Receding Hamiltonian-Informed Optimal Neural Control and State Estimation for Closed-Loop Dynamical Systems

2024-11-02

arXiv.org

AI Summary

This work addresses the challenge of simultaneously achieving customizable transient dynamics, closed-loop feedback, and real-time nonlinear predictive control in neural controllers for dynamic systems. Methodologically, we propose a Hamiltonian-principle-based optimal neural control framework: (i) a novel Hamiltonian information embedding mechanism that unifies state estimation with explicit nonlinear model predictive control (eNMPC); and (ii) a T-mano neural ODE architecture integrating Pontryagin’s maximum principle and multi-scale Taylor expansion, subject to Hamiltonian structural constraints to ensure training stability and estimation fidelity. Experiments across diverse linear and nonlinear dynamical systems demonstrate high-accuracy state estimation and millisecond-scale optimal control solution times. The framework significantly enhances transient response adaptability and closed-loop robustness while preserving physical interpretability and computational efficiency.

Technology Category

• Intelligent Robots: State Estimation
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Search and Optimization: Learning to Search

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• User Modeling, Personalization and Recommendation: Federated recommendation systems and personalization

Abstract

This paper formalizes Hamiltonian-Informed Optimal Neural (Hion) controllers, a novel class of neural network-based controllers for dynamical systems and explicit non-linear model predictive control. Hion controllers estimate future states and compute optimal control inputs using Pontryagin's Maximum Principle. The proposed framework allows for customization of transient behavior, addressing limitations of existing methods. The Taylored Multi-Faceted Approach for Neural ODE and Optimal Control (T-mano) architecture facilitates training and ensures accurate state estimation. Optimal control strategies are demonstrated for both linear and non-linear dynamical systems.

Problem

• Develop neural controllers for dynamical systems
• Estimate future states and optimal control
• Address limitations of existing control methods

Innovation

• Neural network-based Hamiltonian-Informed Optimal controllers
• T-mano architecture for Neural ODE and control
• Pontryagin's Maximum Principle for state estimation