This work considers artificial feed-forward neural networks as parametric approximators in optimal control of discrete-time systems. Two different approaches are introduced to take polytopic input constraints into account. The first approach determines (sub-)optimal inputs by the application of gradient methods. Closed-form expressions for the gradient of general neural networks with respect to their inputs are derived. The approach allows to consider state-dependent input constraints, as well as to ensure the satisfaction of state constraints by exploiting recursive reachable set computations. The second approach makes use of neural networks with softmax output units to map states into parameters, which determine (sub-)optimal inputs by a convex combination of the vertices of the input constraint set. The application of both approaches in model predictive control is discussed, and results obtained for a numerical example are used for illustration.

中文翻译：

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基于神经网络的基于学习的最优控制中的多面体输入约束

这项工作将人工前馈神经网络视为离散时间系统最优控制中的参数逼近器。引入了两种不同的方法来考虑多主题输入约束。第一种方法是通过应用梯度方法确定（次优）最优输入。推导了通用神经网络相对于其输入的梯度的闭式表达式。该方法允许考虑与状态有关的输入约束，以及通过利用递归可到达集合计算来确保满足状态约束。第二种方法利用具有softmax输出单元的神经网络将状态映射到参数，这些参数通过输入约束集的顶点的凸组合确定（次）最优输入。