Optimal input sets for time minimality in quantized control systems

Limited capacity of communication channels has brought to the attention of many researchers the analysis of control systems subject to a quantized input set. In some fundamental cases such systems can be reduced to quantized control system of type x+=x+u, where the u takes values in a set of 2m+1 in...

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Published inMathematics of control, signals, and systems Vol. 18; no. 2; pp. 101 - 146
Main Author Marigo, Alessia
Format Journal Article
LanguageEnglish
Published London Springer Nature B.V 01.05.2006
Subjects
Control systems
Controllers
Mathematics
Optimization
System theory
Systems analysis
Time
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ISSN0932-4194
1435-568X
DOI10.1007/s00498-005-0156-5

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Summary:Limited capacity of communication channels has brought to the attention of many researchers the analysis of control systems subject to a quantized input set. In some fundamental cases such systems can be reduced to quantized control system of type x+=x+u, where the u takes values in a set of 2m+1 integer numbers, symmetric with respect to 0. In this paper we consider these types of systems and analyse the reachable set after K steps. Our aim is to find a set of m input values such that the reachable set after K steps contains an interval of integers [-N, . . . , N] with N as large as possible. For m=2,3 and 4, we completely solve the problem and characterize the metric associated to this quantized control system. [PUBLICATION ABSTRACT]
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ISSN:0932-4194
1435-568X
DOI:10.1007/s00498-005-0156-5