Properties Of Interpolated Mapping System Identification With Regard To Linear Systems

✍ Scribed by F.H. Bursal; B.H. Tongue

• Publisher: Elsevier Science
• Year: 1993
• Tongue: English
• Weight: 320 KB
• Volume: 168
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1006/jsvi.1993.1372

✦ Synopsis

In this paper, we present some analytical results regarding the performance of a recently introduced method of system identification based on Interpolated Mapping (IM). The results are restricted to linear systems even though the method is intended, and appears to work well, for non-linear systems. The algorithm assumes the presence of sampled values of system states, based on which a map is defined that takes initial conditions on a grid in the state space to their respective images. Using the map with time step (T), maps with time steps (T / 2, T / 4, \ldots), are found; ultimately, when the time step has become small enough, difference quotients furnish good estimates of the derivatives of the states. A function fit to these derivatives furnishes the equations of motion of the system. The methodology of IM is used to approximate the images of states that are not on the primary grid.

We show in this paper that the IM approximation is actually exact when the underlying system is linear. Moreover, we derive relations between the dynamics of the underlying system and those of the iteration procedures used in the new identification algorithm. This development is used to verify the convergence characteristics of the method, and to select proper values for the parameters that appear in the iterative corrections.