Minimal K-step event observation policy for on-line observability of discrete event systems

In practical systems, in order to save energy of sensors and the bandwidth of communication networks which often are critical resources, we need to activate the sensors and use the communication networks as little as possible. Such problem can be formulated as a minimal event observation problem with discrete event system framework. State estimation is usually implemented on-line and how to find a minimal on-line event observation policy becomes meaningful. Observablity is an important property of state estimation for supervisory control and a minimal event observation policy which changes the observable event set whenever there is an output has been proposed. However, If the occurrences of observation events are frequent, then we need to activate/inactivate the smart sensors frequently. Frequently activating/inactivating the smart sensors need more communication resources and may do damage to the smart sensors. So we sometimes need to make a tradeoff between minimal event observation and frequency of changing the observable event set dynamically. Here we propose a minimal K-step event observation policy. That is, we change the observable event set dynamically after we observe K observable events occurred. By such way, we can change the state of the sensors much less and such policy can largely reduce the communication data between the observer and the sensors when the observer runs.