Control With Minimal Cost-Per-Symbol Encoding and Quasi-Optimality of Event-Based Encoders

We consider the problem of stabilizing a continuous-time linear time-invariant system subject to communication constraints. A noiseless finite-capacity communication channel connects the process sensors to the controller/actuator. The sensor's state measurements are encoded into symbols from a...

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Veröffentlicht in:	IEEE transactions on automatic control Jg. 62; H. 5; S. 2286 - 2301
Hauptverfasser:	Pearson, Justin, Hespanha, Joao P., Liberzon, Daniel
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	New York IEEE 01.05.2017 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:	Actuators Clocks Coders Communication Communication channels Communications systems Consumption Continuous time systems Controllers Decoding Eigenvalues Eigenvalues and eigenfunctions Encoders-Decoders Encoding Optimization Process control Sensors Time invariant systems
ISSN:	0018-9286, 1558-2523
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Abstract	We consider the problem of stabilizing a continuous-time linear time-invariant system subject to communication constraints. A noiseless finite-capacity communication channel connects the process sensors to the controller/actuator. The sensor's state measurements are encoded into symbols from a finite alphabet, transmitted through the channel, and decoded at the controller/actuator. We suppose that the transmission of each symbol costs one unit of communication resources, except for one special symbol in the alphabet that is "free" and effectively signals the absence of transmission. We explore the relationship between the encoder's average bit-rate, its average consumption of communication resources, and the ability of the controller and encoder/decoder pair to stabilize the process. We present a necessary and sufficient condition for the existence of a stabilizing controller and encoder/decoder pair, which depends on the encoder's average bit-rate, its average resource consumption, and the unstable eigenvalues of the process. Moreover, if this condition is satisfied, a stabilizing encoding scheme can be constructed that consumes resources at an arbitrarily small rate, provided the encoder has access to a sufficiently precise clock or large memory. The paper concludes with the analysis of a simple emulation-based controller and event-based encoder/decoder pair that are easy to implement, stabilize the process, and have average bit-rate and resource consumption within a constant factor of the optimal bound.
AbstractList	We consider the problem of stabilizing a continuous-time linear time-invariant system subject to communication constraints. A noiseless finite-capacity communication channel connects the process sensors to the controller/actuator. The sensor's state measurements are encoded into symbols from a finite alphabet, transmitted through the channel, and decoded at the controller/actuator. We suppose that the transmission of each symbol costs one unit of communication resources, except for one special symbol in the alphabet that is “free” and effectively signals the absence of transmission. We explore the relationship between the encoder's average bit-rate, its average consumption of communication resources, and the ability of the controller and encoder/decoder pair to stabilize the process. We present a necessary and sufficient condition for the existence of a stabilizing controller and encoder/decoder pair, which depends on the encoder's average bit-rate, its average resource consumption, and the unstable eigenvalues of the process. Moreover, if this condition is satisfied, a stabilizing encoding scheme can be constructed that consumes resources at an arbitrarily small rate, provided the encoder has access to a sufficiently precise clock or large memory. The paper concludes with the analysis of a simple emulation-based controller and event-based encoder/decoder pair that are easy to implement, stabilize the process, and have average bit-rate and resource consumption within a constant factor of the optimal bound.
Author	Pearson, Justin Liberzon, Daniel Hespanha, Joao P.
Author_xml	– sequence: 1 givenname: Justin surname: Pearson fullname: Pearson, Justin email: jppearson@ece.ucsb.edu organization: Dept. of Electr. & Comput. Eng., Univ. of California, Santa Barbara, Santa Barbara, CA, USA – sequence: 2 givenname: Joao P. surname: Hespanha fullname: Hespanha, Joao P. email: hespanha@ece.ucsb.edu organization: Dept. of Electr. & Comput. Eng., Univ. of California, Santa Barbara, Santa Barbara, CA, USA – sequence: 3 givenname: Daniel surname: Liberzon fullname: Liberzon, Daniel email: liberzon@uiuc.edu organization: Coordinated Sci. Lab., Univ. of Illinois at Urbana-Champaign, Urbana, IL, USA
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Cites_doi	10.1145/2185632.2185669 10.1109/CDC.2000.912906 10.1109/TAC.2013.2241491 10.1109/CDC.2015.7402968 10.1016/j.automatica.2009.10.035 10.1109/CDC.2006.377483 10.1137/S0363012902419965 10.1109/9.867021 10.1016/S0005-1098(02)00285-6 10.1109/CDC.2014.7040336 10.1109/TAC.2007.904277 10.1109/CDC.2002.1184824 10.1137/040621697 10.1109/TAC.2004.831187 10.1109/ACC.2012.6315501
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References	ref13 ref12 ref15 hespanha (ref2) 0 ref20 goebel (ref16) 2012 ref11 ref1 ref17 ref19 tatikonda (ref23) 2000 ref8 åström (ref9) 0; 2 ref7 ref4 lehmann (ref14) 0 ref3 ref6 åström (ref10) 2007 ref5 pearson (ref22) 2016 tallapragada (ref18) 2014 cover (ref21) 2012
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SubjectTerms	Actuators Clocks Coders Communication Communication channels Communications systems Consumption Continuous time systems Controllers Decoding Eigenvalues Eigenvalues and eigenfunctions Encoders-Decoders Encoding Optimization Process control Sensors Time invariant systems
Title	Control With Minimal Cost-Per-Symbol Encoding and Quasi-Optimality of Event-Based Encoders
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