题目： Non-coercive ergodic Hamilton-Jacobi-Bellman equations: controllable v.s. non-controllable case

报告人：Cristian Mendico（Università di Roma Tor Vergata）

时间：2023-09-22 16:00 — 17:00

地点：蒙民伟楼1105室

摘要: The long-time average behavior of the value function in the classical calculus of variation is known to be connected with the existence of solutions of the so-called critical equations, that is, a stationary Hamilton-Jacobi equation which includes a sort of nonlinear eigenvalue called the critical constant (or effective Hamiltonian). In this talks, we will address a similar issues for the dynamic programming equation of an optimal control problem, with nonlinear state equation, for which coercivity of the Hamiltonian is non longer true. We will focus the attention on three particular cases, namely:

1. control affine systems,

2. control of acceleration,

3. non controllable system with general state equation,

for which we can prove either the time-average asymptotic behavior or the complete long-time behavior. Besides the interests in all the positive answer we have, we will describe the open problems and the possible ways to solve them from the new ideas developed in the above cases. This talk is based on a series of research papers in collaboration with Piermarco Cannarsa, Pierre Cardaliaguet, Stephane Gaubert and Marc Quincampoix.

邀请人：程伟 老师