multivariable controlled autoregressive autoregressive moving average sys-tems and the multivariable Box-Jenkins system and we present the least squares iterativealgorithm based on the auxiliary model and the matrix decomposition.In summary, this thesis mainly studies the decomposition based identifcation method.Simulation results demonstrate the efectiveness of the proposed algorithm. The analysisof calculation costs shows the proposed algorithm has the less computational costs thanthe least squares iterative algorithm.