Discrete-time Mean-field Stochastic $H_2/H_\infty$ Control
Zhang Weihai, Ma Limin
TL;DR
This paper addresses the discrete-time mean-field stochastic $H_2/H_ $ control problem, deriving key lemmas and conditions for control design based on coupled matrix equations.
Contribution
It introduces a mean-field stochastic bounded real lemma and provides new solvability conditions for $H_2/H_ $ control in discrete-time mean-field systems.
Findings
Derived a mean-field stochastic bounded real lemma.
Established sufficient conditions for control problem solvability.
Connected control existence to coupled matrix equations.
Abstract
The finite horizon control problem of mean-field type for discrete-time systems is considered in this paper. Firstly, we derive a mean-field stochastic bounded real lemma (SBRL). Secondly, a sufficient condition for the solvability of discrete-time mean-field stochastic linear-quadratic (LQ) optimal control is presented. Thirdly, based on SBRL and LQ results, this paper establishes a sufficient condition for the existence of discrete-time stochastic control of mean-field type via the solvability of coupled matrix-valued equations.
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Taxonomy
TopicsStability and Control of Uncertain Systems · Stochastic processes and financial applications · Stability and Controllability of Differential Equations