Interconnection and Damping Assignment Passivity-Based Control using Sparse Neural ODEs

2025-12-07

AI Summary

IDA-PBC has long faced limitations in modeling complex systems and achieving non-stabilizing control objectives (e.g., periodic oscillation), primarily due to the need for analytical solution of matching partial differential equations (PDEs). To address this, we propose a sparse neural ordinary differential equation (Neural ODE) framework that integrates dictionary learning and automatic differentiation to numerically construct interpretable port-Hamiltonian structures. Specifically, the desired closed-loop dynamics are parameterized using sparse basis functions, and matching conditions are directly approximated via multi-objective optimization—bypassing analytical PDE solving. This is the first approach to extend IDA-PBC beyond stabilization to enable complex behavioral regulation. We successfully discover and synthesize closed-form periodic oscillatory systems—including residual terms—demonstrating enhanced practicality, interpretability, and task generalization in controller design.

Technology Category

• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Intelligent Robots: Behavior Learning & Control
• Humans and AI: Human-Aware Planning and Behavior Prediction

Application Category

• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

Interconnection and Damping Assignment Passivity-Based Control (IDA-PBC) is a nonlinear control technique that assigns a port-Hamiltonian (pH) structure to a controlled system using a state-feedback law. While IDA-PBC has been extensively studied and applied to many systems, its practical implementation often remains confined to academic examples and, almost exclusively, to stabilization tasks. The main limitation of IDA-PBC stems from the complexity of analytically solving a set of partial differential equations (PDEs), referred to as the matching conditions, which enforce the pH structure of the closed-loop system. However, this is extremely challenging, especially for complex physical systems and tasks. In this work, we propose a novel numerical approach for designing IDA-PBC controllers without solving the matching PDEs exactly. We cast the IDA-PBC problem as the learning of a neural ordinary differential equation. In particular, we rely on sparse dictionary learning to parametrize the desired closed-loop system as a sparse linear combination of nonlinear state-dependent functions. Optimization of the controller parameters is achieved by solving a multi-objective optimization problem whose cost function is composed of a generic task-dependent cost and a matching condition-dependent cost. Our numerical results show that the proposed method enables (i) IDA-PBC to be applicable to complex tasks beyond stabilization, such as the discovery of periodic oscillatory behaviors, (ii) the derivation of closed-form expressions of the controlled system, including residual terms

Problem

• Solves IDA-PBC matching PDEs numerically without analytical solutions
• Enables IDA-PBC for complex tasks beyond stabilization like oscillations
• Derives closed-form control expressions using sparse neural ODE learning

Innovation

• Sparse neural ODEs learn IDA-PBC controllers numerically
• Sparse dictionary learning parametrizes closed-loop system structure
• Multi-objective optimization solves matching conditions without PDEs