用神经微分方程设计稳定控制器，确保机械系统可控。
Negative Imaginary Neural ODEs: Learning to Control Mechanical Systems with Stability Guarantees
- 在哈密顿框架中构建带性质约束的神经网络控制器
- 保证共位力控与位置传感系统渐近稳定
- 适合需要稳定保证的机械控制场景
我们提出一种神经控制方法，通过新型负虚部神经常微分方程（NINODE）控制器，为机械系统提供可保证的稳定性。具体地，在哈密顿框架中使用具有期望特性的神经网络作为状态空间函数矩阵，确保系统具备负虚部（NI）特性。该NINODE系统可在特定条件下作为控制器，使NI受控对象实现渐近稳定。对于具有共位力执行器与位置传感器的机械系统，我们证明所有稳定性条件均可转化为控制器中神经网络的正则性约束。通过一个非线性弹簧-质量系统的实例，展示了NINODE控制器的有效性、实用性和稳定性保证。
原文摘要 · Abstract (English)
We propose a neural control method to provide guaranteed stabilization for mechanical systems using a novel negative imaginary neural ordinary differential equation (NINODE) controller. Specifically, we employ neural networks with desired properties as state-space function matrices within a Hamiltonian framework to ensure the system possesses the NI property. This NINODE system can serve as a controller that asymptotically stabilizes an NI plant under certain conditions. For mechanical plants with colocated force actuators and position sensors, we demonstrate that all the conditions required for stability can be translated into regularity constraints on the neural networks used in the controller. We illustrate the utility, effectiveness, and stability guarantees of the NINODE controller through an example involving a nonlinear mass-spring system.
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