eess.SYApr 14, 2026

Structure- and Stability-Preserving Learning of Port-Hamiltonian Systems

Authors: Binh Nguyen, Nam T. Nguyen, Truong X. Nghiem

Organizations: Department of Electrical and Computer Engineering, College of Engineering and Computer Science, University of Central Florida, Orlando, FL 32816, USA

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Abstract

This paper investigates the problem of data-driven modeling of port-Hamiltonian systems while preserving their intrinsic Hamiltonian structure and stability properties. We propose a novel neural-network-based port-Hamiltonian modeling technique that relaxes the convexity constraint commonly imposed by neural network-based Hamiltonian approximations, thereby improving the expressiveness and generalization capability of the model. By removing this restriction, the proposed approach enables the use of more general non-convex Hamiltonian representations to enhance modeling flexibility and accuracy. Furthermore, the proposed method incorporates information about stable equilibria into the learning process, allowing the learned model to preserve the stability of multiple isolated equilibria rather than being restricted to a single equilibrium as in conventional methods. Two numerical experiments are conducted to validate the effectiveness of the proposed approach and demonstrate its ability to achieve more accurate structure- and stability-preserving learning of port-Hamiltonian systems compared with a baseline method.

Figures & tables

Fig. 1 : Illustration of h(σ(∥x∥2))h(\sigma(\|{\mathbf{x}}\|_{2})) at xeq=0{\mathbf{x}}_{\mathrm{eq}}={\bf 0} .
Fig. 2 : Responses of the actual PHS, PH-ICNN, and proposed models to the sinusoid test signal for the Toda lattice system.
Fig. 3 : Responses of the actual PHS, PH-ICNN, and proposed models to the pulse test signal for the Toda lattice system.
Fig. 4 : A double pendulum system.
Fig. 5 : State trajectories of the double pendulum system from three different initial states x0(1)=[0,0,10,−2]⊤\mathbf{x}_{0}^{(1)}=[0,0,10,-2]^{\top} , x0(2)=[0,0,1,−1]⊤\mathbf{x}_{0}^{(2)}=[0,0,1,-1]^{\top} , and x0(3)=[0,0,−8,1]⊤\mathbf{x}_{0}^{(3)}=[0,0,-8,1]^{\top} . These cases illustrate different stable equilibria xeq(1)=[2π,2π,0,0]⊤{\mathbf{x}}_{\mathrm{eq}}^{(1)}=[2\pi,2\pi,0,0]^{\top} , xeq(2)=[0,0,0,0]⊤{\mathbf{x}}_{\mathrm{eq}}^{(2)}=[0,0,0,0]^{\top} , and xeq(3)=[−2π,0,0,0]⊤{\mathbf{x}}_{\mathrm{eq}}^{(3)}=[-2\pi,0,0,0]^{\top} .

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