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Prefix-Free Coding for LQG Control [article]

Travis Cuvelier and Takashi Tanaka and Robert W. Heath Jr
2022 arXiv   pre-print
In this work, we develop quantization and variable-length source codecs for the feedback links in linear-quadratic-Gaussian (LQG) control systems.  ...  For single-input single-output (SISO) plants, we prove that it suffices to consider time-invariant quantization and source coding.  ...  In Section II we formulate the problem of LQG control with minimum rate prefix-free coding in the feedback link.  ... 
arXiv:2204.00588v3 fatcat:nmrtln3d7rd7xemd2n2oob2x54

Time-invariant prefix-free source coding for MIMO LQG control [article]

Travis C. Cuvelier and Takashi Tanaka and Robert W. Heath Jr
2022 arXiv   pre-print
The architecture conforms to the strict prefix constraint and does not require time-varying lossless source coding, in contrast to the prior art.  ...  We develop a data compression architecture that provably achieves a near minimum time-average expected bitrate for a fixed constraint on the LQG performance.  ...  Related Work Our work follows from the architecture for LQG control with minimum bitrate prefix-free variable-length coding in [3] .  ... 
arXiv:2207.12614v1 fatcat:eii7swnsmzgltj5j2lbg4cawoq

A Lower-bound for Variable-length Source Coding in LQG Feedback Control [article]

Travis C. Cuvelier and Takashi Tanaka and Robert W. Heath Jr
2022 arXiv   pre-print
We then derive a lower bound on the rate of prefix-free coding in terms of directed information; in particular we show that a previously known bound still holds in the case with shared randomness.  ...  In this letter, we consider a Linear Quadratic Gaussian (LQG) control system where feedback occurs over a noiseless binary channel and derive lower bounds on the minimum communication cost (quantified  ...  Deriving lower bounds and achievability results for time-invariant prefix-free codecs is an opportunity for future work.  ... 
arXiv:2203.12467v2 fatcat:5cteo7twgzcinfpgt3c23npime

Rate of prefix-free codes in LQG control systems

Takashi Tanaka, Karl Henrik Johansson, Tobias Oechtering, Henrik Sandberg, Mikael Skoglund
2016 2016 IEEE International Symposium on Information Theory (ISIT)  
We derive a lower bound of the rate achievable by the class of prefix-free codes attaining the required LQG control performance.  ...  coding.  ...  Remark 1: Note that prefix-free may not always be a strict requirement for a code used in feedback control, although this assumption is taken for granted in the previous work [1] .  ... 
doi:10.1109/isit.2016.7541729 dblp:conf/isit/TanakaJOSS16 fatcat:zp7hs3rfrbe3jpqwlswzcsfsbq

Rate of Prefix-free Codes in LQG Control Systems with Side Information [article]

Travis C. Cuvelier, Takashi Tanaka
2021 arXiv   pre-print
Use of the channel incurs a communication cost, quantified as the time-averaged expected length of prefix-free binary codeword.  ...  In this work, we study an LQG control system where one of two feedback channels is discrete and incurs a communication cost.  ...  We bound the expected length of the prefix-free codeword a t at every t by bounding the length of lossless prefix-free source code that encodes a t itself.  ... 
arXiv:2101.09329v3 fatcat:vbwjnygkezf6zkkrjrzpctiw4m

Tracking and Control of Gauss-Markov Processes over Packet-Drop Channels with Acknowledgments [article]

Anatoly Khina, Victoria Kostina, Ashish Khisti, Babak Hassibi
2018 arXiv   pre-print
For the scenario where only one process is tracked by the observer-state estimator system, we further show that variable-length coding techniques are within a small gap of the many-process outer bound.  ...  We demonstrate the usefulness of the proposed approach for the simple setting of discrete-time scalar linear quadratic Gaussian control with a limited data-rate feedback that is susceptible to packet erasures  ...  Nonetheless, the results of this paper can be easily adjusted to the prefix-free coding case by adding an extra bit on the right hand side of (5) -the maximal loss of prefix-free entropy coding above the  ... 
arXiv:1702.01779v4 fatcat:vy7i3iq7svad5dshl7cnnx4n7a

Cumulative subject index

1978 Information and Control  
, 37, 234 Normal forms chain free, propagation for E0L systems, 36, 309 O Observation sharing pattern one-step delay, two-criteria LQG deci- sion problems with, 38, 21 Operator reducing, for  ...  : for zero-memory re- placement problem, 37, 90 Control networks asynchronous, interconnecting, 38, 343 Convolutional codes generalized permutations in, 38, 213 Correlations multivariate symmetric  ... 
doi:10.1016/s0019-9958(78)90707-6 fatcat:3g6qa5hi2zc2lgyyvndbar65di

