  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.
