A Characterization of the Minimal Average Data Rate That Guarantees a Given Closed-Loop Performance Level

Silva, Eduardo I.; Derpich, Milan S.; Østergaard, Jan; Encina, Marco A.

doi:10.1109/tac.2015.2500658

Cited by 50 publications

(79 citation statements)

References 67 publications

(144 reference statements)

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“…While this result is compatible to ours, it is noteworthy that the proof technique there is different from ours and is based on fundamental inequalities for directed information obtained in [39]. In comparison to [24], we additionally prove that the optimal control policy can be realized by a state space model with a three-stage structure (shown in Figure 3, 4), which appears to be a new observation to the best of our knowledge.…”

Section: Connections To Existing Resultssupporting

confidence: 83%

“…In this section, we revisit a networked LQG control problem considered in [22]- [24]. Here we consider time-invariant MIMO plants while [22]- [24] focus on SISO plants. For simplicity, we consider fully observable plants only.…”

Section: Operational Meaningmentioning

confidence: 99%

“…Second, it is recently reported by Silva et al [22]- [24] that directed information has an important operational meaning in a practical NCS setup. Starting from an LQG control problem over a noiseless binary channel with prefix-free codewords, they show that the directed information obtained by solving the aforementioned optimization problem provides a tight lower bound for the minimum data-rate (defined operationally) required to achieve the desired level of control performance.…”

Section: Introductionmentioning

confidence: 99%

“…As a natural next step, the rate-performance trade-offs are of great interest from both theoretical and practical perspectives. The trade-off between Linear-Quadratic-Gaussian (LQG) performance and the required data-rate has attracted attention in the literature [11]- [24]. Generalized interpretations of the classical Bode's integral also provide fundamental performance limitations of closed-loop systems in the information-theoretic terms [25]- [28].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

LQG Control With Minimum Directed Information: Semidefinite Programming Approach

Tanaka

Esfahani

Mitter

2018

IEEE Trans. Automat. Contr.

139

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We consider a discrete-time Linear-Quadratic-Gaussian (LQG) control problem in which Massey's directed information from the observed output of the plant to the control input is minimized while required control performance is attainable. This problem arises in several different contexts, including joint encoder and controller design for data-rate minimization in networked control systems. We show that the optimal control law is a Linear-Gaussian randomized policy. We also identify the state space realization of the optimal policy, which can be synthesized by an efficient algorithm based on semidefinite programming. Our structural result indicates that the filter-controller separation principle from the LQG control theory, and the sensor-filter separation principle from the zero-delay rate-distortion theory for Gauss-Markov sources hold simultaneously in the considered problem. A connection to the data-rate theorem for mean-square stability by Nair & Evans is also established.

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Section: Connections To Existing Resultssupporting

confidence: 83%

Section: Operational Meaningmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

LQG Control With Minimum Directed Information: Semidefinite Programming Approach

Tanaka

Esfahani

Mitter

2018

IEEE Trans. Automat. Contr.

139

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“…Causal rate-distortion function is challenging to evaluate, and beyond the scalar Gauss-Markov source [2], [23], no closed-form expression is known for it. For stationary scalar Gaussian processes, Derpich and Ostergaard [32] showed an upper bound and Silva et al [29] a lower bound. For vector Gauss-Markov sources, Tanaka et al developed a semidefinite program to compute exactly the minimum directed mutual information in quantization [33] and control [34].…”

Section: Prior Artmentioning

confidence: 98%

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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Dynamic output feedback under quantization based on spherical polar coordinate quantizer

Wang

2021

Intl J Robust & Nonlinear

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Different from uniform quantizer and logarithmic quantizer, this article utilizes a novel quantizer based on spherical polar coordinates for the design problems of quantized feedback systems with dynamic output feedback. This quantizer has a desired relation between the quantized vector and the corresponding quantization error, by which in this article the quantization error is converted to the uncertainty of the systems and stabilization problems of linear systems via dynamic output feedback under quantization can be converted to the corresponding robust control problems. From a practical point of view, we are concerned with quantized feedback control with finite data rate and use the quantizer with finite data rate to design quantized feedback systems. Under the quantizer with finite data rate, a time‐varying bounded quantization region needs to be determined to contain the quantized vector as the system evolves. Under this circumstance, some entries of the quantized vector are not available to the quantizer with finite data rate such that the vector cannot be quantized directly, so we propose a quantization and controller design method to solve this problem.

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A Characterization of the Minimal Average Data Rate That Guarantees a Given Closed-Loop Performance Level

Cited by 50 publications

References 67 publications

LQG Control With Minimum Directed Information: Semidefinite Programming Approach

LQG Control With Minimum Directed Information: Semidefinite Programming Approach

Rate-cost tradeoffs in control

Dynamic output feedback under quantization based on spherical polar coordinate quantizer

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