We discuss nonlinear model predictive control (NMPC) for multi-body dynamics via physics-informed machine learning methods. Physics-informed neural networks (PINNs) are a promising tool to approximate (partial) differential equations. PINNs are not suited for control tasks in their original form since they are not designed to handle variable control actions or variable initial values. We thus present the idea of enhancing PINNs by adding control actions and initial conditions as additional network inputs. The high-dimensional input space is subsequently reduced via a sampling strategy and a zero-hold assumption. This strategy enables the controller design based on a PINN as an approximation of the underlying system dynamics. The additional benefit is that the sensitivities are easily computed via automatic differentiation, thus leading to efficient gradient-based algorithms. Finally, we present our results using our PINN-based MPC to solve a tracking problem for a complex mechanical system, a multi-link manipulator.
翻译:我们讨论了通过物理知情的机器学习方法对多机体动态的非线性模型预测控制(NMPC)的问题。物理知情神经网络(PINNs)是接近(部分)差异方程式的一个很有希望的工具。 PINN并不适合于最初形式的控制任务,因为它们的设计不是为了处理可变的控制动作或可变初始值。因此我们提出了通过增加网络投入来增加控制动作和初始条件来增强PINN的构想。随后,通过取样战略和零位假设减少了高维输入空间。这一战略使基于 PINN 的控制器设计成为基本系统动态的近似。额外的好处是,通过自动区分很容易地计算这些灵敏度,从而导致高效的梯度算法。最后,我们用基于 PINN 的 MPC 来展示我们的结果,用我们的 PINN MPC 来解决复杂的机械系统(多链接操纵器)的跟踪问题。