Recursive Identification Methods For Feedback Nonlinear Systems Under White Noise Disturbances

In our actual life, nonlinear systems can be found almost everywhere, and the systemsare in feedback state. The identifcation algorithms for linear systems are more and moremature. The theory of how to extend the linear systems into the nonlinear systems is thesubject of the thesis. Furthermore, it has become a very active and important branchof automatic control theory. Under the condition of the modelling and simulation, thethesis studies and derives the recursive identifcation algorithms for the feedback nonlinearsystems. The theory in algorithm for the nonlinear systems identifcation is meaningfuland valuable, the main contributions can be obtained as follows.1. For the controlled autoregressive feedback nonlinear systems under white noise dis-turbances, a recursive least squares using the decomposition technique identifcationalgorithm and a recursive least squares identifcation algorithm are developed. Thebasic idea is to compute the unknown terms in the information vector. Those un-known noise terms which are included in information vector are replaced with theparameter estimates at their preceding time by means of the interactive estimationtheory in the hierarchical identifcation principle.2. Based on the idea above and the gradient search principle, a stochastic gradientalgorithm using the decomposition technique is suggested. In order to improve theaccuracy of identifcation algorithm, the multi-innovation stochastic gradient algorith-m with the decomposition technique is derived by extending the innovation length.Finally, the simulation results are given.3. For the output error feedback nonlinear systems under white noise disturbances, basedon the hierarchical identifcation principle, an auxiliary model recursive least squaresusing the decomposition technique algorithm and an auxiliary model recursive leastsquares algorithm are proposed, and the calculation of the former one is smaller.Furthermore, an auxiliary model multi-innovation stochastic gradient algorithm withthe decomposition technique is ofered, based on the multi-innovation identifcationtheory and auxiliary model idea. The algorithm improves the identifcation accuracyby extending the scalar innovation.4. Auxiliary model identifcation method has been generalized in the identifcation forthe input nonlinear and output error type systems. For the unknown terms in in-formation vector of the identifcation model, the paper establishs an auxiliary modelof the system with measurable information, and substitute the uncertain variables of system with the auxiliary model output (namely, unknown term of the informationvector). At last, this thesis gives the detailed derivation procedure and the simulationresults proved the validity of proposed algorithms.In summary, this thesis studies and derives the identifcation algorithms for feedbacknonlinear systems under white noise disturbances, the efectiveness of the algorithms isillustrated by Matlab simulations.