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Pareto-Optimal Strategy for Linear Mean-Field Stochastic Systems With H∞ Constraint
IEEE Transactions on Cybernetics
|October 15, 2020
Summary
This study develops a Pareto-optimal strategy for linear mean-field stochastic systems with H∞ constraints, addressing external disturbances. The research provides a necessary and sufficient condition for designing this optimal control strategy.
Area of Science:
- Control Theory
- Stochastic Systems
- Mean-Field Theory
Background:
- Linear mean-field stochastic systems are susceptible to external disturbances.
- Designing Pareto-optimal strategies under H∞ constraints is crucial for system performance and stability.
- Existing methods may not fully address the complexities of mean-field interactions and stochasticity.
Purpose of the Study:
- To design a Pareto-optimal control strategy for linear mean-field stochastic systems subject to H∞ constraints.
- To investigate the conditions for the existence of such a strategy.
- To derive a method for obtaining the Pareto frontier for systems with state-dependent noise.
Main Methods:
- Integration of stochastic H∞ control theory and stochastic mean-field theory.
- Derivation of the stochastic bounded real lemma (SBRL) for the considered systems.
- Utilizing mean-field forward-backward stochastic differential equations to solve the Pareto-optimal problem.
- Analysis of coupled generalized differential Riccati equations and four-coupled matrix-valued equations.
Main Results:
- The existence of a closed-loop Pareto-optimal strategy is proven to be equivalent to the solvability of coupled generalized differential Riccati equations.
- A necessary and sufficient condition for the Pareto-optimal strategy under H∞ constraint is established via four-coupled matrix-valued equations.
- The Pareto frontier for mean-field stochastic systems with state-dependent noise is derived.
- A practical example demonstrates the effectiveness of the proposed methodology.
Conclusions:
- The study successfully designs a Pareto-optimal strategy for linear mean-field stochastic systems under H∞ constraints.
- The derived conditions and methods provide a robust framework for analyzing and controlling such complex systems.
- The results offer valuable insights for applications requiring optimal trade-offs in stochastic environments.
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