DocumentCode :
40643
Title :
Stabilization of Networked Multi-Input Systems With Channel Resource Allocation
Author :
Li Qiu ; Guoxiang Gu ; Wei Chen
Author_Institution :
Dept. of Electron. & Comput. Eng., Hong Kong Univ. of Sci. & Technol., Kowloon, China
Volume :
58
Issue :
3
fYear :
2013
fDate :
Mar-13
Firstpage :
554
Lastpage :
568
Abstract :
In this paper, we study the problem of state feedback stabilization of a linear time-invariant (LTI) discrete-time multi-input system with imperfect input channels. Each input channel is modeled in three different ways. First it is modeled as an ideal transmission system together with an additive norm bounded uncertainty, introducing a multiplicative uncertainty to the plant. Then it is modeled as an ideal transmission system together with a feedback norm bounded uncertainty, introducing a relative uncertainty to the plant. Finally it is modeled as an additive white Gaussian noise channel. For each of these models, we properly define the capacity of each channel whose sum yields the total capacity of all input channels. We aim at finding the least total channel capacity for stabilization. Different from the single-input case that is available in the literature and boils down to a typical H or H2 optimal control problem, the multi-input case involves allocation of the total capacity among the input channels in addition to the design of the feedback controller. The overall process of channel resource allocation and the controller design can be considered as a case of channel-controller co-design which gives rise to modified nonconvex optimization problems. Surprisingly, the modified nonconvex optimization problems, though appear more complicated, can be solved analytically. The main results of this paper can be summarized into a universal theorem: The state feedback stabilization can be accomplished by the channel-controller co-design, if and only if the total input channel capacity is greater than the topological entropy of the open-loop system.
Keywords :
AWGN channels; H control; H2 control; channel allocation; channel capacity; concave programming; control system synthesis; discrete time systems; linear systems; networked control systems; resource allocation; stability; state feedback; uncertain systems; H optimal control problem; H2 optimal control problem; LTI discrete-time multiple-input system; additive norm bounded uncertainty; additive white Gaussian noise channel; channel capacity; channel resource allocation; channel-controller codesign; feedback controller design; feedback norm bounded uncertainty; ideal transmission system; imperfect input channels; linear time-invariant discrete time multiple-input system; modified nonconvex optimization problem; multiplicative uncertainty; networked multiinput system stabilization; state feedback stabilization; Channel capacity; Channel models; Entropy; Quantization; Signal to noise ratio; State feedback; Uncertainty; Channel resource allocation; Mahler measure; networked control system; networked stabilization; topological entropy;
fLanguage :
English
Journal_Title :
Automatic Control, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9286
Type :
jour
DOI :
10.1109/TAC.2012.2218065
Filename :
6298000
Link To Document :
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