| 摘要: |
|
| 关键词: |
| DOI：10.1007/s11768-010-0020-0 |
| Received:January 20, 2010Revised:January 20, 2010 |
| 基金项目:The first author was partly supported by Conacyt; the second author was partly supported by NSF award under the FIND initiative CNS 0626380. |
|
| Limitations in tracking systems |
| Ivan Lopez HURTADO,Chaouki T. ABDALLAH,Sudharman K. JAYAWEERA |
| (Northern New Mexico College;University of New Mexico) |
| Abstract: |
| In this paper, we obtain information theoretical conditions for tracking in linear time-invariant control
systems. We consider the particular case where the closed loop contains a channel in the feedback loop. The mutual
information rate between the feedback signal and the reference input signal is used to quantify information about the
reference signal that is available for feedback. This mutual information rate must be maximized in order to improve the
tracking performance. The mutual information is shown to be upper bounded by a quantity that depends on the unstable
eigenvalues of the plant and on the channel capacity. If the channel capacity reaches a lower limit, the feedback signal
becomes completely uncorrelated with the reference signal, rendering feedback useless. We also find a lower bound on the
expected squared tracking error in terms of the entropy of a random reference signal.We show a misleading case where the
mutual information rate does not predict the expected effect of nonminimum phase zeros. However, mutual information rate
helps generalize the concept that there is a tradeoff when tracking and disturbance rejection are simultaneous goals, and a
constraint communication channel is present in the feedback loop. Examples and simulations are provided to demonstrate
some of the results. |
| Key words: Limited channel capacity Tracking systems Constraint feedback |
