Robust incentive Stackelberg strategy for Markov jump linear stochastic systems via static output feedback

In this study, a robust static output feedback (SOF) incentive Stackelberg game for a Markov jump linear stochastic system governed by Itô differential equations with multiple leaders and multiple followers is investigated. The existence conditions for the SOF incentive Stackelberg strategies are de...

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Bibliographic Details
Published in:IET control theory & applications Vol. 14; no. 9; pp. 1246 - 1254
Main Authors: Mukaidani, Hiroaki, Saravanakumar, Ramasamy, Xu, Hua
Format: Journal Article
Language:English
Published: The Institution of Engineering and Technology 11.06.2020
Subjects:
bilinear matrix inequality
Brief Paper
CCSALTEs
classical Lagrange multiplier technique
computational complexity
differential equations
feedback
game theory
higher‐order cross‐coupled stochastic algebraic Lyapunov type equations
iterative methods
Itô differential equations
Krasnoselskii–Mann iterative algorithm
linear matrix inequalities
linear systems
Lyapunov methods
Markov jump linear stochastic system
NP‐hard problem
robust control
robust incentive Stackelberg strategy
robust static output feedback incentive Stackelberg game
SOF incentive Stackelberg strategies
SOF strategies
stochastic systems
iterative methods
Itô differential equations
Krasnoselskii–Mann iterative algorithm
bilinear matrix inequality
game theory
linear systems
CCSALTEs
differential equations
robust incentive Stackelberg strategy
feedback
SOF strategies
NP-hard problem
linear matrix inequalities
robust static output feedback incentive Stackelberg game
Markov jump linear stochastic system
stochastic systems
robust control
higher-order cross-coupled stochastic algebraic Lyapunov type equations
SOF incentive Stackelberg strategies
classical Lagrange multiplier technique
computational complexity
Lyapunov methods
ISSN:1751-8644, 1751-8652
Online Access:Get full text
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Summary:In this study, a robust static output feedback (SOF) incentive Stackelberg game for a Markov jump linear stochastic system governed by Itô differential equations with multiple leaders and multiple followers is investigated. The existence conditions for the SOF incentive Stackelberg strategies are derived in terms of the solvability of a set of higher-order cross-coupled stochastic algebraic Lyapunov type equations (CCSALTEs). A classical Lagrange multiplier technique is employed to solve the CCSALTEs; therefore, the solution of the bilinear matrix inequality, which is a common NP-hard problem when designing SOF strategies, is not required. A heuristic algorithm is developed based on the CCSALTEs. In particular, it is shown that a robust convergence is guaranteed by combining the Krasnoselskii–Mann iterative algorithm with a new convergence condition. The performance of the proposed algorithm is discussed and a simple practical example is provided to demonstrate the effectiveness of the proposed algorithm and the SOF incentive Stackelberg strategies.
ISSN:1751-8644
1751-8652
DOI:10.1049/iet-cta.2019.0917