Adaptive Uncertainty Quantification for Scenario-based Control Using Meta-learning of Bayesian Neural Networks
Yajie Bao, Javad Mohammadpour Velni
TL;DR
The paper tackles time-varying uncertainty in constrained nonlinear control by learning an adaptable Bayesian neural network (BNN) for the disturbance term g, using model-agnostic meta-learning (MAML) to obtain a global model w* and a trajectory-driven updating law for fast online adaptation. The local BNN theta(k)=w*+Delta_theta_psi(tau) refines uncertainty estimates at each time step, enabling adaptive scenario generation for scenario-based MPC with a probabilistic safety certificate. Key contributions include a MAML-BNN framework for online adaptation, a safe scheme for scenario generation via mean-variance-based discretization, and experimental validation showing improved uncertainty quantification and closed-loop performance over a fixed offline BNN baseline. The approach reduces conservatism in uncertainty handling while enforcing safety across generated scenarios, with practical impact on nonlinear, unknown-dynamics control where data drift and time-varying uncertainty are prevalent.
Abstract
Scenario-based optimization and control has proven to be an efficient approach to account for system uncertainty. In particular, the performance of scenario-based model predictive control (MPC) schemes depends on the accuracy of uncertainty quantification. However, current learning- and scenario-based MPC (sMPC) approaches employ a single timeinvariant probabilistic model (learned offline), which may not accurately describe time-varying uncertainties. Instead, this paper presents a model-agnostic meta-learning (MAML) of Bayesian neural networks (BNN) for adaptive uncertainty quantification that would be subsequently used for adaptive-scenario-tree model predictive control design of nonlinear systems with unknown dynamics to enhance control performance. In particular, the proposed approach learns both a global BNN model and an updating law to refine the BNN model. At each time step, the updating law transforms the global BNN model into more precise local BNN models in real time. The adapted local model is then used to generate scenarios for sMPC design at each time step. A probabilistic safety certificate is incorporated in the scenario generation to ensure that the trajectories of the generated scenarios contain the real trajectory of the system and that all the scenarios adhere to the constraints with a high probability. Experiments using closed-loop simulations of a numerical example demonstrate that the proposed approach can improve the performance of scenario-based MPC compared to using only one BNN model learned offline for all time steps.