In this paper we extend the adaptive gradient descent (AdaGrad) algorithm to the optimal distributed control of parabolic partial differential equations with uncertain parameters. This stochastic optimization method achieves an improved convergence rate through adaptive scaling of the gradient step size. We prove the convergence of the algorithm for this infinite dimensional problem under suitable regularity, convexity, and finite variance conditions, and relate these to verifiable properties of the underlying system parameters. Finally, we apply our algorithm to the optimal thermal regulation of lithium battery systems under uncertain loads.

翻译：在本文中,我们将适应性梯度下降算法(AdaGrad)推广到对参数不确定的抛物线部分差异方程式的最佳分布式控制。 这种随机优化法通过梯度梯度大小的适应性缩放,实现了更好的趋同率。 我们证明,在适当的规律性、凝固性和有限差异条件下,这一无限维度问题的算法已经趋同,并且与系统参数的可核实特性相关。 最后,我们运用我们的算法来对含不确定负荷的锂电池系统进行最佳热调节。