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Mean-Field Selective Optimal Control via Transient Leadership
Giacomo Albi1, Stefano Almi2, Marco Morandotti3
1Dipartimento di Informatica, Università di Verona, Strada Le Grazie 14, Ca Vignal 2, 37134 Verona, Italy.
Applied Mathematics and Optimization
|May 10, 2022
Summary
This study introduces a mean-field optimal control method for multipopulation systems, enabling targeted interventions by identifying influential agents. The approach ensures convergence of control strategies for complex dynamics.
Area of Science:
- Optimal control theory
- Statistical physics
- Agent-based modeling
Background:
- Mean-field models simplify complex systems by considering average behavior.
- Optimal control aims to find the best strategy to influence system dynamics.
- Multipopulation dynamics involve interactions between distinct groups.
Purpose of the Study:
- To develop a mean-field selective optimal control framework for multipopulation systems.
- To enable policy makers to target specific agents based on their influence.
- To analyze the convergence of optimal control strategies in such systems.
Main Methods:
- Formulation of a mean-field selective optimal control problem.
- Analysis of a finite-particle system and its mean-field limit using epsilon-convergence.
- Derivation of the governing equation for mean-field optimal control (a continuity-type equation).
Main Results:
- Identification of the mean-field limit for the optimal control problem.
- Demonstration of convergence for optimal control strategies.
- The mean-field dynamics are described by a diffusionless continuity equation.
Conclusions:
- The proposed method provides a rigorous framework for selective optimal control in multipopulation systems.
- Transient leadership and agent influence are key factors in selective control.
- The approach is applicable to real-world scenarios like opinion dynamics.
Keywords:
Leader-follower dynamicsMean-field optimal controlPopulation dynamicsSelective controlSuperposition principleMore Related Videos
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