MPC of Uncertain Nonlinear Systems with Meta-Learning for Fast
  Adaptation of Neural Predictive Models
Jiaqi Yan Ankush Chakrabarty Alisa Rupenyan John Lygeros
In this paper, we consider the problem of reference tracking in uncertain
nonlinear systems. A neural State-Space Model (NSSM) is used to approximate the
nonlinear system, where a deep encoder network learns the nonlinearity from
data, and a state-space component captures the temporal relationship. This
transforms the nonlinear system into a linear system in a latent space,
enabling the application of model predictive control (MPC) to determine
effective control actions. Our objective is to design the optimal controller
using limited data from the \textit{target system} (the system of interest). To
this end, we employ an implicit model-agnostic meta-learning (iMAML) framework
that leverages information from \textit{source systems} (systems that share
similarities with the target system) to expedite training in the target system
and enhance its control performance. The framework consists of two phases: the
(offine) meta-training phase learns a aggregated NSSM using data from source
systems, and the (online) meta-inference phase quickly adapts this aggregated
model to the target system using only a few data points and few online training
iterations, based on local loss function gradients. The iMAML algorithm
exploits the implicit function theorem to exactly compute the gradient during
training, without relying on the entire optimization path. By focusing solely
on the optimal solution, rather than the path, we can meta-train with less
storage complexity and fewer approximations than other contemporary
meta-learning algorithms. We demonstrate through numerical examples that our
proposed method can yield accurate predictive models by adaptation, resulting
in a downstream MPC that outperforms several baselines.