Meta-Learning for Rapid Adaptation in Reference Tracking of Uncertain Nonlinear Systems

In this paper, we address the problem of reference tracking for uncertain nonlinear systems. Since collecting data from the target system (i.e., the system of interest) is often challenging, our objective is to design optimal controllers using limited target system data. Meta-learning provides a promising paradigm by leveraging offline data from source systems (systems sharing structural similarities with the target system) to accelerate training and enhance control performance. Motivated by this idea, we propose a meta-learning-based control framework that tailors the implicit model-agnostic meta-learning (iMAML) algorithm to the control setting. The framework operates in two phases: an (offline) meta-training phase, where an aggregated representation is learned from source data to capture the shared system dynamics among similar systems, and an (online) meta-adaptation phase, where this representation is fine-tuned on the target system using only a few data samples and limited adaptation steps. We formulate this framework as a bi-level optimization problem and provide an efficient solution with reduced storage complexity and few approximations. The proposed framework is general, allowing various learning algorithms to be integrated. To demonstrate this flexibility, we propose two specific learning algorithms that can be incorporated into our framework based on a neural state-space model and a deep Q-network, respectively. The primary distinction between these approaches is whether explicit system identification is required. Numerical simulations and hardware experiments demonstrate that the proposed methods enhance control performance and consistently outperform baseline approaches.

Parameter-Robust MPPI for Safe Online Learning of Unknown Parameters

Robots deployed in dynamic environments must remain safe even when key physical parameters are uncertain or change over time. We propose Parameter-Robust Model Predictive Path Integral (PRMPPI) control, a framework that integrates online parameter learning with probabilistic safety constraints. PRMPPI maintains a particle-based belief over parameters via Stein Variational Gradient Descent, evaluates safety constraints using Conformal Prediction, and optimizes both a nominal performance-driven and a safety-focused backup trajectory in parallel. This yields a controller that is cautious at first, improves performance as parameters are learned, and ensures safety throughout. Simulation and hardware experiments demonstrate higher success rates, lower tracking error, and more accurate parameter estimates than baselines.