中国科学院数学与系统科学研究院
数学研究所
数学科学全国重点实验室
动力系统研讨班
Speaker: Piermarco Cannarsa（University of Rome Tor Vergata）
Inviter: 张建路
Language: English
Title: Long-Time Asymptotic Behavior of Hamilton–Jacobi–Bellman Equations for Control-Affine Systems
Time & Venue: 2026年6月25日（星期四）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.
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