Sequential Source Coding for Stochastic Systems Subject to Finite Rate Constraints [article]

Photios A. Stavrou, Mikael Skoglund, Takashi Tanaka
2020 arXiv   pre-print
Our non-asymptotic lower bound on the quantized LQG control problem, reveals the absolute minimum data-rates for (mean square) stability of our time-varying plant for any fixed finite time horizon.  ...  (b) A time-varying quantized LQG closed-loop control system, with identically distributed spatial components and with a random data-rate allocation.  ...  Charalambous for reading the paper and proposing the idea of bisection method for Algorithm 1. They are also grateful to Prof. J.  ... 
arXiv:1906.04217v2 fatcat:nn246dr7b5b4dh4oifqly3grru

Value of Information in Minimum-Rate LQG Control

Touraj Soleymani, Sandra Hirche, John S. Baras
2017 IFAC-PapersOnLine  
The framework we develop in this paper is for partially observed linear quadratic Gaussian (LQG) control over communication networks in which the forward channel transporting measurements is modeled by  ...  Making use of dynamic programming, we characterize the optimal control and the optimal sampling policies that achieve the minimum data rate required for a guaranteed level of control performance.  ...  ACKNOWLEDGMENT This work has been carried out with the support of the Technische Universität München -Institute for Advanced Study, funded by the German Excellence Initiative and the DFG Priority Program  ... 
doi:10.1016/j.ifacol.2017.08.1322 fatcat:pjbtvgczbrgfxd4dafedppfyue

LQG Control With Minimum Directed Information: Semidefinite Programming Approach

Takashi Tanaka, Peyman Mohajerin Esfahani, Sanjoy K. Mitter
2018 IEEE Transactions on Automatic Control  
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  ...  This problem arises in several different contexts, including joint encoder and controller design for data-rate minimization in networked control systems.  ...  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  ... 
doi:10.1109/tac.2017.2709618 fatcat:o76ys6dyobdh5gk5js7deo2gfe

LQG Control with Minimum Directed Information: Semidefinite Programming Approach [article]

Takashi Tanaka, Peyman Mohajerin Esfahani, Sanjoy K. Mitter
2017 arXiv   pre-print
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  ...  This problem arises in several different contexts, including joint encoder and controller design for data-rate minimization in networked control systems.  ...  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  ... 
arXiv:1510.04214v3 fatcat:hr4w3hikv5h6tbuqsiibpdrsnm

Percolation on triangulations: a bijective path to Liouville quantum gravity [article]

Olivier Bernardi, Nina Holden, Xin Sun
2021 arXiv   pre-print
We set the foundation for a series of works aimed at proving strong relations between uniform random planar maps and Liouville quantum gravity (LQG).  ...  Combining these two correspondences allows us to relate uniform site-percolated triangulations to √(8/3)-LQG and SLE_6.  ...  Acknowledgements: We thank Ewain Gwynne and Scott Sheffield for helpful discussions. We thank Cyril Banderier for comments on the draft.  ... 
arXiv:1807.01684v5 fatcat:2pm5qr2ke5aujiqlyxnmpjqvpi

Rate-cost tradeoffs in control [article]

Victoria Kostina, Babak Hassibi
2018 arXiv   pre-print
, and for control over noisy channels.  ...  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  ...  Accordingly, the theorems in Section II-A and Section II-B also characterize the operational rate-cost tradeoff for control with variable rate prefix-free quantizers. III.  ... 
arXiv:1612.02126v3 fatcat:sotpwnaxfrdmllaciqfjhqyxxu

Interplay Between Transmission Delay, Average Data Rate, and Performance in Output Feedback Control over Digital Communication Channels [article]

Mohsen Barforooshan, Jan Østergaard, Milan S. Derpich
2017 arXiv   pre-print
The rate-limited channel connects the single measurement output of the plant to its single control input through a causal, but otherwise arbitrary, coder-controller pair.  ...  The performance of a noisy linear time-invariant (LTI) plant, controlled over a noiseless digital channel with transmission delay, is investigated in this paper.  ...  Then the main idea followed in [11] , [12] (that is, minimizing directed information rate to get lower bound and entropy coding for upper bound) is applied to LQG control of a fully-observable multiple-input  ... 
arXiv:1702.06445v1 fatcat:tx4ijxt74ngxdjhjdwj2uwnxdi

Rate-Cost Tradeoffs in Control

Victoria Kostina, Babak Hassibi
2019 IEEE Transactions on Automatic Control  
, and for control over noisy channels.  ...  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  ...  Accordingly, the theorems in Section II-A and Section II-B also characterize the operational rate-cost tradeoff for control with variable-length prefix-free quantizers. III.  ... 
doi:10.1109/tac.2019.2912256 fatcat:l2yq4ylw2jas3m2pksei6jxdfm
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