On The Ill-posed Problems In The Modeling Process Of Data-driven Control

Recently, with the development of computer technology, it is easy tostore and process data, this makes the use of data-driven modelingmethods possible. This method does not need to neither know the priorknowledge and basic rules of the actual system, nor analysis the internalmechanism in detail, just involving the input and output data in theindustrial production process. Therefore, it is suitable for complexindustrial modeling with high nonlinearity and uncertainty.Data-driven control method is merely makes use of outline andinline input-output data of controlled system and the knowledge obtainedfrom data process to design controller, also be the theoretical methoddirectly from data to controller, which makes the data-driven controlmethod has some limitations in use. In practical problems, the output ofthe system is unknown, and always accompanied by noise, while in themodeling process of Data-driven control, the condition number ofequations to be solved is too large, and always accomplished by ill-posedphenomenon, which makes the calculated results meaningless.This thesis focuses on the ill-posed problems in the modelingprocess of data-driven control methods. The main work completed issummarized as follows:1. Considering the shortcoming of poor anti-interference ability inthe multiple linear regression process, we use Tikhonov regularizationmethod, which is a classical method in solving the ill-posed problems,adding regularized functional in objective functional to solve ill-posedproblems. In the end, Bayesian method is used to calculate theregularization parameter and the specific algorithm is presented.Simulation results show the effectiveness of the method.2. Considering the ill-posedness of the consequent part of thefuzzy identification process, Tikhonov regularization method is applied,introducing regularized functional in minimizing functional to solveill-posed problems. Furthermore, Bayesian method is used to calculatethe regularization parameter.Simulation results show that this method haswell-posedness.