Stochastic H_2/H_∞ Control for Mean-Field Stochastic Differential Systems with ( x , u , v )-Dependent Noise

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS(2023)

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摘要
This paper studies a continuous-time stochastic H_2/H_∞ control problem for mean-field stochastic differential systems, with random initial value and diffusion coefficients depending explicitly on the state, control and disturbance as well as their expectations. A mean-field stochastic bounded real lemma is first established, characterizing the equivalence between H_∞ robust stability and the solvability of two indefinite differential Riccati equations. Based on this extremely useful result, an equivalent condition for the existence of H_2/H_∞ controller is proposed by utilizing the solution of two sets of cross-coupled indefinite Riccati equations. Moreover, when an H_2/H_∞ controller exists, both the optimal control input and the corresponding worst-case disturbance admit linear feedback representations of the state and its mathematical expectation.
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关键词
H_2/H_∞ control,Stochastic bounded real lemma,Mean-field,Indefinite Riccati differential equations
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