Game-Theoretic Analysis of Optimal Control and Sampling for Linear Stochastic Systems

Guanze Peng, Quanyan Zhu

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

The growing deployment of Internet of Things (IoT) technologies has enabled highly distributed cyber-physical systems in which the sensors and controllers are physically separated and operated by distinct entities who may not able to coordinate. In this work, we formulate a game-theoretic design framework to capture the non-cooperative behaviors between a sampler and a controller. At the cyber layer, the sampler aims to find the best sampling scheme to achieve its design objective. At the physical layer, the controller aims to solve a class of linear-quadratic Gaussian (LQG) problems subject to the arrivals of the sampled observations. The system performance under the uncoordinated sampling and control can be characterized by the Nash equilibrium of the nonzero-sum game. We completely solve the controller's problem under a given information structure and provide a sufficient condition for the game to admit a unique equilibrium. Under mild conditions, we show that the sampling scheme at the Nash equilibrium results in a worse performance of both the sampler and the controller due to the lack of coordination. We use numerical examples to corroborate the analytical results and show that there exists a fundamental threshold on the sampling rate for an unstable system to be stabilized.

Original languageEnglish (US)
Title of host publication2019 57th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2019
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages647-654
Number of pages8
ISBN (Electronic)9781728131511
DOIs
StatePublished - Sep 2019
Event57th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2019 - Monticello, United States
Duration: Sep 24 2019Sep 27 2019

Publication series

Name2019 57th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2019

Conference

Conference57th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2019
CountryUnited States
CityMonticello
Period9/24/199/27/19

Keywords

  • Nash game
  • Stochastic optimal control
  • dynamic programming
  • fixed point equation
  • geometric distribution

ASJC Scopus subject areas

  • Artificial Intelligence
  • Computer Networks and Communications
  • Hardware and Architecture
  • Safety, Risk, Reliability and Quality
  • Control and Optimization

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