View source for Towards a Packet-Based Control Theory - Part I: Stabilization over a Packet-Based Network

{{HTDB paper
| authors = Ling Shi and Richard M. Murray
| title = Towards a Packet-Based Control Theory - Part I: Stabilization over a Packet-Based Network
| source = 2005 American Control Conference (ACC)
| year = 2004
| type = Conference Paper
| funding = NSF/ITR
| url = http://www.cds.caltech.edu/~murray/preprints/sm05b-acc.pdf
| abstract = 
In this paper, we study the classical problem
of stabilizing a Linear Time Invariant (LTI) system in a
packet-based network setting. We assume that the LTI system
is unstable but both controllable and observable. The state
information is transmitted to the controller over a packetbased
network. We also assume that there is a perfect link
from the controller to the plant. We give a set of sufficient
conditions under which the system can be stabilized for a
given data rate C. In particular, these conditions can yield an
upper bound on the minimum C for which the system can
be stabilized. A recursive encoding-decoding scheme and an
associated control law are proposed to achieve stability for
rate exceeding this bound. An optimal bit allocation problem
is investigated in which we ask about how to allocate the
bits in a single packet for a subsystem of a general LTI
system such that a minimum upper bound on the data rate is
achieved.We then formulate the optimal bit allocation problem
as a Linear Matrix Inequality (LMI) optimization problem
which can be solved efficiently using standard Semi-definite
Programming (SDP) solvers. Examples and simulations are
given to demonstrate the results.
| flags = 
| tag = sm05b-acc
| id = 2004z
}}