7 research outputs found
Optimal Local and Remote Controllers with Unreliable Communication
We consider a decentralized optimal control problem for a linear plant
controlled by two controllers, a local controller and a remote controller. The
local controller directly observes the state of the plant and can inform the
remote controller of the plant state through a packet-drop channel. We assume
that the remote controller is able to send acknowledgments to the local
controller to signal the successful receipt of transmitted packets. The
objective of the two controllers is to cooperatively minimize a quadratic
performance cost. We provide a dynamic program for this decentralized control
problem using the common information approach. Although our problem is not a
partially nested LQG problem, we obtain explicit optimal strategies for the two
controllers. In the optimal strategies, both controllers compute a common
estimate of the plant state based on the common information. The remote
controller's action is linear in the common estimated state, and the local
controller's action is linear in both the actual state and the common estimated
state
Zero-Delay Rate Distortion via Filtering for Vector-Valued Gaussian Sources
We deal with zero-delay source coding of a vector-valued Gauss-Markov source
subject to a mean-squared error (MSE) fidelity criterion characterized by the
operational zero-delay vector-valued Gaussian rate distortion function (RDF).
We address this problem by considering the nonanticipative RDF (NRDF) which is
a lower bound to the causal optimal performance theoretically attainable (OPTA)
function and operational zero-delay RDF. We recall the realization that
corresponds to the optimal "test-channel" of the Gaussian NRDF, when
considering a vector Gauss-Markov source subject to a MSE distortion in the
finite time horizon. Then, we introduce sufficient conditions to show existence
of solution for this problem in the infinite time horizon. For the asymptotic
regime, we use the asymptotic characterization of the Gaussian NRDF to provide
a new equivalent realization scheme with feedback which is characterized by a
resource allocation (reverse-waterfilling) problem across the dimension of the
vector source. We leverage the new realization to derive a predictive coding
scheme via lattice quantization with subtractive dither and joint memoryless
entropy coding. This coding scheme offers an upper bound to the operational
zero-delay vector-valued Gaussian RDF. When we use scalar quantization, then
for "r" active dimensions of the vector Gauss-Markov source the gap between the
obtained lower and theoretical upper bounds is less than or equal to 0.254r + 1
bits/vector. We further show that it is possible when we use vector
quantization, and assume infinite dimensional Gauss-Markov sources to make the
previous gap to be negligible, i.e., Gaussian NRDF approximates the operational
zero-delay Gaussian RDF. We also extend our results to vector-valued Gaussian
sources of any finite memory under mild conditions. Our theoretical framework
is demonstrated with illustrative numerical experiments.Comment: 32 pages, 9 figures, published in IEEE Journal of Selected Topics in
Signal Processin