When Bode Meets Shannon: Control-Oriented Feedback Communication Schemes

Elia, Nicola

doi:10.1109/tac.2004.834119

Cited by 315 publications

(351 citation statements)

References 25 publications

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“…, the rates (R 1 , R 2 ) that make the matrix A stable while the transmission rate R = R 1 + R 2 is minimum, are (R 1 , R 2 )= (3, 5), (5,3), (4,4), in which for this system we choose (R 1 , R 2 ) = (4, 4). For these rates, L ] and stay there despite of uncertainties in dynamic model and distortion due to quantization.…”

Section: Simulation Resultsmentioning

confidence: 99%

“…Some results addressing basic problems in state estimation and/or stability of dynamic systems over communication channels subject to imperfections can be found in [3]- [17]. In [15] the authors addressed the problem of state estimation of an uncontrolled noiseless nonlinear Lipschitz system over the digital noiseless channel with asymptotically zero mean square estimation error.…”

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confidence: 99%

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Stability Of Nonlinear Uncertain Lipschitz Systems Over The Digital Noiseless Channel

Farhadi

2017

Scientia Iranica

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This paper is concerned with the stability of nonlinear Lipschitz systems subject to bounded process and measurement noises when transmission from sensor to controller is subject to distortion due to quantization. A stabilizing technique and a sufficient condition relating transmission rate to Lipschitz coefficients are presented for almost sure asymptotic bounded stability of nonlinear uncertain Lipschitz systems. In the absence of process and measurement noises, it is shown that the proposed stabilizing technique results in almost sure asymptotic stability. Computer simulations illustrate the satisfactory performance of the proposed technique for almost sure asymptotic bounded stability and asymptotic stability. Index TermsNetworked control system, Lipschitz nonlinear system, uncertain dynamic system, the digital noiseless channel.

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Section: Simulation Resultsmentioning

confidence: 99%

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confidence: 99%

Stability Of Nonlinear Uncertain Lipschitz Systems Over The Digital Noiseless Channel

Farhadi

2017

Scientia Iranica

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“…There might be rare sequences of channel noise that will cause the state to grow outside any boundary. 7 A looser sense of stability is given by:…”

Section: The Control Problemmentioning

confidence: 99%

“…Alternatively, we can consider the requirement that the probability be bounded with a uniform bound over all possible disturbance sequences. 7 Consider a network control model where packets might be erased with some probability. If the system is allowed to run for a long time, then it becomes increasingly certain that a run of bad luck on the channel will occur sometime.…”

Section: The Control Problemmentioning

confidence: 99%

“…[18] Subsequently, there was also related work by Elia that used ideas from robust control to deal with communication uncertainty in a mixed continuous/discrete context. [7,8] The area of control with The equivalence between stabilization over noisy feedback channels and reliable communication over noisy channels with feedback is the main result established in this paper.…”

Section: Introductionmentioning

confidence: 99%

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The necessity and sufficiency of anytime capacity for control over a noisy communication link

Sahai

2004

2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601)

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We review how Shannon's classical notion of capacity is not enough to characterize a noisy communication channel if we intend to use that channel as a part of a feedback loop to stabilize an unstable linear system. While classical capacity is not enough, another parametric sense of capacity called "anytime capacity" is shown to be necessary for the stabilization of an unstable process. The rate required is given by the log of the system gain and the sense of reliability required comes from the sense of stability desired. A consequence of this necessity result is a sequential generalization of the Schalkwijk/Kailath scheme for communication over the AWGN channel with feedback.In cases of sufficiently rich information patterns between the encoder and decoder, we show that adequate anytime capacity is also sufficient for there to exist a stabilizing controller. These sufficiency results are then generalized to cases with noisy observations and without any explicit feedback between the observer and the controller. Both necessary and sufficient conditions are extended to the continuous time case as well.In part II, the vector-state generalizations are established. Here, it is the magnitudes of the unstable eigenvalues that play an essential role. The channel is no longer summarized by a single number, or even a single function. Instead, the concept of the anytime-rate-region is introduced in which we ask for the region of rates that the channel can support while still meeting different reliability targets for parallel bitstreams. For cases where there is no explicit feedback of the noisy channel outputs, the intrinsic delay of the control system tells us what the feedback delay needs to be while evaluating the anytime reliability of the channel.

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