Model Predictive Control (MPC) is a state-of-the-art (SOTA) control technique which requires solving hard constrained optimization problems iteratively. For uncertain dynamics, analytical model based robust MPC imposes additional constraints, increasing the hardness of the problem. The problem exacerbates in performance-critical applications, when more compute is required in lesser time. Data-driven regression methods such as Neural Networks have been proposed in the past to approximate system dynamics. However, such models rely on high volumes of labeled data, in the absence of symbolic analytical priors. This incurs non-trivial training overheads. Physics-informed Neural Networks (PINNs) have gained traction for approximating non-linear system of ordinary differential equations (ODEs), with reasonable accuracy. In this work, we propose a Robust Adaptive MPC framework via PINNs (RAMP-Net), which uses a neural network trained partly from simple ODEs and partly from data. A physics loss is used to learn simple ODEs representing ideal dynamics. Having access to analytical functions inside the loss function acts as a regularizer, enforcing robust behavior for parametric uncertainties. On the other hand, a regular data loss is used for adapting to residual disturbances (non-parametric uncertainties), unaccounted during mathematical modelling. Experiments are performed in a simulated environment for trajectory tracking of a quadrotor. We report 7.8% to 43.2% and 8.04% to 61.5% reduction in tracking errors for speeds ranging from 0.5 to 1.75 m/s compared to two SOTA regression based MPC methods.

翻译：模型预测控制（MPC）作为一种最先进的控制技术，需迭代求解硬约束优化问题。针对具有不确定性的动力学系统，基于分析模型的鲁棒MPC需额外施加约束条件，进一步加剧了问题求解难度。在性能关键型应用中，当需要在更短时间内完成更多计算时，该问题尤为突出。现有研究提出采用神经网络等数据驱动回归方法逼近系统动力学，但此类模型在缺乏符号化分析先验知识时高度依赖大规模标注数据，导致训练开销显著增加。物理信息神经网络（PINN）因能以较高精度逼近非线性常微分方程组而备受关注。本文提出基于PINN的鲁棒自适应MPC框架（RAMP-Net），该框架采用部分由简单常微分方程训练、部分由数据训练的神经网络。通过物理损失项学习表征理想动力学的简单常微分方程，损失函数中包含的分析函数作为正则化器，有效增强对参数化不确定性的鲁棒性。同时，利用常规数据损失项对数学建模中未考虑的残余扰动（非参数化不确定性）进行自适应补偿。在四旋翼飞行器轨迹跟踪的仿真实验中，当飞行速度范围为0.5至1.75米/秒时，相较于两种基于回归的SOTA MPC方法，本文方法将跟踪误差分别降低7.8%至43.2%和8.04%至61.5%。