ABSTRACT
In this chapter, we consider the multi-player stochastic https://www.w3.org/1998/Math/MathML"> H ∞ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429432941/63df2486-ef31-4a70-9449-3488247ff9a8/content/inline8_1.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> cooperative and non-cooperative game strategy design for a class of stochastic jump diffusion control system with external disturbance. To attenuate the effect from competitive strategies of other players and unpredictable external disturbance on the target tracking performance of each player, a multi-player stochastic https://www.w3.org/1998/Math/MathML"> H ∞ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429432941/63df2486-ef31-4a70-9449-3488247ff9a8/content/inline8_2.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> non-cooperative game strategy design problem is proposed at first and then transformed by an indirect method to a multi-tuple Hamilton–Jacobi–Issac inequalities (HJIIs)-constrained multi-objective optimization problem (MOP) with a Nash equilibrium solution. Also, the multi-player stochastic https://www.w3.org/1998/Math/MathML"> H ∞ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429432941/63df2486-ef31-4a70-9449-3488247ff9a8/content/inline8_3.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> cooperative game strategy design problem is discussed and then transformed to a HJII-constrained single-objective optimization problem (SOP). For the convenience of design and in order to overcome the difficulty of solving HJII, we use Takagi–Sugeno (T-S) fuzzy model to approximate the nonlinear stochastic system so that the HJIIS-constrained MOP could be transformed into a linear matrix inequalities (LMIs)-constrained MOP. Besides, an LMIs-constrained multi-objective evolution algorithm (MOEA) is developed to efficiently solve the non-cooperative multi-player control game strategy design problem. In the case of stochastic https://www.w3.org/1998/Math/MathML"> H ∞ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429432941/63df2486-ef31-4a70-9449-3488247ff9a8/content/inline8_4.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> cooperative game, by using the T-S fuzzy interpolation method, the HJII-constrained SOP is transformed into an equivalent LMI-constrained SOP. A financial market with multiple investors is provided as a simulation example to demonstrate the effectiveness of the proposed non-cooperative and cooperative stochastic https://www.w3.org/1998/Math/MathML"> H ∞ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429432941/63df2486-ef31-4a70-9449-3488247ff9a8/content/inline8_5.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> game investment strategies.
