5 research outputs found
A Hybrid Observer for a Distributed Linear System with a Changing Neighbor Graph
A hybrid observer is described for estimating the state of an channel,
-dimensional, continuous-time, distributed linear system of the form
. The system's state is
simultaneously estimated by agents assuming each agent senses and
receives appropriately defined data from each of its current neighbors.
Neighbor relations are characterized by a time-varying directed graph
whose vertices correspond to agents and whose arcs depict
neighbor relations. Agent updates its estimate of at "event
times" using a local observer and a local parameter
estimator. The local observer is a continuous time linear system whose input is
and whose output is an asymptotically correct estimate of
where a matrix with kernel equaling the unobservable space of .
The local parameter estimator is a recursive algorithm designed to estimate,
prior to each event time , a constant parameter which satisfies the
linear equations , where is a small
positive constant and is the state estimation error of local observer
. Agent accomplishes this by iterating its parameter estimator state
, times within the interval , and by making use of
the state of each of its neighbors' parameter estimators at each iteration. The
updated value of at event time is then . Subject to the assumptions that (i) the neighbor graph
is strongly connected for all time, (ii) the system whose state
is to be estimated is jointly observable, (iii) is sufficiently large, it
is shown that each estimate converges to exponentially fast as
at a rate which can be controlled.Comment: 7 pages, the 56th IEEE Conference on Decision and Contro