Multi-leader-Follower Incentive Stackelberg Game for Infinite-Horizon Markov Jump Linear Stochastic Systems with H_∞ Constraint

2018 ◽  
Author(s):  
Hiroaki Mukaidani ◽  
Hua Xu ◽  
Tadashi Shima ◽  
Mostak Ahmed
Keyword(s):  
Stochastic Systems ◽  
Stackelberg Game ◽  
Infinite Horizon ◽  
Markov Jump ◽  
Linear Stochastic Systems

Differential Games for Weakly Coupled Large-Scale Linear Stochastic Systems with an H∞-Constraint

2018 ◽  
Vol 20 (01) ◽  
pp. 1750025
Author(s):  
Hiroaki Mukaidani ◽  
Hua Xu
Keyword(s):  
Large Scale ◽  
Stochastic Systems ◽  
Necessary Conditions ◽  
Design Method ◽  
Infinite Horizon ◽  
Efficient Design ◽  
Reduced Order ◽  
Riccati Differential Equations ◽  
Weakly Coupled ◽  
Linear Stochastic Systems

A differential game approach for the finite-horizon stochastic control problem with an [Formula: see text]-constraint is considered for a class of large-scale linear systems. First, necessary conditions for the existence of a control strategy set are established by means of cross-coupled stochastic Riccati differential equations (CSRDEs). Second, an efficient design method to obtain a reduced-order parameter-independent approximate strategy set is proposed. Moreover, the performance degradation is estimated. Infinite-horizon case is also discussed. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed design scheme.

scholarly journals H∞ Control for Nonlinear Infinite Markov Jump Systems

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Yueying Liu ◽  
Ting Hou
Keyword(s):  
Stochastic Systems ◽  
Design Method ◽  
Infinite Horizon ◽  
Mean Square ◽  
State Control ◽  
Markov Jump ◽  
Nonlinear Stochastic Systems ◽  
Markov Jump Systems ◽  
Jump Systems ◽  
Infinite State

In this paper, we discuss the infinite horizon H∞ control problem for a class of nonlinear stochastic systems with state, control, and disturbance dependent noise. The jumping parameters are modelled as an infinite-state Markov chain. Based on the solvability of a set of coupled Hamilton-Jacobi inequalities (HJIs), the exponential mean square H∞ controller for the considered nonlinear stochastic systems is obtained. A numerical example is given to show the effectiveness of the proposed design method.

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