# Controlling a system with delayed measurements

Assume I have a rather simple system I want to control, but all sensor measurements exhibit considerable time delay, i.e.:

$z_t = h(x_{(t-d)}) \neq h(x_t)$

With my limited knowledge about control, I could imagine the following setup:

• One observer estimates the delayed state $x_{(t-d)}$ using control input and (delayed) measurements.
• A second observer uses the delayed observer's estimate and predicts the current state $x_t$ using the last control inputs between delayed measurement and current time.
• The second observer's estimate is used to control the system.

Can I do any better than that? What is the standard approch to this problem? And is there any literature or research about this topic?

• I think the approach is correct and something tells me the second step is done with a Markov chain. – Shahbaz Jun 13 '14 at 14:46
• How long is the delay relative to your sample rate? There is an interesting paper at scholarworks.sjsu.edu/cgi/… that analyzes behavior of PID loops in systems with high time delay and describes a technique for tuning for these systems. – Jason C Jun 17 '14 at 20:17
• Thanks for the various pointers. In addition to what was posted in the answers and comments, I also found this paper helpful. – sebsch Jun 23 '14 at 13:17