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Matches in SemOpenAlex for { <https://semopenalex.org/work/W3212606888> ?p ?o ?g. }

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• W3212606888 abstract "We consider an unstable scalar linear stochastic system, <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink><tex-math notation=LaTeX>$X_{n+1}=a X_n + Z_n - U_n$</tex-math></inline-formula> , where <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink><tex-math notation=LaTeX>$a geq 1$</tex-math></inline-formula> is the system gain, <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink><tex-math notation=LaTeX>$Z_n$</tex-math></inline-formula> s are independent random variables with bounded <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink><tex-math notation=LaTeX>$alpha$</tex-math></inline-formula> th moments, and <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink><tex-math notation=LaTeX>$U_n$</tex-math></inline-formula> s are the control actions that are chosen by a controller who receives a single element of a finite set <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink><tex-math notation=LaTeX>$lbrace 1, ldots, Mrbrace$</tex-math></inline-formula> as its only information about system state <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink><tex-math notation=LaTeX>$X_i$</tex-math></inline-formula> . We show new proofs that <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink><tex-math notation=LaTeX>$M > a$</tex-math></inline-formula> is necessary and sufficient for <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink><tex-math notation=LaTeX>$beta$</tex-math></inline-formula> -moment stability, for any <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink><tex-math notation=LaTeX>$beta < alpha$</tex-math></inline-formula> . 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." @default.
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• W3212606888 date "2022-10-01" @default.
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• W3212606888 title "Exact Minimum Number of Bits to Stabilize a Linear System" @default.
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• W3212606888 doi "https://doi.org/10.1109/tac.2021.3126679" @default.
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