This paper formalizes Hamiltonian-Informed Optimal Neural (Hion) controllers, a novel class of neural network-based controllers for dynamical systems and explicit non-linear model predictive control. Hion controllers estimate future states and compute optimal control inputs using Pontryagin's Maximum Principle. The proposed framework allows for customization of transient behavior, addressing limitations of existing methods. The Taylored Multi-Faceted Approach for Neural ODE and Optimal Control (T-mano) architecture facilitates training and ensures accurate state estimation. Optimal control strategies are demonstrated for both linear and non-linear dynamical systems.

翻译：本文形式化地提出了一类新颖的基于神经网络的控制器——哈密顿信息最优神经（Hion）控制器，适用于动力系统及显式非线性模型预测控制。Hion控制器利用庞特里亚金极大值原理估计未来状态并计算最优控制输入。所提出的框架允许对瞬态行为进行定制，从而解决了现有方法的局限性。为神经常微分方程与最优控制量身定制的多层面方法（T-mano）架构促进了训练过程，并确保了精确的状态估计。研究在线性与非线性动力系统中均展示了最优控制策略的有效性。