This work is concerned with stability analysis of stationary and time-varying equilibria in a class of mean-field games that relate to multi-agent control problems of flocking and swarming. The mean-field game framework is a non-cooperative model of distributed optimal control in large populations, and characterizes the optimal control for a representative agent in Nash-equilibrium with the population. A mean-field game model is described by a coupled PDE system of forward-in-time Fokker-Planck (FP) equation for density of agents, and a backward-in-time Hamilton-Jacobi-Bellman (HJB) equation for control. The linear stability analysis of fixed points of these equations typically proceeds via numerical computation of spectrum of the linearized MFG operator. We explore the Evans function approach that provides a geometric alternative to solving the characteristic equation.
- Dynamic Systems and Control Division
Stability Analysis in Mean-Field Games via an Evans Function Approach
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Grover, P. "Stability Analysis in Mean-Field Games via an Evans Function Approach." Proceedings of the ASME 2018 Dynamic Systems and Control Conference. Volume 3: Modeling and Validation; Multi-Agent and Networked Systems; Path Planning and Motion Control; Tracking Control Systems; Unmanned Aerial Vehicles (UAVs) and Application; Unmanned Ground and Aerial Vehicles; Vibration in Mechanical Systems; Vibrations and Control of Systems; Vibrations: Modeling, Analysis, and Control. Atlanta, Georgia, USA. September 30–October 3, 2018. V003T30A001. ASME. https://doi.org/10.1115/DSCC2018-8926
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