Gradient Based Discrete-Time Modeling and Control of Hamiltonian Systems

A gradient based discrete-time model of continuous Hamiltonian systems with input is proposed and a procedure is given to construct the discrete-time model. The model validation for both separable and non-separable case is done considering the energy relation, additionally stabilizability condition is given and the model is also tested especially for the well-known non-separable Hamiltonian systems by simulations. After then, the discrete-time counterpart of PBC technique is developed for n-degree of freedom mechanical systems using this proposed discrete-time model. The discrete-time control rules which correspond to potential energy shaping and damping assignment are designed directly using the discrete time model of the desired system and the discrete time model of the open loop systems. To illustrate the effectiveness of the proposed method, two non-separable examples are investigated and the simulation results are given.