Robust Neural IDA-PBC: passivity-based stabilization under approximations
<|reference_start|>Robust Neural IDA-PBC: passivity-based stabilization under approximations: 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.<|reference_end|>
@article{sanchez-escalonilla2024robust,
    title={Robust Neural IDA-PBC: passivity-based stabilization under
  approximations},
    author={Santiago Sanchez-Escalonilla, Samuele Zoboli and Bayu Jayawardhana},
    journal={arXiv preprint arXiv:2409.16008},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.16008},
    primaryClass={eess.SY cs.LG cs.SY math.OC}
}