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Model Predictive Control (MPC) is a state-of-the-art (SOTA) control techniquewhich requires solving hard constrained optimization problems iteratively. Foruncertain dynamics, analytical model based robust MPC imposes additionalconstraints, increasing the hardness of the problem. The problem exacerbates inperformance-critical applications, when more compute is required in lessertime. Data-driven regression methods such as Neural Networks have been proposedin the past to approximate system dynamics. However, such models rely on highvolumes of labeled data, in the absence of symbolic analytical priors. Thisincurs non-trivial training overheads. Physics-informed Neural Networks (PINNs)have gained traction for approximating non-linear system of ordinarydifferential equations (ODEs), with reasonable accuracy. In this work, wepropose a Robust Adaptive MPC framework via PINNs (RAMP-Net), which uses aneural network trained partly from simple ODEs and partly from data. A physicsloss is used to learn simple ODEs representing ideal dynamics. Having access toanalytical functions inside the loss function acts as a regularizer, enforcingrobust behavior for parametric uncertainties. On the other hand, a regular dataloss is used for adapting to residual disturbances (non-parametricuncertainties), unaccounted during mathematical modelling. Experiments areperformed in a simulated environment for trajectory tracking of a quadrotor. Wereport 7.8% to 43.2% and 8.04% to 61.5% reduction in tracking errors for speedsranging from 0.5 to 1.75 m/s compared to two SOTA regression based MPC methods.

RAMP-Net: A Robust Adaptive MPC for Quadrotors via Physics-informed Neural Network