Affiliation:
1. Science and Information College, Qingdao Agricultural University, Qingdao 266109, China
2. College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao 266590, China
Abstract
The relationship between finite-horizon mean-field stochastic H2/H∞ control and Nash equilibrium strategies is investigated in this technical note. First, the finite-horizon mean-field stochastic bounded real lemma (SBRL) is established, which is key to developing the H∞ theory. Second, for mean-field stochastic differential equations (MF-SDEs) with control- and state-dependent noises, it is revealed that the existence of Nash equilibrium strategies is equivalent to the solvability of generalized differential Riccati equations (GDREs). Furthermore, the existence of Nash equilibrium strategies is equivalent to the solvability of H2/H∞ control for MF-SDEs with control- and state-dependent noises. However, for mean-field stochastic systems with disturbance-dependent noises, these two problems are not equivalent. Finally, a sufficient and necessary condition is presented via coupled matrix-valued equations for the finite-horizon H2/H∞ control of mean-field stochastic differential equations with disturbance-dependent noises.
Funder
National Natural Science Foundation of China
Advanced Talents Foundation of QAU
Crosswise tasks
Subject
Process Chemistry and Technology,Chemical Engineering (miscellaneous),Bioengineering
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