Exact minimum number of bits to stabilize a linear system

Victoria Kostina, Yuval Peres, Gireeja Ranade, Mark Sellke
2018 2018 IEEE Conference on Decision and Control (CDC)  
We consider an unstable scalar linear stochastic system, Xn+1 = aXn + Zn − Un, where a ≥ 1 is the system gain, Zn's are independent random variables with bounded αth moments, and Un'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 that M = ⌊a⌋+1 is necessary and sufficient for β-moment stability, for any β < α. Our achievable scheme is a uniform quantizer of zoom-in /
more » ... m-out type whose performance is analyzed using probabilistic arguments. The matching converse is shown using information-theoretic techniques. The analysis generalizes to vector systems, to systems with dependent Gaussian noise, and to the scenario in which a small fraction of transmitted messages is lost.
doi:10.1109/cdc.2018.8619156 dblp:conf/cdc/KostinaPRS18 fatcat:6sxup3q4bfhrdgaukf7q4wzgui