Time-varying Stabilization of Hamiltonian Systems via Generalized Canonical Transformations

This paper focuses on the stabilization of port-controlled Hamiltonian systems employing possibly time-varying controllers. At first we refer to the generalized canonical transformation which preserves the structure of Hamiltonian systems and the passivity property that physical systems innately possess. Next we show a general stabilization strategy for port-controlled Hamiltonian systems based on it which is a natural generalization of well-known passivity based control. Finally we utilize this method to mechanical Hamiltonian systems with nonholonomic constraints by modifying the kinetic energy of the system. Furthermore some examples are given to show how this technique works for physical systems.