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Internal Stability of Dynamically Quantised Control for Stochastic Scalar Plants

Assaf Gurt, Girish N. Nair
2008 IFAC Proceedings Volumes  
In this paper, we remove this assumption and explicitly construct a finite-dimensional coding and control policy that yields mean square stability of all state variables, for a random initial plant state  ...  In this paper we study conditions under which an unstable stochastic scalar linear plant with unbounded noise can be internally stabilised using 'zooming'-like coding and control schemes having dynamic  ...  As a consequence, many papers have appeared recently in the literature which addressed the problem of controlling an unstable plant using quantised control schemes with limited bit rate; see Nair et al  ... 
doi:10.3182/20080706-5-kr-1001.00873 fatcat:pv7al5t2jfd5rjabyhz77sg64m

Data Rate Theorem for Stabilization Over Time-Varying Feedback Channels

Paolo Minero, Massimo Franceschetti, Subhrakanti Dey, Girish N. Nair
2009 IEEE Transactions on Automatic Control  
A data rate theorem for stabilization of a linear, discrete-time, dynamical system with arbitrarily large disturbances, over a rate-limited, time-varying communication channel is presented.  ...  Necessary and sufficient conditions for stabilization are derived, their implications and relationships with related results in the literature are discussed.  ...  in systems with unbounded disturbances.  ... 
doi:10.1109/tac.2008.2010887 fatcat:ohjesy6m2zdfdlfdencmnlvfgu

Non-coherence in estimation and control

Gireeja Ranade, Anant Sahai
2013 2013 51st Annual Allerton Conference on Communication, Control, and Computing (Allerton)  
The paper considers the estimation and control of a discretetime linear system with continuous random observation gain, i.e. through a non-coherent channel.  ...  In contrast to other results with rate-limited feedback, the paper shows that the system can be closed-loop mean-square stabilized in a certain parameter regime even though its open-loop counterpart is  ...  ACKNOWLEDGEMENTS We acknowledge support of the NSF through the grant CNS-0932410 and a GRF.  ... 
doi:10.1109/allerton.2013.6736523 dblp:conf/allerton/RanadeS13 fatcat:77vir347fvge7eyqf4zz3tnknq

Optimal estimation in networked control systems subject to random delay and packet loss

Luca Schenato
2006 Proceedings of the 45th IEEE Conference on Decision and Control  
We present two time-invariant estimator architectures and, surprisingly, we show that stability does not depend on packet delay but only on the packet loss probability.  ...  In this paper we study optimal estimation design for sampled linear systems where the sensors measurements are transmitted to the estimator site via a generic digital communication network.  ...  Scenario (D) corresponds to a DCN with no packet loss but with unbounded random packet delay.  ... 
doi:10.1109/cdc.2006.377700 dblp:conf/cdc/000106 fatcat:ulq7c2xmyjemrh2k73a5calcte

Control Capacity [article]

Gireeja Ranade, Anant Sahai
2017 arXiv   pre-print
Control capacity allows us to answer questions of stabilizability for scalar linear systems: a system with actuation uncertainty is stabilizable if and only if the control capacity is larger than the log  ...  We develop a notion of "control capacity" that gives a fundamental limit (in bits) on the rate at which a controller can dissipate the uncertainty from a system, i.e. stabilize to a known fixed point.  ...  Unlike the case with deterministic system gains, ADT models would not suffice to understand systems with random control gains, since they only capture bit shifts.  ... 
arXiv:1701.04187v1 fatcat:ivskk2wn6radnad2wr6izwyaia

Towards a Packet-based Control Theory - Part II: Rate Issues

Ling Shi, R.M. Murray
2006 2006 American Control Conference  
Specifically, networks with finite bandwidth and packet drops and systems with finite control inputs are studied in detail.  ...  Following our first paper of stabilizing a Linear Time Invariant (LTI) system in a packet-based network, which appeared in ACC 05, this paper further studies various rate issues associated with networked  ...  Acknowledgment The authors would like to thank Michael Epstein for helping simulate the closed loop system in the previous section.  ... 
doi:10.1109/acc.2006.1657257 fatcat:tk5wrgehznf3hlmebhehqifqaq

Exact minimum number of bits to stabilize a linear system

Victoria Kostina, Yuval Peres, Gireeja Ranade, Mark Sellke
2018 2018 IEEE Conference on Decision and Control (CDC)  
We consider an unstable scalar linear stochastic system, Xn+1 = aXn + Zn − Un, where a ≥ 1 is the system gain, Zn's are independent random variables with bounded αth moments, and Un's are the control actions  ...  that are chosen by a controller who receives a single element of a finite set {1, . . . , M } as its only information about system state Xi.  ...  In [12] , we applied a similar strategy to stabilize a system with random gain a (which is constant in the present paper) using finitely many bits at each time step.  ... 
doi:10.1109/cdc.2018.8619156 dblp:conf/cdc/KostinaPRS18 fatcat:6sxup3q4bfhrdgaukf7q4wzgui

