*Published Paper*

**Inserted:** 27 aug 2004

**Last Updated:** 11 feb 2008

**Journal:** Asymptotic Analysis

**Volume:** 45

**Number:** 3-4

**Pages:** 171-190

**Year:** 2005

**Abstract:**

We consider the sequence of optimal control problems having as state equation $y^\prime(t)=a_n(t,y)+b_n(t,u)$ ($t \in (0,T], \: y(0)=x$) and cost functional $J_n(y,u)={\rm ess\: sup }_{t \in [0,T]} f_n(t,y(t),u(t)).$ We prove a $\Gamma$-convergence result and we study the entailed properties on the stability for the related Hamilton-Jacobi equations.

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