Stabilization of Hamiltonian systems with nonholonomic constraints based on time-varying generalized canonical transformations

This paper is concerned with the stabilization of nonholonomic systems in portcontrolled Hamiltonian formulae based on time-varying generalized canonical transformations. A special class of time-varying generalized canonical transformations are introduced which modify the kinetic energy of the original system without changing the generalized Hamiltonian structure with passivity. Utilizing these transformations, time-varying asymptotically stabilizing controllers for the nonholonomic Hamiltonian systems are derived. Since the proposed method is a natural generalization of passivity based control for conventional holonomic systems, it is expected that the tools developed for conventional systems will be applicable to nonholonomic systems based on the proposed method.