论文标题
在学习具有深层操作员网络的非线性控制系统的动态响应时
On Learning the Dynamical Response of Nonlinear Control Systems with Deep Operator Networks
论文作者
论文摘要
我们提出了一个深层运算符网络〜（DeepOnet）框架，以从数据中学习连续时间非线性控制系统的动态响应。为此，我们首先构建并训练一个近似控制系统的本地解决方案操作员的deponet。然后，我们设计了一个数值方案，该方案递归地使用训练有素的Dewonet来模拟控制系统的长/中期动态响应，以适应给定的控制输入和初始条件。我们伴随提出的方案，并估算了相关累积误差的误差结合。此外，我们设计了一个数据驱动的runge-kutta〜（RK）显式方案，该方案使用deeponet正向通行证和自动差异化，以便在数值方案的步长足够小时更好地近似系统的响应。对捕食者捕集，摆和卡车极系统进行的数值实验证实，我们的DeepOnet框架学会了有效地近似非线性控制系统的动态响应。
We propose a Deep Operator Network~(DeepONet) framework to learn the dynamic response of continuous-time nonlinear control systems from data. To this end, we first construct and train a DeepONet that approximates the control system's local solution operator. Then, we design a numerical scheme that recursively uses the trained DeepONet to simulate the control system's long/medium-term dynamic response for given control inputs and initial conditions. We accompany the proposed scheme with an estimate for the error bound of the associated cumulative error. Furthermore, we design a data-driven Runge-Kutta~(RK) explicit scheme that uses the DeepONet forward pass and automatic differentiation to better approximate the system's response when the numerical scheme's step size is sufficiently small. Numerical experiments on the predator-prey, pendulum, and cart pole systems confirm that our DeepONet framework learns to approximate the dynamic response of nonlinear control systems effectively.
