Comparisions And Studies Of Identification Methods For Multivariable Systems: Ⅰ

Along with the development of modern industry, industrial systems no longer limit to the single-variable system, but to the multivariable systems with complex structure. Therefore, this thesis is not only significant in theory, but also potentially valuable in applications. The thesis bases on the project "Study of Modelling and Identification of a Class of Nonlinear Systems (The National Nature Science Foundation of China 60574051)". This thesis is a kind of basal research and have meaning both in thearoy and applications. After correlative references are refered by the author, the convergence properties and computation load of the methods propesed are analysed. After a deep research, the innovation research results in the thesis are as follows.1. For the multivariable system, this thesis proposes the stochastic gradient algorithm and subsystem stochastic gradient algorithm based on gradient search principle, and compared with the hierarchical stochastic gradient algorithm in the computation load and convergence properties, the hierarchical stochastic gradient algorithm has the least computation load and highest efficiency among the three algorithms, but the parameter estimation performance is situated between the stochastic gradient algorithm and the subsystem stochastic gradient algorithm.2. The thesis also proposes the gradient iteration algorithm and subsystem gradient iteration algorithm using iteration technique, and compared with the hierarchical gradient iteration algorithm, the performance of the three algorithms are similar to the performance of the above algorithms, but the value of the convergence factor affects the convergence of the algorithms, for the definite system, the convergence factor is larger, the parameter estimation error is smaller. Finally, we compare these algorithms by a simulation example.3. Based on the studies of the multivariable system, the thesis proposes subsystem least squares algorithm, compared with the existing least squares algorithm and hierarchical least squares algorithm, the performance of the algorithm is close to the others, but the computation load of the hierarchical least squares algorithm is least and the second is subsystem least squares algorithm.4. For the multivariable system, the thesis also proposes the least squares iteration algorithm and hierarchical least squares iteration algorithm using least squares iteration technique, compared with the existing hierarchical least squares iteration algorithm, the performance of the algorithms are close to the others, but the computation load of the hierarchical least squares iteration algorithm is least. A simulation example is given. 5. For the subsystem stochastic gradient algorithm above, reduce the coupled variable through decomposing the algorithm, then proposes the subsystem stochastic gradient coupled algorithm, which avoids repeating estimation and reduces computation load, and a simulation example is included.6. The least squares algorithm has huge computation load, in order to reduce the computation, the thesis unifies the subsystem decomposition thought and hierarchical identification principle, proposes the subsystem least squares hierarchical algorithm, this algorithm reduced the computation load, the analysis indicates that the parameter estimation error given by the proposed algorithm converges to zero under the persistent excitation, and the simulation result indicates that the algorithm proposed is effective.7. Unifying the multi-innovation theory and hierarchical principle, this thesis proposes hierarchical multi-innovation stochastic gradient identification algorithm and hierarchical multi-innovation least squares identification algorithm. Because the multi-innovation could suppress the influence of the bad data to the parameter estimation, and have the good identification effect, the convergence rate and the identification precision of the algorithms have great improvement. Finally a simulation example is included.Finally, a simple conclusion of this thesis is given. The difficulties and further research are also simply outlined in the end, for example, some proposed algorithms are given without any proof, moreover, the identification algorithm are deserved study deeply in the complex industrial control process.