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

Aneel Tanwani; Quanyan Zhu

doi:10.1109/CDC.2018.8619628

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

Aneel Tanwani, Quanyan Zhu

Electrical and Computer Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference 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 language	English (US)
Title of host publication	2018 IEEE Conference on Decision and Control, CDC 2018
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	1124-1129
Number of pages	6
ISBN (Electronic)	9781538613955
DOIs	https://doi.org/10.1109/CDC.2018.8619628
State	Published - Jul 2 2018
Event	57th IEEE Conference on Decision and Control, CDC 2018 - Miami, United States Duration: Dec 17 2018 → Dec 19 2018

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
Volume	2018-December
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Conference

Conference	57th IEEE Conference on Decision and Control, CDC 2018
Country/Territory	United States
City	Miami
Period	12/17/18 → 12/19/18

ASJC Scopus subject areas

Control and Systems Engineering
Modeling and Simulation
Control and Optimization

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10.1109/CDC.2018.8619628

Cite this

Tanwani, A., & Zhu, Q. (2018). 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). Article 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., 2018. p. 1124-1129 8619628 (Proceedings of the IEEE Conference on Decision and Control; Vol. 2018-December).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Tanwani, A & Zhu, Q 2018, 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. 2018. p. 1124-1129. 8619628. (Proceedings of the IEEE Conference on Decision and Control). doi: 10.1109/CDC.2018.8619628

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AB - 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.

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

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