2002/12/22 by Francesco Bullo, Daniel Liberzon, Bullo, Francesco +1
Mathematics · #90C25 #93C10 #93C41 #FOS: Mathematics #Optimization and Control (math.OC) #math.OC #msc:90C25 #msc:93C10 #msc:93C41
paper · pdf · doi:10.48550/arxiv.math/0212307
arxiv created 2002/12/22 · arxiv updated 2009/11/30
This paper studies state quantization schemes for feedback stabilization of control systems with limited information. The focus is on designing the least destabilizing quantizer subject to a given information constraint. We explore several ways of measuring the destabilizing effect of a quantizer on the closed-loop system, including (but not limited to) the worst-case quantization error. In each case, we show how quantizer design can be naturally reduced to a version of the so-called multicenter problem from locational optimization. Algorithms for solving such problems are discussed. In particular, an iterative solver is developed for a novel weighted multicenter problem which most accurately represents the least destabilizing quantizer design.