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Published December 2016 | public
Journal Article

Linear Time-Invariant Anytime Codes for Control Over Noisy Channels

Abstract

The problem of stabilizing an unstable plant over a noisy communication link is an increasingly important one that arises in problems of distributed control and networked control systems. Although the work of Schulman, and Sahai and Mitter over the past two decades, and their development of the notions of "tree codes" and "anytime capacity" respectively, provides the theoretical framework for studying such problems, there has been scant practical progress in this area because explicit constructions of tree codes with efficient encoding and decoding did not exist. To stabilize an unstable plant driven by bounded noise over a noisy channel one often needs real-time encoding and real-time decoding and a reliability which increases exponentially with delay, which is what tree codes guarantee. We propose an ensemble of random causal linear codes with a time invariant structure and show that they are tree codes with probability one. For erasure channels, we show that the average complexity of maximum likelihood decoding is bounded by a constant for all time if the code rate is smaller than the computational cutoff rate. For rates larger than the computational cutoff rate, we present an alternate way to perform maximum likelihood decoding with a complexity that grows linearly with time. We give novel sufficient conditions on the rate and reliability required of the tree codes to stabilize vector plants and argue that they are asymptotically tight.

Additional Information

© 2016 IEEE. Manuscript received October 5, 2015; revised January 13, 2016 and January 15, 2016; accepted January 31, 2016. Date of publication February 12, 2016; date of current version December 2, 2016. This work was supported in part by the National Science Foundation under Grants CCF-0729203, CNS-0932428, and CCF-1018927, in part by the Office of Naval Research under the MURI Grant N00014-08-1-0747, and in part by Caltech's Lee Center for Advanced Networking. Recommended by Associate Editor S. Zampieri.

Additional details

Created:
August 19, 2023
Modified:
March 5, 2024