Quantized control via locational optimization

• Published in: IEEE transactions on automatic control Vol. 51; no. 1; pp. 2 - 13
• Main Authors: Bullo, F., Liberzon, D.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.01.2006; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Adaptive control; Applied sciences; Asymptotic stability; Computer science; control theory; systems; Control systems; Control theory. Systems; Counters; Design engineering; Design optimization; Error analysis; Exact sciences and technology; Feedback stabilization; Iterative algorithms; locational optimization; Optimization; Quantization; quantized control; Shape control; Solvers; Stabilization; State feedback; State feedback; Voronoï diagram; locational optimization; Quantization error; Information system; Worst case method; Quantization; Feedback regulation; Iterative method; Information control; Optimization; Closed feedback; quantized control; Quantized signal; Quantifier; Feedback stabilization
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2005.861688

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 obtaining solutions to such problems, all in terms of suitable Voronoi quantizers, are discussed. In particular, an iterative solver is developed for a novel weighted multicenter problem which most accurately represents the least destabilizing quantizer design. A simulation study is also presented.