### Abstract

This paper studies the minimal rate requirements for state estimation in linear time-invariant (LTI) systems where the controller and the plant are connected via a noiseless bandlimited channel. Using information theoretic arguments, we obtain first for scalar systems lower bounds on the data rates required for state estimation under three different stability criteria; monotonie boundedness of distortion, terminaltime distortion minimization and stability in support size. The minimum data rate achievable by any source-coder is computed under each of these criteria, and the best rate achievable with quantization (operational source-coding) is shown to be in agreement with the information-theoretic bounds in some specific cases (such as if the system coefficient is an integer or if the criterion is an asymptotic one). The optimal variable-rate and fixed-rate quantizers are studied and constructed for each of these criteria. We then extend these results to multi-dimensional systems, replacing the distortion measure in the first criterion with differential entropy. One byproduct of this analysis is the message that entropy is not an appropriate measure of uncertainty in multi-dimensional systems for control purposes.

Original language | English (US) |
---|---|

Pages (from-to) | 4503-4508 |

Number of pages | 6 |

Journal | Proceedings of the IEEE Conference on Decision and Control |

Volume | 4 |

State | Published - Dec 1 2004 |

Event | 2004 43rd IEEE Conference on Decision and Control (CDC) - Nassau, Bahamas Duration: Dec 14 2004 → Dec 17 2004 |

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### ASJC Scopus subject areas

- Control and Systems Engineering
- Modeling and Simulation
- Control and Optimization

### Cite this

*Proceedings of the IEEE Conference on Decision and Control*,

*4*, 4503-4508.

**Minimum rate coding for state estimation over noiseless channels.** / Yüksel, Serdar; Basar, M Tamer.

Research output: Contribution to journal › Conference article

*Proceedings of the IEEE Conference on Decision and Control*, vol. 4, pp. 4503-4508.

}

TY - JOUR

T1 - Minimum rate coding for state estimation over noiseless channels

AU - Yüksel, Serdar

AU - Basar, M Tamer

PY - 2004/12/1

Y1 - 2004/12/1

N2 - This paper studies the minimal rate requirements for state estimation in linear time-invariant (LTI) systems where the controller and the plant are connected via a noiseless bandlimited channel. Using information theoretic arguments, we obtain first for scalar systems lower bounds on the data rates required for state estimation under three different stability criteria; monotonie boundedness of distortion, terminaltime distortion minimization and stability in support size. The minimum data rate achievable by any source-coder is computed under each of these criteria, and the best rate achievable with quantization (operational source-coding) is shown to be in agreement with the information-theoretic bounds in some specific cases (such as if the system coefficient is an integer or if the criterion is an asymptotic one). The optimal variable-rate and fixed-rate quantizers are studied and constructed for each of these criteria. We then extend these results to multi-dimensional systems, replacing the distortion measure in the first criterion with differential entropy. One byproduct of this analysis is the message that entropy is not an appropriate measure of uncertainty in multi-dimensional systems for control purposes.

AB - This paper studies the minimal rate requirements for state estimation in linear time-invariant (LTI) systems where the controller and the plant are connected via a noiseless bandlimited channel. Using information theoretic arguments, we obtain first for scalar systems lower bounds on the data rates required for state estimation under three different stability criteria; monotonie boundedness of distortion, terminaltime distortion minimization and stability in support size. The minimum data rate achievable by any source-coder is computed under each of these criteria, and the best rate achievable with quantization (operational source-coding) is shown to be in agreement with the information-theoretic bounds in some specific cases (such as if the system coefficient is an integer or if the criterion is an asymptotic one). The optimal variable-rate and fixed-rate quantizers are studied and constructed for each of these criteria. We then extend these results to multi-dimensional systems, replacing the distortion measure in the first criterion with differential entropy. One byproduct of this analysis is the message that entropy is not an appropriate measure of uncertainty in multi-dimensional systems for control purposes.

UR - http://www.scopus.com/inward/record.url?scp=14244256362&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=14244256362&partnerID=8YFLogxK

M3 - Conference article

AN - SCOPUS:14244256362

VL - 4

SP - 4503

EP - 4508

JO - Proceedings of the IEEE Conference on Decision and Control

JF - Proceedings of the IEEE Conference on Decision and Control

SN - 0191-2216

ER -