ABSTRACT
A fuzzy stochastic https://www.w3.org/1998/Math/MathML"> H 2 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429432941/63df2486-ef31-4a70-9449-3488247ff9a8/content/inline7_1.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> game theory is proposed to solve the https://www.w3.org/1998/Math/MathML"> n https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429432941/63df2486-ef31-4a70-9449-3488247ff9a8/content/inline7_2.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> -person (or https://www.w3.org/1998/Math/MathML"> n https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429432941/63df2486-ef31-4a70-9449-3488247ff9a8/content/inline7_3.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> -player) nonlinear stochastic noncooperative https://www.w3.org/1998/Math/MathML"> H 2 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429432941/63df2486-ef31-4a70-9449-3488247ff9a8/content/inline7_4.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> game and cooperative https://www.w3.org/1998/Math/MathML"> H 2 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429432941/63df2486-ef31-4a70-9449-3488247ff9a8/content/inline7_5.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> game (team) problems, which are not easily tackled by the conventional methods. In this chapter, both noncooperative and cooperative quadratic ( https://www.w3.org/1998/Math/MathML"> H 2 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429432941/63df2486-ef31-4a70-9449-3488247ff9a8/content/inline7_6.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> ) stochastic games are considered. First, the nonlinear stochastic system is approximated by a T-S fuzzy system. Based on the T-S fuzzy system, a fuzzy observer-based controller is proposed to deal with nonlinear stochastic control system based on the noncooperative stochastic https://www.w3.org/1998/Math/MathML"> H 2 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429432941/63df2486-ef31-4a70-9449-3488247ff9a8/content/inline7_7.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> game in the sense of Nash equilibrium strategy or on the cooperative stochastic https://www.w3.org/1998/Math/MathML"> H 2 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429432941/63df2486-ef31-4a70-9449-3488247ff9a8/content/inline7_8.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> game in the sense of Pareto-optimal strategy. Using a suboptimal approach, the outcomes of the fuzzy stochastic games for both the noncooperative and the cooperative stochastic https://www.w3.org/1998/Math/MathML"> H 2 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429432941/63df2486-ef31-4a70-9449-3488247ff9a8/content/inline7_9.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> game strategies are solved in terms of an iterative update eigenvalue problem. Since the state variables are usually unavailable, a suboptimal fuzzy observer is also proposed to estimate the states for these stochastic noncooperative and cooperative https://www.w3.org/1998/Math/MathML"> H 2 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429432941/63df2486-ef31-4a70-9449-3488247ff9a8/content/inline7_10.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> game design problems. Finally, simulation examples of noncooperative and cooperative stochastic https://www.w3.org/1998/Math/MathML"> H 2 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429432941/63df2486-ef31-4a70-9449-3488247ff9a8/content/inline7_11.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> games of a three-machine interconnected system are given to illustrate the design procedures and to indicate the stochastic control performance of the proposed stochastic https://www.w3.org/1998/Math/MathML"> H 2 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429432941/63df2486-ef31-4a70-9449-3488247ff9a8/content/inline7_12.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> game methods.
