<p style='text-indent:20px;'>A non-autonomous random dynamical system is called to be controllable if there is a pullback random attractor (PRA) such that each fibre of the PRA converges upper semi-continuously to a nonempty compact set (called a controller) as the time-parameter goes to minus infinity, while the PRA is called to be asymptotically autonomous if there is a random attractor for another (autonomous) random dynamical system as a controller. We establish the criteria for ensuring the existence of the minimal controller and the asymptotic autonomy of a PRA respectively. The abstract results are illustrated in possibly non-autonomous stochastic p-Laplace lattice equations with tempered convergent external forces.</p>

中文翻译：

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随机 p-Laplace 晶格方程的随机吸引子的控制器和渐近自治

<p style='text-indent:20px;'>如果存在一个回拉随机吸引子（PRA）使得PRA的每根纤维上半连续收敛到一个非空的，则称一个非自治的随机动力系统是可控的当时间参数趋于负无穷时，紧集（称为控制器），而如果存在另一个（自治）随机动力系统作为控制器的随机吸引子，则称 PRA 是渐近自治的。我们分别建立了确保最小控制器存在和 PRA 渐近自治的标准。抽象的结果用可能是非自治的随机p-拉普拉斯晶格方程和回火收敛外力来说明。</p>