General Framework of Trajectory Tracking Control of Hamiltonian Systems via Generalized Canonical Transformations

Abstract

This paper is devoted to trajectory tracking control of port-controlled Hamiltonian systems based on generalized canonical transformations. A general framework of tracking control utilizing the passivity property is proposed. Firstly, it is shown how to construct an error system, which describes the dynamics of the tracking error, by a passive port-controlled Hamiltonian system. Secondly, a practical procedure to construct tracking controllers of port-controlled Hamiltonian systems including nonholonomic systems is derived. Finally, a simple example of tracking control of a nonholonomic system demonstrates the effectiveness of the proposed method. This method is a natural extension of the conventional passivity based control and is expected to derive robustly stable control systems.