Robust Neural IDA-PBC: passivity-based stabilization under approximations

TL;DR

This paper introduces a robust neural IDA-PBC method that ensures stability and robustness in passivity-based control, even under approximations and for complex port-Hamiltonian systems, validated through simulations on standard benchmarks.

Contribution

It reformulates Neural IDA-PBC as an optimization problem with stability constraints, enabling application to systems where classical solutions are infeasible.

Findings

Ensures practical and asymptotic stability under approximations.

Extends Neural IDA-PBC to port-Hamiltonian systems without exact matching.

Validated on benchmarks including double pendulum and cartpole.

Abstract

In this paper, we restructure the Neural Interconnection and Damping Assignment - Passivity Based Control (Neural IDA-PBC) design methodology, and we formally analyze its closed-loop properties. Neural IDA-PBC redefines the IDA-PBC design approach as an optimization problem by building on the framework of Physics Informed Neural Networks (PINNs). However, the closed-loop stability and robustness properties under Neural IDA-PBC remain unexplored. To address the issue, we study the behavior of classical IDA-PBC under approximations. Our theoretical analysis allows deriving conditions for practical and asymptotic stability of the desired equilibrium point. Moreover, it extends the Neural IDA-PBC applicability to port-Hamiltonian systems where the matching conditions cannot be solved exactly. Our renewed optimization-based design introduces three significant aspects: i) it involves a novel optimization objective including stability and robustness constraints issued from our theoretical analysis; ii) it employs separate Neural Networks (NNs), which can be structured to reduce the search space to relevant functions; iii) it does not require knowledge about the port-Hamiltonian formulation of the system's model. Our methodology is validated with simulations on three standard benchmarks: a double pendulum, a nonlinear mass-spring-damper and a cartpole. Notably, classical IDA-PBC designs cannot be analytically derived for the latter.