期刊
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
卷 56, 期 5, 页码 1014-1029出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TAC.2010.2081730
关键词
Information theory; networked control systems; stochastic control; stochastic stability
资金
- National Science Foundation [CCR 00-85917 ITR]
- AFOSR [FA9550-09-1-0249]
- Natural Sciences and Engineering Research Council of Canada (NSERC)
We consider the problem of remotely controlling a continuous-time linear time-invariant system driven by Brownian motion process, when communication takes place over noisy memoryless discrete-or continuous-alphabet channels. What makes this class of remote control problems different from most of the previously studied models is the presence of noise in both the forward channel (connecting sensors to the controller) and the reverse channel (connecting the controller to the plant). For stability of the closed-loop system, we look for the existence of an invariant distribution for the state, for which we show that it is necessary that the entire control space and the state space be encoded, and that the reverse channel be at least as reliable as the forward channel. We obtain necessary conditions and sufficient conditions on the channels and the controllers for stabilizability. Using properties of the underlying sampled Markov chain, we show that under variable-length coding and some realistic channel conditions, stability can be achieved over discrete-alphabet channels even if the entire state and control spaces are to be encoded and the number of bits that can be transmitted per unit time is strictly bounded. For control over continuous-alphabet channels, however, a variable rate scheme is not necessary. We also show that memoryless policies are rate-efficient for Gaussian channels.
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