Lyapunov Neural ODE 状态反馈控制策略
Lyapunov Neural ODE State-Feedback Control Policies
AI总结：
本文提出 L-NODEC 方法，利用结合指数稳定控制 Lyapunov 函数的新颖 Lyapunov 损失学习状态反馈神经控制策略，解决了连续时间最优控制问题，保证了受控系统的指数稳定性和对抗鲁棒性，并减少了推理时间。
摘要：
深度神经网络正越来越多地被用作各种基于学习的控制范式中控制策略的有效参数化方法。对于许多决策任务至关重要的连续时间最优控制问题，控制策略学习可以转化为神经常微分方程（NODE）问题，其中状态和控制约束得到自然满足。本文提出了一种 NODE 方法，用于在已知受约束非线性系统围绕目标状态稳定的情况下求解连续时间 OCP。该方法被称为 Lyapunov-NODE 控制（L-NODEC），使用一种新颖的 Lyapunov 损失公式，结合指数稳定控制 Lyapunov 函数来学习状态反馈神经控制策略，弥合了通过 NODE 求解连续时间 OCP 且具有稳定性保证的差距。所提出的 Lyapunov 损失使 L-NODEC 能够保证受控系统的指数稳定性，以及其对初始状态扰动的对抗鲁棒性。L-NODEC 的性能在两个问题中得到了说明，包括等离子体医学中的剂量输送问题。在这两种情况下，尽管存在对初始状态的扰动，L-NODEC 仍有效地将受控系统稳定在目标状态周围，并减少了达到目标所需的推理时间。
英文摘要：
Deep neural networks are increasingly used as an effective parameterization of control policies in various learning-based control paradigms. For continuous-time optimal control problems (OCPs), which are central to many decision-making tasks, control policy learning can be cast as a neural ordinary differential equation (NODE) problem wherein state and control constraints are naturally accommodated. This paper presents a NODE approach to solving continuous-time OCPs for the case of stabilizing a known constrained nonlinear system around a target state. The approach, termed Lyapunov-NODE control (L-NODEC), uses a novel Lyapunov loss formulation that incorporates an exponentially-stabilizing control Lyapunov function to learn a state-feedback neural control policy, bridging the gap of solving continuous-time OCPs via NODEs with stability guarantees. The proposed Lyapunov loss allows L-NODEC to guarantee exponential stability of the controlled system, as well as its adversarial robustness to perturbations to the initial state. The performance of L-NODEC is illustrated in two problems, including a dose delivery problem in plasma medicine. In both cases, L-NODEC effectively stabilizes the controlled system around the target state despite perturbations to the initial state and reduces the inference time necessary to reach the target.
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