Internal stability of dynamic quantised control for stochastic linear plants

Assaf Gurt, Girish N. Nair
2009 Automatica  
In this article, we consider partially observed, unstable linear time-invariant plants, with unbounded and possibly non-Gaussian noise, and propose a modified zooming-like scheme with finite-dimensional  ...  Existing analyses of 'zooming' quantisation schemes for bit-rate-limited control systems rely on the encoder and controller being initialised with identical internal states.  ...  Acknowledgements The authors acknowledge insightful discussions on this topic with colleagues Dr. T. Kameneva and Prof. D. Nesic at Uni. Melbourne.  ... 
doi:10.1016/j.automatica.2009.02.016 fatcat:teumhlgkqfdjjddabpk7uj6yfm

The Necessity and Sufficiency of Anytime Capacity for Stabilization of a Linear System Over a Noisy Communication Link—Part I: Scalar Systems

A. Sahai, S. Mitter
2006 IEEE Transactions on Information Theory  
an unstable scalar linear system.  ...  The required rate is given by the log of the unstable system gain and the required reliability comes from the sense of stability desired.  ...  They thank Nicola Elia for several constructive discussions about the subject matter of this paper and Sekhar Tatikonda for many discussions over a long period of time which have influenced this work in  ... 
doi:10.1109/tit.2006.878169 fatcat:dqphgtzve5a2na6slzjpy6ln6m

Slotted Gaussian Multiple Access Channel: Stable Throughput Region and Role of Side Information

Vaneet Aggarwal, Ashutosh Sabharwal
2008 EURASIP Journal on Wireless Communications and Networking  
The first notion is the conventional Shannon capacity which relies on large coding block lengths for finite SNR, while the second uses finite code blocks with high SNR.  ...  We find that the stable throughput region coincides with the Shannon capacity region for many scenarios of side information, where side information is defined as a mix of statistical description and instantaneous  ...  A. Sabharwal was partially supported by NSF Awards CCF-0635331 and CNS-0325971.  ... 
doi:10.1155/2008/695894 fatcat:uvnthwo73jdn5i64q2r5uno2xu

Optimal Estimation in Networked Control Systems Subject to Random Delay and Packet Drop

Luca Schenato
2008 IEEE Transactions on Automatic Control  
Moreover, this estimator is independent of the communication protocol and can be implemented using a finite memory buffer if and only if the delivered packets have a finite maximum delay.  ...  For example consider a WSN deployed in a forest whose nodes are equipped with temperature and humidity sensors, as graphically shown in the left panel of Fig. 1 .  ...  random packet delay with packet loss (C); unbounded random packet delay with no packet loss (D).  ... 
doi:10.1109/tac.2008.921012 fatcat:xbltno356jd5rogorvdkgbgvcu

Elements of Information Theory for Networked Control Systems [chapter]

Massimo Franceschetti, Paolo Minero
2014 Lecture notes in control and information sciences  
This motivated, at the turning of the millennium, the birth of a new chapter of control theory relating the ability to control dynamical systems to the characteristics of the communication channels used  ...  and interacting with the physical world.  ...  rate channels with unbounded system disturbances.  ... 
doi:10.1007/978-3-319-02150-8_1 fatcat:p7t5op24crhsba5khmjwjoecuq

Exact minimum number of bits to stabilize a linear system [article]

Victoria Kostina, Yuval Peres, Gireeja Ranade, Mark Sellke
2021 arXiv   pre-print
We consider an unstable scalar linear stochastic system, X_n+1=a X_n + Z_n - U_n, where a ≥ 1 is the system gain, Z_n's are independent random variables with bounded α-th moments, and U_n's are the control  ...  actions that are chosen by a controller who receives a single element of a finite set {1, ..., M} as its only information about system state X_i.  ...  In [28] , we applied a similar strategy to stabilize a system with random gain a (which is constant in the present paper) using finitely many bits at each time step.  ... 
arXiv:1807.07686v3 fatcat:v4bbe764dbec3awtyaqrj5umyu

Stabilization using both noisy and noiseless feedback [article]

Anant Sahai
2006 arXiv   pre-print
Using the standard toy example of scalar stabilization, this paper shows how a small amount of noiseless feedback can perform a "supervisory" role and thereby boost the effectiveness of noisy feedback.  ...  When designing a distributed control system, the system designer has a choice in how to connect the different units through communication channels.  ...  Definition 2.2: A discrete time discrete memoryless channel (DMC) is a probabilistic system with an input.  ... 
arXiv:cs/0610141v1 fatcat:whposlvm6rbajefw5algewo46e

Localization and topology protected quantum coherence at the edge of hot matter

Yasaman Bahri, Ronen Vosk, Ehud Altman, Ashvin Vishwanath
2015 Nature Communications  
This is in sharp contrast to the general expectation that quantum bits strongly coupled with a hot many-body system will rapidly lose coherence.  ...  However, disorder can localize an isolated many-body system, potentially allowing for a sharply defined topological phase even in a highly excited state.  ...  Acknowledgements We acknowledge illuminating discussions with D. Huse  ... 
doi:10.1038/ncomms8341 pmid:26159426 fatcat:64vznsxpsbc2dmsqo2tpc2c2gq
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