Research Of Interval Robust Identification Of System With Uncertainty

Research of the relations between identification and control is one of the most challenging fields in the control theory. The traditional identification methods are all in fact statistical, aiming at finding the parameter estimate point, which is thought to generate the observation data most probably. The robust identification methods studied here, however, views the system uncertainty as premise, and aims at finding the so-called Parameter Feasible Set (PFS), which is no longer a parameter point, but a set of feasible parameter points. PFS represents the system抯 uncertainty. Robust identification is essential for the robust control. Only when the robust identification problem is solved, can the robust control theory be put into practice. Based on the bounded errors assumption, we study three algorithms in this paper. Polyhedron Algorithm reduces into finding its finite vertexes representing the PFS. The exact description of the polyhedron is often too complex for intended use with the increase of measurement, and, thus coarser algorithms, which can be performed recursively and make sure that the exact PFS is included in it as tightly as possible, is of practical interest. Two coarser algorithms different from the Fogel-Huang抯 ellipsoid algorithm are presented here. Linear Programming Algorithm takes advantage of the constraints arising from the bounded error assumption and then gets the PFS. The Uncertainty Interval of the parameters to be identified can be obtained by optimizing an objective with finite constraints, which turns Out to be a linear programming problem for a linear system. And based on the idea of using only limited length of data, we present a recursive algorithm to solve the linear programming. When only a point in the PFS is needed, we can use the center of PFS or adopt the traditional Least Square (LS) method. We present a new recursive batch LS identification algorithm with constant observation matrix dimension. All the simulations of the three algorithms are made with MATLAB language. Based on the general principles of structure identification, we study the structure -selecting problem in robust identification and put forward two practical methods. Taking advantage of Interval Math, we analyzed the stability and output prediction problems in interval model, and their use in the electronic gauge system. Other related problems, such as influence of structure uncertainty, are also analyzed in this paper.