Feedback Nash Equilibrium for Markov Jump Games under Differential-Algebraic Constraints with Application to Robust Control

Aneel Tanwani, Quanyan Zhu

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

Abstract

As a subclass of stochastic differential games with algebraic constraints, this article studies dynamic noncooperative games where the constraints are described by jump Markov differential-algebraic equations (DAEs). Theoretical tools, which require computing the infinitesimal generator and deriving Hamiton-Jacobi-Bellman equation for Markov jump DAEs, are developed. These fundamental results lead to pure feedback optimal strategies to compute the Nash equilibrium in noncooperative setting. In case of quadratic cost and linear dynamics, these strategies are obtained by solving coupled Riccati differential equations. The problem of robust control can be formulated as a two-player zero sum game and is solved by applying the results developed in this paper.

Original languageEnglish (US)
Title of host publication2018 IEEE Conference on Decision and Control, CDC 2018
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages1124-1129
Number of pages6
ISBN (Electronic)9781538613955
DOIs
StatePublished - Jan 18 2019
Event57th IEEE Conference on Decision and Control, CDC 2018 - Miami, United States
Duration: Dec 17 2018Dec 19 2018

Publication series

NameProceedings of the IEEE Conference on Decision and Control
Volume2018-December
ISSN (Print)0743-1546

Conference

Conference57th IEEE Conference on Decision and Control, CDC 2018
CountryUnited States
CityMiami
Period12/17/1812/19/18

Fingerprint

Algebraic Differential Equations
Robust control
Robust Control
Nash Equilibrium
Jump
Differential equations
Jacobi Equation
Game
Stochastic Differential Games
Feedback
Riccati Differential Equation
Bellman Equation
Dynamic Games
Non-cooperative Game
Zero sum game
Infinitesimal Generator
Optimal Strategy
Computing
Costs
Strategy

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

Cite this

Tanwani, A., & Zhu, Q. (2019). Feedback Nash Equilibrium for Markov Jump Games under Differential-Algebraic Constraints with Application to Robust Control. In 2018 IEEE Conference on Decision and Control, CDC 2018 (pp. 1124-1129). [8619628] (Proceedings of the IEEE Conference on Decision and Control; Vol. 2018-December). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2018.8619628

Feedback Nash Equilibrium for Markov Jump Games under Differential-Algebraic Constraints with Application to Robust Control. / Tanwani, Aneel; Zhu, Quanyan.

2018 IEEE Conference on Decision and Control, CDC 2018. Institute of Electrical and Electronics Engineers Inc., 2019. p. 1124-1129 8619628 (Proceedings of the IEEE Conference on Decision and Control; Vol. 2018-December).

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

Tanwani, A & Zhu, Q 2019, Feedback Nash Equilibrium for Markov Jump Games under Differential-Algebraic Constraints with Application to Robust Control. in 2018 IEEE Conference on Decision and Control, CDC 2018., 8619628, Proceedings of the IEEE Conference on Decision and Control, vol. 2018-December, Institute of Electrical and Electronics Engineers Inc., pp. 1124-1129, 57th IEEE Conference on Decision and Control, CDC 2018, Miami, United States, 12/17/18. https://doi.org/10.1109/CDC.2018.8619628
Tanwani A, Zhu Q. Feedback Nash Equilibrium for Markov Jump Games under Differential-Algebraic Constraints with Application to Robust Control. In 2018 IEEE Conference on Decision and Control, CDC 2018. Institute of Electrical and Electronics Engineers Inc. 2019. p. 1124-1129. 8619628. (Proceedings of the IEEE Conference on Decision and Control). https://doi.org/10.1109/CDC.2018.8619628
Tanwani, Aneel ; Zhu, Quanyan. / Feedback Nash Equilibrium for Markov Jump Games under Differential-Algebraic Constraints with Application to Robust Control. 2018 IEEE Conference on Decision and Control, CDC 2018. Institute of Electrical and Electronics Engineers Inc., 2019. pp. 1124-1129 (Proceedings of the IEEE Conference on Decision and Control).
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