标题： 神经协态调节器：一种具有输入约束的实时最优控制数据驱动范式 显示英文标题

标题： Neural Co-state Regulator: A Data-Driven Paradigm for Real-time Optimal Control with Input Constraints

摘要： 我们提出了一种新颖的无监督学习框架，用于实时解决具有输入约束的非线性最优控制问题（OCPs）。 在此框架中，神经网络（NN）学习预测最优共状态轨迹，该轨迹在给定系统的任何状态下，基于庞特里亚金最小原理（PMP）使控制哈密顿量最小化。 具体而言，神经网络被训练以找到同时满足非线性系统动力学并最小化二次调节成本的范数最优共状态解。 然后通过求解二次规划（QP）从预测的最优共状态轨迹中提取控制输入，以满足输入约束和最优性条件。 我们创造了“神经共状态调节器”（NCR）这一术语来描述共状态神经网络和控制输入二次规划求解器的结合。 为了展示NCR的有效性，我们将它的反馈控制性能与专家非线性模型预测控制（MPC）求解器在单车模型上的性能进行了比较。 由于NCR的训练不依赖于通常次优的专家非线性控制求解器，因此即使在系统条件超出其原始训练域的情况下，NCR也能在收敛误差和输入轨迹平滑性方面优于非线性MPC求解器。 同时，NCR的计算时间比非线性MPC少两个数量级。 显示英文摘要

摘要： We propose a novel unsupervised learning framework for solving nonlinear optimal control problems (OCPs) with input constraints in real-time. In this framework, a neural network (NN) learns to predict the optimal co-state trajectory that minimizes the control Hamiltonian for a given system, at any system's state, based on the Pontryagin's Minimum Principle (PMP). Specifically, the NN is trained to find the norm-optimal co-state solution that simultaneously satisfies the nonlinear system dynamics and minimizes a quadratic regulation cost. The control input is then extracted from the predicted optimal co-state trajectory by solving a quadratic program (QP) to satisfy input constraints and optimality conditions. We coin the term neural co-state regulator (NCR) to describe the combination of the co-state NN and control input QP solver. To demonstrate the effectiveness of the NCR, we compare its feedback control performance with that of an expert nonlinear model predictive control (MPC) solver on a unicycle model. Because the NCR's training does not rely on expert nonlinear control solvers which are often suboptimal, the NCR is able to produce solutions that outperform the nonlinear MPC solver in terms of convergence error and input trajectory smoothness even for system conditions that are outside its original training domain. At the same time, the NCR offers two orders of magnitude less computational time than the nonlinear MPC.