Passivity Based Control of Stochastic Port-Hamiltonian Systems

This paper introduces Stochastic Port-Hamiltonian Systems (SPHS's), whose dynamics are described by Ito stochastic differential equations. SPHS's are extension of the deterministic port-Hamiltonian systems which are used to express various passive systems. First, we show a necessary and sufficient condition to preserve the stochastic port-Hamiltonian structure of the system under a class of coordinate transformations. Second, we derive a condition for the system to be stochastic passive. Third, we equip Stochastic Generalized Canonical Transformations (SGCT's), which are pairs of coordinate and feedback transformations preserving the stochastic port-Hamiltonian structure. Finally, we propose a stochastic stabilization framework based on stochastic passivity and SGCT's.