Augmented Hamiltonian Formulation and Energy-Based Control Design of Uncertain Mechanical Systems

This paper mainly investigates augmented Hamiltonian formulation for both fully actuated and underactuated uncertain mechanical systems. First, a high-order partial derivative operator, called the unified partial derivative operator (UPDO), is given, and its properties are investigated, which plays a very important role in presenting the main results of this paper. Secondly, using the tool UPDO, the idea of shaping potential energy, and the pre-feedback technique, an augmented Hamiltonian structure with dissipation is provided for both fully actuated and underactuated uncertain mechanical systems. It is shown that the augmented Hamiltonian formulation has some nice properties for further analysis and control, and at the same time, its matching condition in the underactuated case becomes a set of algebraic equations, which are much easier to solve in comparison with solving a set of partial differential equations. Finally, as an application, the energy-based robust adaptive control is studied by using the augmented Hamiltonian formulation, and a new energy-based adaptive L ₂ disturbance attenuation controller is designed for the uncertain mechanical systems. Study of an illustrative example with simulations shows that the controller obtained in this paper works very well in handling disturbances and uncertainties in the systems.