Systems with automatic feedback control may consist of several remote devices, connected only by unreliable communication channels. It is necessary in these conditions to have a method for accurate, real-time state estimation in the presence of channel noise. This problem is addressed, for the case of polynomial-growth-rate state spaces, through a new type of error-correcting code that is online and computationally efficient. This solution establishes a constructive analog, for some applications in estimation and control, of the Shannon coding theorem.
Bibliographical noteFunding Information:
Manuscript received August 30, 2006; revised June 16, 2008. Current version published June 24, 2009. The work of R. Ostrovsky was supported in part by the Institute for Pure and Applied Mathematics (IPAM); in part by a gift from Teradata, Intel equipment Grant, IBM Faculty Award, Xerox Innovation Group Award, National Science Foundation under Grants 0430254, 0716835, 0716389, 0830803, a U.C. MICRO Grant, and Okawa Foundation. The work of Y. Ra-bani was supported by the Israel Science Foundation under Grant 52/03 and by United States–Israel Binational Science Foundation under Grant 2002282. This work was also supported in part while Y. Rabani was visiting the Institute for Pure and Applied Mathematics in the University of California at Los Angeles. The work of L. J. Schulman was supported by the National Science Foundatio (NSF) under Grants CCF-0515342, NSA H98230-06-1-0074, NSF under Grant ITR CCR-0326554, and the Okawa Foundation. The material in this paper was presented in part at the 46th Annual Symposium on Foundations of Computer Science (FOCS), Pittsburgh, PA, October 2005.
- Control theory
- Lovász local lemma
- State estimation
- Tree codes