Algorithms for optimal control with fixed-rate feedback

Anatoly Khina; Yorie Nakahira; Yu Su; Babak Hassibi

doi:10.1109/CDC.2017.8264569

Algorithms for optimal control with fixed-rate feedback

Anatoly Khina, Yorie Nakahira, Yu Su, Babak Hassibi

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

18 Scopus citations

Abstract

We consider a discrete-Time linear quadratic Gaussian networked control setting where the (full information) observer and controller are separated by a fixed-rate noiseless channel. The minimal rate required to stabilize such a system has been well studied. However, for a given fixed rate, how to quantize the states so as to optimize performance is an open question of great theoretical and practical significance. We concentrate on minimizing the control cost for first-order scalar systems. To that end, we use the Lloyd-Max algorithm and leverage properties of logarithmically-concave functions to construct the optimal quantizer that greedily minimizes the cost at every time instant. By connecting the globally optimal scheme to the problem of scalar successive refinement, we argue that its gain over the proposed greedy algorithm is negligible. This is significant since the globally optimal scheme is often computationally intractable. All the results are proven for the more general case of disturbances with logarithmically-concave distributions.

Original language	English (US)
Title of host publication	2017 IEEE 56th Annual Conference on Decision and Control (CDC)
Publisher	IEEE
Pages	6015-6020
Number of pages	6
ISBN (Print)	9781509028733
DOIs	https://doi.org/10.1109/CDC.2017.8264569
State	Published - Jan 23 2018
Externally published	Yes

Bibliographical note

KAUST Repository Item: Exported on 2022-06-28
Acknowledgements: The work of A. Khina has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 708932. The work of Y. Nakahira was funded by grants from AFOSR and NSF, and gifts from Cisco, Huawei, and Google. The work of Y. Su was supported in part by NSF through AitF-1637598. The work of B. Hassibi was supported in part by the NSF under grants CNS-0932428, CCF-1018927, CCF-1423663 and CCF-1409204, by a grant from Qualcomm Inc., by NASA’s Jet Propulsion Laboratory through the President and Director’s Fund, by King Abdulaziz University, and by King Abdullah University of Science and Technology.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

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10.1109/CDC.2017.8264569

Cite this

@inproceedings{683053c449324eef80dfd9eeb11de988,

title = "Algorithms for optimal control with fixed-rate feedback",

abstract = "We consider a discrete-Time linear quadratic Gaussian networked control setting where the (full information) observer and controller are separated by a fixed-rate noiseless channel. The minimal rate required to stabilize such a system has been well studied. However, for a given fixed rate, how to quantize the states so as to optimize performance is an open question of great theoretical and practical significance. We concentrate on minimizing the control cost for first-order scalar systems. To that end, we use the Lloyd-Max algorithm and leverage properties of logarithmically-concave functions to construct the optimal quantizer that greedily minimizes the cost at every time instant. By connecting the globally optimal scheme to the problem of scalar successive refinement, we argue that its gain over the proposed greedy algorithm is negligible. This is significant since the globally optimal scheme is often computationally intractable. All the results are proven for the more general case of disturbances with logarithmically-concave distributions.",

author = "Anatoly Khina and Yorie Nakahira and Yu Su and Babak Hassibi",

note = "KAUST Repository Item: Exported on 2022-06-28 Acknowledgements: The work of A. Khina has received funding from the European Union{\textquoteright}s Horizon 2020 research and innovation programme under the Marie Sk{\l}odowska-Curie grant agreement No 708932. The work of Y. Nakahira was funded by grants from AFOSR and NSF, and gifts from Cisco, Huawei, and Google. The work of Y. Su was supported in part by NSF through AitF-1637598. The work of B. Hassibi was supported in part by the NSF under grants CNS-0932428, CCF-1018927, CCF-1423663 and CCF-1409204, by a grant from Qualcomm Inc., by NASA{\textquoteright}s Jet Propulsion Laboratory through the President and Director{\textquoteright}s Fund, by King Abdulaziz University, and by King Abdullah University of Science and Technology. This publication acknowledges KAUST support, but has no KAUST affiliated authors.",

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N1 - KAUST Repository Item: Exported on 2022-06-28 Acknowledgements: The work of A. Khina has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 708932. The work of Y. Nakahira was funded by grants from AFOSR and NSF, and gifts from Cisco, Huawei, and Google. The work of Y. Su was supported in part by NSF through AitF-1637598. The work of B. Hassibi was supported in part by the NSF under grants CNS-0932428, CCF-1018927, CCF-1423663 and CCF-1409204, by a grant from Qualcomm Inc., by NASA’s Jet Propulsion Laboratory through the President and Director’s Fund, by King Abdulaziz University, and by King Abdullah University of Science and Technology. This publication acknowledges KAUST support, but has no KAUST affiliated authors.

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N2 - We consider a discrete-Time linear quadratic Gaussian networked control setting where the (full information) observer and controller are separated by a fixed-rate noiseless channel. The minimal rate required to stabilize such a system has been well studied. However, for a given fixed rate, how to quantize the states so as to optimize performance is an open question of great theoretical and practical significance. We concentrate on minimizing the control cost for first-order scalar systems. To that end, we use the Lloyd-Max algorithm and leverage properties of logarithmically-concave functions to construct the optimal quantizer that greedily minimizes the cost at every time instant. By connecting the globally optimal scheme to the problem of scalar successive refinement, we argue that its gain over the proposed greedy algorithm is negligible. This is significant since the globally optimal scheme is often computationally intractable. All the results are proven for the more general case of disturbances with logarithmically-concave distributions.

AB - We consider a discrete-Time linear quadratic Gaussian networked control setting where the (full information) observer and controller are separated by a fixed-rate noiseless channel. The minimal rate required to stabilize such a system has been well studied. However, for a given fixed rate, how to quantize the states so as to optimize performance is an open question of great theoretical and practical significance. We concentrate on minimizing the control cost for first-order scalar systems. To that end, we use the Lloyd-Max algorithm and leverage properties of logarithmically-concave functions to construct the optimal quantizer that greedily minimizes the cost at every time instant. By connecting the globally optimal scheme to the problem of scalar successive refinement, we argue that its gain over the proposed greedy algorithm is negligible. This is significant since the globally optimal scheme is often computationally intractable. All the results are proven for the more general case of disturbances with logarithmically-concave distributions.

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DO - 10.1109/CDC.2017.8264569

M3 - Conference contribution

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BT - 2017 IEEE 56th Annual Conference on Decision and Control (CDC)

PB - IEEE

ER -

Algorithms for optimal control with fixed-rate feedback

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