Long-Time Asymptotic Behavior of Hamilton–Jacobi–Bellman Equations for Control-Affine Systems

Speaker: Piermarco Cannarsa，University of Rome Tor Vergata

Inviter: 张建路

Title: Long-Time Asymptotic Behavior of Hamilton–Jacobi–Bellman Equations for Control-Affine Systems

Language: English

Time & Venue: 2026.06.25   14:00-15:00   南楼N913

Abstract: I will discuss the long-time asymptotic behavior of value functions associated with optimal control problems governed by control-affine dynamics, allowing for a nonzero drift and without assuming small-time local controllability. The corresponding Hamilton–Jacobi–Bellman equations are typically non-coercive and may fail to admit classical ergodic correctors.The talk will present the construction of the ergodic constant and the characterization of long-time averaged limits through suitable probability measures, extending ideas from weak KAM and Aubry–Mather theory beyond the coercive or fully controllable setting. I will also address the vanishing discount problem for control-affine systems with restricted reachable sets, showing that their asymptotic behavior can still be described even in the possible absence of correctors.The presentation will conclude with a brief discussion of some open problems and possible applications to mean-field games and multi-agent systems.