Port-Hamiltonian Systems and Boundary Control Techniques

Port-Hamiltonian systems are an energy-centric modelling paradigm that unifies the representation of physical processes through Hamiltonian energy functions and interconnection structures known as Dirac structures. In spatially distributed systems governed by partial differential equations, energy exchange with the environment is handled via boundary ports, paving the way for boundary control and observation. This formalism emphasises modularity: mechanical, electrical and fluid subsystems can be interconnected through power-conserving ports while preserving stability properties. Boundary control techniques exploit passivity to design feedback laws that achieve robustness and performance objectives, even in the presence of in-domain instabilities or anti-damping. Recent theoretical breakthroughs have extended the framework to non-conservative and moving spatial domains on Riemannian manifolds, enabling coordinate-free descriptions of complex fluid–structure interactions. On the computational side, structure-preserving discretisation schemes—such as finite element exterior calculus and dual-field methods—ensure that discrete models retain symplectic geometry and exact energy balances. Applications span flexible-beam control with smart actuators, thermodynamically consistent two-phase flow, and real-time simulation of shallow-water phenomena. Advanced boundary control designs, including scattering and Lyapunov-based approaches, now guarantee exponential stability and energy shaping in infinite-dimensional settings. Through its energy-based language, the port-Hamiltonian paradigm offers a coherent foundation for analysis, simulation and control across a broad spectrum of engineering systems with spatial extent.

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Port-Hamiltonian Systems and Boundary Control Techniques publication trend

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Technical terms

Port-Hamiltonian system: A model of physical systems described by an energy (Hamiltonian) function and interconnected via structures that ensure power-conserving exchanges between storage, dissipation and ports.

Boundary port: A designated interface on the spatial boundary of a distributed-parameter system through which energy, momentum or other conserved quantities flow to controllers or the environment.

Dirac structure: A bilinear geometric relation that generalises symplectic and Poisson structures, encoding the interconnection rules that preserve power balance among energy variables and co-variables.

Stokes–Dirac structure: An extension of Dirac structures to infinite-dimensional systems, combining differential operators (exterior derivative and its adjoint) with boundary terms to capture energy flow in space and through boundaries.

Passivity: A system property asserting that net energy output cannot exceed energy input, often used to guarantee stability and facilitate energy-based controller design.

References

1. Energy-Based Modeling and Hamiltonian LQG Control of a Flexible Beam Actuated by IPMC Actuators. IEEE Access (2022).
2. Dual field structure-preserving discretization of port-Hamiltonian systems using finite element exterior calculus. Journal of Computational Physics (2022).
3. Energetic decomposition of distributed systems with moving material domains: The port-Hamiltonian model of fluid-structure interaction. Journal of Geometry and Physics (2022).
4. Port-Hamiltonian formulation of two-phase flow models. Systems & Control Letters (2021).
5. Stabilization of Unstable Distributed Port-Hamiltonian Systems in Scattering Form. IEEE Control Systems Letters (2022).
6. Port-Hamiltonian formulations for the modeling, simulation and control of fluids. Computers & Fluids (2024).
7. Stokes-Dirac structures for distributed parameter port-Hamiltonian systems: An analytical viewpoint. Communications in Analysis and Mechanics (2023).