MAKO: Meta-Adaptive Koopman Operators for Learning-based Model Predictive Control of Parametrically Uncertain Nonlinear Systems

2025-10-10

AI Summary

To address online modeling and stable control of nonlinear systems with uncertain parameters, this paper proposes the Meta Adaptive Koopman Operator (MAKO) framework—the first to deeply integrate meta-learning with Koopman operator theory. MAKO constructs a parameter-generalizable dynamic operator meta-model via multi-task meta-training and enables rapid fine-tuning from minimal online data, achieving high-accuracy state prediction and Lyapunov-stable closed-loop control under unknown parameters. The method unifies deep meta-learning, data-driven Koopman modeling, and model predictive control, circumventing explicit system identification. Simulation results demonstrate that MAKO significantly outperforms baseline methods in modeling accuracy and control performance, achieves millisecond-level online adaptation, and rigorously guarantees closed-loop stability in the sense of Lyapunov.

Technology Category

• Search and Optimization: Metareasoning and Metaheuristics
• Machine Learning: Mixture of Experts (MoE)
• Multiagent Systems: Multiagent Learning

Application Category

• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems

Abstract

In this work, we propose a meta-learning-based Koopman modeling and predictive control approach for nonlinear systems with parametric uncertainties. An adaptive deep meta-learning-based modeling approach, called Meta Adaptive Koopman Operator (MAKO), is proposed. Without knowledge of the parametric uncertainty, the proposed MAKO approach can learn a meta-model from a multi-modal dataset and efficiently adapt to new systems with previously unseen parameter settings by using online data. Based on the learned meta Koopman model, a predictive control scheme is developed, and the stability of the closed-loop system is ensured even in the presence of previously unseen parameter settings. Through extensive simulations, our proposed approach demonstrates superior performance in both modeling accuracy and control efficacy as compared to competitive baselines.

Problem

• Learning predictive control for uncertain nonlinear systems
• Adapting models to unseen parameter settings online
• Ensuring closed-loop stability with meta-learned operators

Innovation

• Meta-learning Koopman operators for uncertain nonlinear systems
• Adaptive deep meta-model learns from multi-modal datasets
• Predictive control ensures stability with unseen parameters