Adaptive control of time‐varying uncertain non‐linear systems with input delay: a Hamiltonian approach

Abstract

The adaptive control problem of a class of time-varying non-linear systems with uncertainties and input delay is addressed via a Hamiltonian approach in this study. The delay is assumed to be a constant and the uncertainties are small parametric perturbations. First, the non-linear system is equivalently transformed into a Hamiltonian system form and the Casimir-like function is proposed to help shaping the Hamiltonian as a candidate of Lyapunov function in the extended systems. Second, the adaptive control problem is investigated based on the time-varying dissipative Hamiltonian system with input delay. The feedback controller is designed to guarantee the stability of the closed-loop system for all admissible uncertainties, as well as constant delay. Sufficient conditions are presented to ensure the rationality of the proposed control law, which are derived based on Lyapunov function method. Stabilisation problem is also considered while there are no uncertain parameters in the delay non-linear systems. Finally, several examples are presented to illustrate the effectiveness of the results obtained in this study.