Speaker
Description
Port-Hamiltonian (pH) systems provide a highly structured and physically motivated framework for modeling and controlling complex dynamical systems by explicitly capturing energy-based dynamics, dissipation, and interconnection geometry. However, many practical physical systems exhibit non-polynomial non-linearities that hinder the application of modern constructive control design methods, such as sum-of-squares (SOS) optimization, which typically require polynomial system representations.
We address the fundamental problem of transforming non-polynomial port-Hamiltonian systems into equivalent polynomial representations without sacrificing their favorable structural properties. We explore a novel lifted immersion technique that combines conceptual ideas from system lifting and immersion to construct a higher-dimensional polynomial port-Hamiltonian system that preserves the essential features of the original system along system trajectories. Specifically, we prove that the proposed immersion preserves:
(i) the internal interconnection geometry with identical rational Hamiltonian,
(ii) the port structure and conjugated input-output relationship, and
(iii) the dissipation and passivity properties with respect to the original Hamiltonian on an invariant embedded submanifold.
The resulting polynomial pH system structure enables the design of stabilizing feedback laws by combining interconnection and damping assignment passivity-based control with sum-of-squares optimization techniques. We demonstrate the effectiveness of this approach through several illustrative examples, showing how polynomial immersions bridge the gap between the structural advantages of port-Hamiltonian systems and the computational benefits of polynomial control design methods.