Port-Hamiltonian Systems and Optimal Control

Port-Hamiltonian systems provide a unified framework for modelling multiphysics dynamics by explicitly representing energy storage, dissipation and power‐conserving interconnections. Originating in network theory and classical mechanics, this formalism expresses system behaviour through a Hamiltonian function that captures total energy and a port structure that encodes exchanges with the environment. The resulting models are often cast as differential‐algebraic equations, preserving key structural properties such as passivity. Optimal control理论 for port‐Hamiltonian systems seeks to determine inputs that minimise or constrain performance indices—typically energy, fuel consumption or error—while respecting the intrinsic energy‐based constraints. Methods range from Pontryagin’s minimum principle tailored to port‐Hamiltonian structure, through algebraic Riccati equations that exploit the system’s symplectic geometry, to convex‐optimisation approaches for linear and nonlinear instances. This synergy between energy‐aware modelling and optimal control has enabled advances in robotics, power networks and mechatronic systems, delivering controllers that guarantee stability, robustness and efficient resource allocation.

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Port-Hamiltonian Systems and Optimal Control publication trend

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Technical terms

Port‐Hamiltonian system: A model that represents a physical system in terms of energy storage (Hamiltonian), energy flow ports and interconnection structure, ensuring power balance and passivity.

Differential‐algebraic equation (DAE): A system of equations combining differential relations and algebraic constraints, typical of interconnected energy systems with kinematic or circuit constraints.

Passivity: A property signifying that a system cannot generate energy; the supplied energy always exceeds or equals the sum of stored and dissipated energy, supporting stability.

Controllability: The ability to drive the state of a system from any initial condition to any desired final condition by appropriate inputs over a finite time interval.

Stabilizability: The property that all unstable modes of a system can be rendered asymptotically stable through suitable feedback control.

Hamiltonian function: A scalar energy function, typically the sum of kinetic and potential energies, which governs the evolution and performance objectives of the system.

References

1. Port-Hamiltonian descriptor systems are relative generically controllable and stabilizable. Mathematics of Control, Signals, and Systems (2024).
2. Differential–algebraic systems with dissipative Hamiltonian structure. Mathematics of Control, Signals, and Systems (2023).
3. The difference between port-Hamiltonian, passive and positive real descriptor systems. Mathematics of Control, Signals, and Systems (2023).