Adaptive H∞ Control for Nonlinear Hamiltonian Systems with Time Delay and Parametric Uncertainties

This paper addresses the adaptive H∞ control problem for a class of nonlinear Hamiltonian systems with time delay and parametric uncertainties. The uncertainties under consideration are some small parameter perturbations involved in the structure of the Hamiltonian system. Both delay-independent and delay-dependent criteria are established based on the dissipative structural properties of the Hamiltonian systems and the Lyapunov-Krasovskii functional approach. In order to construct the adaptive H∞controller, the situation that the parameter perturbation is inexistent in the system is also studied and the controller is designed.The adaptive H∞ control problem is solved under some sufficient conditions which ensure the asymptotic stability and the L2 gain performance of the resulted closed-loop system. Numerical example is given to illustrate the applicability of the theoretical results.