Least Squares Learning Identification For Time-varying Systems Over A Finite Interval

The recursive least squares identification algorithm can be used in online identifica-tion, and has a fast convergence speed, and it has capability of achieving the convergenceresults, even under weaker condition, have been receiving ever increasing attention. Thecurrently researches on least squares identification algorithms are mainly focus on the timeinvariant system. However, the recursive least squares can hardly identify the time-varyingparameters in processing time-varying systems. Therefore, researchers have been workingon the upper bound of time-varying parameter estimation error. Thesis aims to exploretime-varying systems identification over a Finite Interval. Propose several learning algo-rithms for identifying time-varying systems repetitively operate over a finite interval. Themain work includes following4aspects:1. Elaborate current research status on the field of system identification. Take a classicoverview on some typical system identification methods. We focus on the learning identifi-cation among them as for it is highly relevant to my paper.2. The recursive algorithm and learning algorithm of the ARX model is proposed. Itshowed that the recursive algorithm has a good ability to track the invariant systems andsuits to online identification. Meanwhile, the learning algorithm can achieve repetitiveconsistence estimate to time-varying parameters in complex dynamic systems over a finiteinterval under white noise condition.3. Two learning algorithms including iterative learning identification and periodicallylearning identification are proposed based on ARMAX model. Furthermore, we analysisconvergence of the learning identification algorithm under colored interference condition,based on the current learning identification research. The results show that the algorithmcan achieve effective track on any parameters in time-varying system over a finite inter-val. Numerical results prove the algorithm can obtain effective estimate to time-varyingparameters under colored noise condition. 4. Iterative learning algorithms are proposed based on several common output errormodels in engineering applications, including OE, OEMA, OEAR and Box-Jenkins mod-els via building corresponding auxiliary models. In addition, numerical results prove iter-ative learning algorithms can obtain the consistent estimate on time-varying parameters indynamic system.In this thesis, the learning identification algorithms on time-varying systems are basedon the repetitively operate over a finite interval. The variation of time-varying parametersare static along the repeat axis. That is, the parameters iteration are independent. Based onthis law, parameters estimation can converge to the true values.