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）是一种最先进的控制技术，需要迭代求解硬约束优化问题。对于不确定动力学系统，基于解析模型的鲁棒MPC会引入额外约束，进一步加剧问题求解难度。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。过去已有研究提出神经网络等数据驱动回归方法来逼近系统动力学，但此类模型在缺乏符号解析先验知识时严重依赖大规模标注数据，导致训练开销显著。物理信息神经网络（PINN）因能以合理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。物理损失函数用于学习表征理想动力学的简单常微分方程，将解析函数嵌入损失函数可作为正则化项，强制模型对参数不确定性保持鲁棒行为。同时，常规数据损失函数用于自适应数学建模中未考虑的残余扰动（非参数不确定性）。在四旋翼轨迹跟踪仿真环境中的实验表明：与两种基于回归的最先进MPC方法相比，本方法在0.5至1.75米/秒速度范围内分别实现7.8%-43.2%和8.04%-61.5%的跟踪误差降低。