1 research outputs found
Sequential Source Coding for Stochastic Systems Subject to Finite Rate Constraints
In this paper, we revisit the sequential source coding framework to analyze
fundamental performance limitations of discrete-time stochastic control systems
subject to feedback data-rate constraints in finite-time horizon. The basis of
our results is a new characterization of the lower bound on the minimum
total-rate achieved by sequential codes subject to a total (across time)
distortion constraint and a computational algorithm that allocates optimally
the rate-distortion for any fixed finite-time horizon. This characterization
facilitates the derivation of analytical, non-asymptotic, and
finite-dimensional lower and upper bounds in two control-related scenarios. (a)
A parallel time-varying Gauss-Markov process with identically distributed
spatial components that is quantized and transmitted through a noiseless
channel to a minimum mean-squared error (MMSE) decoder. (b) A time-varying
quantized LQG closed-loop control system, with identically distributed spatial
components and with a random data-rate allocation. Our non-asymptotic lower
bound on the quantized LQG control problem, reveals the absolute minimum
data-rates for (mean square) stability of our time-varying plant for any fixed
finite time horizon. We supplement our framework with illustrative simulation
experiments.Comment: 40 pages, 6 figure