Doulitsa Press Release Submission

News that change your days

A Hybrid Observer for a Distributed Linear System with a Changing Neighbor Graph. (arXiv:1706.04235v1 [cs.SY] CROSS LISTED)

[Submitted on 13 Jun 2017] Download PDF Abstract: A hybrid observer is described for estimating the state of an $m>0$ channel, $n$-dimensional, continuous-time, distributed linear system of the form $dot{x} = Ax,;y_i = C_ix,;iin{1,2,ldots, m}$. The system's state $x$ is simultaneously estimated by $m$ agents assuming each agent $i$ senses $y_i$ and receives appropriately defined…

[Submitted on 13 Jun 2017]

Download PDF

Abstract: A hybrid observer is described for estimating the state of an $m>0$ channel,
$n$-dimensional, continuous-time, distributed linear system of the form
$dot{x} = Ax,;y_i = C_ix,;iin{1,2,ldots, m}$. The system’s state $x$ is
simultaneously estimated by $m$ agents assuming each agent $i$ senses $y_i$ and
receives appropriately defined data from each of its current neighbors.
Neighbor relations are characterized by a time-varying directed graph
$mathbb{N}(t)$ whose vertices correspond to agents and whose arcs depict
neighbor relations. Agent $i$ updates its estimate $x_i$ of $x$ at “event
times” $t_1,t_2,ldots $ using a local observer and a local parameter
estimator. The local observer is a continuous time linear system whose input is
$y_i$ and whose output $w_i$ is an asymptotically correct estimate of $L_ix$
where $L_i$ a matrix with kernel equaling the unobservable space of $(C_i,A)$.
The local parameter estimator is a recursive algorithm designed to estimate,
prior to each event time $t_j$, a constant parameter $p_j$ which satisfies the
linear equations $w_k(t_j-tau) =
L_kp_j+mu_k(t_j-tau),;kin{1,2,ldots,m}$, where $tau$ is a small
positive constant and $mu_k$ is the state estimation error of local observer
$k$. Agent $i$ accomplishes this by iterating its parameter estimator state
$z_i$, $q$ times within the interval $[t_j-tau, t_j)$, and by making use of
the state of each of its neighbors’ parameter estimators at each iteration. The
updated value of $x_i$ at event time $t_j$ is then $x_i(t_j) =
e^{Atau}z_i(q)$. Subject to the assumptions that (i) the neighbor graph
$mathbb{N}(t)$ is strongly connected for all time, (ii) the system whose state
is to be estimated is jointly observable, (iii) $q$ is sufficiently large, it
is shown that each estimate $x_i$ converges to $x$ exponentially fast as
$trightarrow infty$ at a rate which can be controlled.

Submission history

From: Lili Wang [view email]


[v1]
Tue, 13 Jun 2017 19:38:31 UTC (96 KB)

About Post Author

WP2Social Auto Publish Powered By : XYZScripts.com