Research On System Identification Based On Linear Programming Method

In recent 20 years, System identification as one of the important ways to establish mathematical model of the controlled object has been developed rapidly and become one of the automatic control theory, a very active and important branch.Least-squares (LS) is a classic method of data processing, as early as the end of the eighteenth century, it was put forward in the calculation of planetary trajectory by Gaussian. Since then, the Least-square method has become the main parameters estimation method according to the experimental data. The Least-square method is simple and easy to be understood. the principle of simple programming is not difficult, so it received attention and a wide range of applications. Which was known as the cornerstone of the estimation theory.The traditional system identification methods have been the development of sound teaching, but there are still some deficiencies and limitations: First, the Least square method and the related improved algorithms are based on the assumptions that use continuous derivative of the smooth search space and gradient information to search, so it is possible to fall into local minimum points, unable to get satisfactory results. Secondly, the Least-squares method requires the relatively low level of input disturbances, and it have poor robustness and large amount of calculation in the identification process, therefore, in view of the above, we need to seek other method to compensate for it. This paper presents two new system identification methods: the simplex method and interior-point method of linear programming. The three methods are used for ARX model parameters identification, The results of simulation ,on one hand, confirms the stronger robustness and effectiveness of the simplex method and interior-point method of linear programming when the input disturbance in the case of higher levels; on the other hand, it also shows that the computational complexity and convergence rate of interior-point method is better than the least single LS method or the simplex method. The advantages and disadvantages of three methods and the application range are also in the experimental analysis.