Multi-rate control over AWGN channels via analog joint source-channel coding

Khina, Anatoly; Pettersson, Gustav M.; Kostina, Victoria; Hassibi, Babak

doi:10.1109/cdc.2016.7799185

Cited by 8 publications

(5 citation statements)

References 30 publications

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“…One remarkable special case when equality in (42) is attained is control of a scalar Gaussian system over a scalar memoryless AWGN channel [2], [49]- [51]. In that case, the channel is probabilistically matched to the data to be transmitted [5], no coding beyond simple amplification is needed, and linearly transmitting the innovation is optimal [49].…”

Section: Proposition 1 a Necessary Condition For Stabilizing The Sys-mentioning

confidence: 99%

“…In practice, such matching rarely occurs, and intelligent joint source-channel coding techniques can lead to a significant performance improvement. One such technique that approaches (42) in a particular scenario is discussed in [51]. In general, how closely the bound in (42) can be approached over noisy channels remains an open problem.…”

Section: Proposition 1 a Necessary Condition For Stabilizing The Sys-mentioning

confidence: 99%

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Rate-Cost Tradeoffs in Control

Kostina

Hassibi

2019

IEEE Trans. Automat. Contr.

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102

158

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Consider a control problem with a communication channel connecting the observer of a linear stochastic system to the controller. The goal of the controller is to minimize a quadratic cost function in the state variables and control signal, known as the linear quadratic regulator (LQR). We study the fundamental tradeoff between the communication rate r bits/sec and the expected cost b. We obtain a lower bound on a certain rate-cost function, which quantifies the minimum directed mutual information between the channel input and output that is compatible with a target LQR cost. The rate-cost function has operational significance in multiple scenarios of interest: among others, it allows us to lower-bound the minimum communication rate for fixed and variable length quantization, and for control over noisy channels. We derive an explicit lower bound to the rate-cost function, which applies to the vector, non-Gaussian, and partially observed systems, thereby extending and generalizing an earlier explicit expression for the scalar Gaussian system, due to Tatikonda el al. [2]. The bound applies as long as the differential entropy of the system noise is not −∞. It can be closely approached by a simple lattice quantization scheme that only quantizes the innovation, that is, the difference between the controller's belief about the current state and the true state. Via a separation principle between control and communication, similar results hold for causal lossy compression of additive noise Markov sources. Apart from standard dynamic programming arguments, our technical approach leverages the Shannon lower bound, develops new estimates for data compression with coding memory, and uses some recent results on high resolution variablelength vector quantization to prove that the new converse bounds are tight.

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Section: Proposition 1 a Necessary Condition For Stabilizing The Sys-mentioning

confidence: 99%

Section: Proposition 1 a Necessary Condition For Stabilizing The Sys-mentioning

confidence: 99%

Rate-Cost Tradeoffs in Control

Kostina

Hassibi

2019

IEEE Trans. Automat. Contr.

Self Cite

102

158

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show abstract

Section: ) Control Over a Noisy Channelmentioning

confidence: 99%

Rate-cost tradeoffs in control

Kostina

Hassibi

2016

2016 54th Annual Allerton Conference on Communication, Control, and Computing (Allerton)

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Abstract-Consider a control problem with a communication channel connecting the observer of a linear stochastic system to the controller. The goal of the controller is to minimize a quadratic cost function in the state variables and control signal, known as the linear quadratic regulator (LQR). We study the fundamental tradeoff between the communication rate r bits/sec and the expected cost b. We obtain a lower bound on a certain rate-cost function, which quantifies the minimum directed mutual information between the channel input and output that is compatible with a target LQR cost. The rate-cost function has operational significance in multiple scenarios of interest: among others, it allows us to lowerbound the minimum communication rate for fixed and variable length quantization, and for control over noisy channels. We derive an explicit lower bound to the rate-cost function, which applies to the vector, non-Gaussian, and partially observed systems, thereby extending and generalizing an earlier explicit expression for the scalar Gaussian system, due to Tatikonda el al. [2]. The bound applies as long as the system noise has a probability density function. It can be closely approached by a simple lattice quantization scheme that only quantizes the innovation, that is, the difference between the controller's belief about the current state and the true state. Via a separation principle between control and communication, similar results hold for causal lossy compression of additive noise Markov sources. Apart from standard dynamic programming arguments, our technical approach leverages the Shannon lower bound, develops new estimates for data compression with coding memory, and uses some recent results on high resolution variable-length vector quantization to prove that the new converse bounds are tight.

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“…accounting for the noise of the system (1) during this delay. Similar to the proof of Theorem 1, we define define ∆ ℓT as the width of the set where the remote estimator knows that the state x ℓT belongs depending on the success or failure of the message at time k = ℓT + d. Moreover we have shown in (16) that |x ℓT − xℓT | ≤ ∆ ℓT /2 holds always. Using this fact and taking expectation of (21) we get that…”

Section: B Steady State Estimation Performancementioning

confidence: 96%

Latency-Reliability Tradeoffs for State Estimation

Gatsis¹,

Hassani²,

Pappas³

2018

Preprint

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The emerging interest in low-latency high-reliability applications, such as connected vehicles, necessitates a new abstraction between communication and control. Thanks to advances in cyber-physical systems over the past decades, we understand this interface for classical bit-rate models of channels as well as packet-loss-type channels. This work proposes a new abstraction characterized as a tradeoff curve between latency, reliability and rate. Our aim is to understand: Do we (control engineers) prefer faster but less reliable communications (with shorter codes), or slower but more reliable communications (with longer codes)? In this paper we examine the tradeoffs between latency and reliability for the problem of estimating dynamical systems over communication channels. Employing different latency-reliability curves derived from practical coding schemes, we develop a co-design methodology, i.e., select the code length depending on the system dynamics to optimize system performance.

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Multi-rate control over AWGN channels via analog joint source-channel coding

Cited by 8 publications

References 30 publications

Rate-Cost Tradeoffs in Control

Rate-Cost Tradeoffs in Control

Rate-cost tradeoffs in control

Latency-Reliability Tradeoffs for State Estimation

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