Exact minimum number of bits to stabilize a linear system
Abstract
We consider an unstable scalar linear stochastic system, X_(n+1) = aX_n + Z_n − U_n , where a ≥ 1 is the system gain, Z_n's are independent random variables with bounded α-th moments, and U_n's are the control actions that are chosen by a controller who receives a single element of a finite set {1,…,M} as its only information about system state Xi. We show new proofs that M > a is necessary and sufficient for β-moment stability, for any β < α. Our achievable scheme is a uniform quantizer of the zoom-in/zoom-out type that codes over multiple time instants for data rate efficiency; the controller uses its memory of the past to correctly interpret the received bits. We analyze the performance of our scheme using probabilistic arguments. We show a simple proof of a matching converse using information-theoretic techniques. Our results generalize to vector systems, to systems with dependent Gaussian noise, and to the scenario in which a small fraction of transmitted messages is lost.
Additional Information
© 2021 IEEE. This work was supported in part by the National Science Foundation (NSF) under Grant CCF-1751356, and by the Simons Institute for the Theory of Computing. Research of Y. Peres was partially supported by NSF grant DMS-1900008. G. Ranade acknowledges the Siebel Energy Institute Seed Funding.Attached Files
Accepted Version - Exact_minimum_number_of_bits_to_stabilize_a_linear_system.pdf
Updated - 1807.07686.pdf
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Additional details
- Eprint ID
- 112526
- Resolver ID
- CaltechAUTHORS:20211217-98215000
- NSF
- CCF-1751356
- Simons Foundation
- NSF
- DMS-1900008
- Siebel Energy Institute
- Created
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2021-12-18Created from EPrint's datestamp field
- Updated
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2022-10-18Created from EPrint's last_modified field