On The Data-driven Control Method-a Total Least Squares Approach

In recent years, the control method based on data hasattracted the attention of many scholars, and it became to be one of theresearch hotspot in the field of control. Due to the rapid development ofindustrial technology, modern industrial processes are becoming moreand more complex. And the scale is becoming larger and larger. Such aschemical industrial processes, network, aerospace, etc. It makes that it ishard to construct or establish an effective and accurate physical model todescribe the dynamic system. On the other hand, with the development ofcomputer science, especially in computing power and storage, and highquality through process tools reliable measurement, etc., makes thedata-driven perspective to study the industrial process.However, most of the data stored in the computers are artificialmeasurement. Inevitably，these data are disturbed by the outside noise.Due to the noise, which may led system solutions appeared in the processof searching for the optimal control strategy of the control consequencesto be ill-posedness. In order to solve this problem, in the process ofsolving matrix equations’ solution, this paper used total least squaresapproach, and combined the idea of Tikhonov regularization, makingsimulation results meet the expected control targets better. This papermainly focus on iterative learning control based on output data, adaptivedynamic programming and discrete singular systems that exist in thediscomfort qualitative conducted a series of research, and achieved somegood results. Three specific aspects of the study are as follows:1. The research in the iterative learning control based on the output dataof the ill-posed problemIn order to achieve tracking, during the process of searching for theoptimal control sequence, further taking noise disturbance into account inthe coefficient matrix of the system. By using total least square approach,and combined with the idea of Tikhonov regularization, reduced the errorcaused by the noise influence and avoided ill-condition solution. Bycomparing with the simulation results of other approaches, furtherillustrate the validity of the approach presented in this paper. 2. The research based on the output data of ill-posed problems in adaptivedynamic programmingIn solving the problem of the optimal control input sequence, at thesame time, considering the both sides of coefficient matrix equationexisted outside-noise disturbance. Adopting the total least squaresapproach based on Tikhonov, making both the output and states of systemachieve stable state. Through the simulation results and compared withthe other two methods, further illustrating the superiority of the methodpresented in this paper.3. The research about ill-posed problems in discrete singular systemsPromoting the problem that studied in the second aspect to thediscrete descriptor system, adopting the same approach, both the outputof the system and the state achieve stable state in the limited iterations.Through the simulation results, which illustrate the approach proposed inthe paper has a wider applicability.