Direct Discrete-Time Design for Sampled-Data Hamiltonian Control Systems

The success in a model-based direct discrete-time design for nonlinear sampled-data control systems depends on the availability of a good discrete-time plant model to use for the design. Unfortunately, even if the continuous-time model of a plant is known, we cannot in general compute the exact discrete-time model of the plant, since it requires computing an explicit analytic solution of a nonlinear differential equation. One way to solve the problem of finding a good model is by using an approximate model of the plant. A general framework for stabilization of sampled-data nonlinear systems via their approximate discrete-time models was presented in [11]. It is suggested that approximate discrete-time models can be obtained using various numerical algorithms, such as Runge-Kutta and multistep methods. Yet, to the best of the authors knowledge, almost all available results on this direction view the systems as dissipative systems, whereas for design purpose, there are many systems that are better modeled as Hamiltonian conservative systems.