State-dependent periodic adaptive disturbance compensation

The state-dependent nonlinear external disturbance compensation problem is considered. No prior information about the disturbance is assumed except the periodicity of the disturbance with respect to a state variable, which is termed a ´state-dependent periodic disturbance.´ The key idea of the proposed new adaptive compensation method is to make use of this known state-dependent periodicity. In the first period, an adaptive compensator is designed to guarantee the L₂-stability of the overall system. From the second period and onwards, a state- periodic adaptive compensator is designed to stabilise the system by using the information stored in the previous period. The Lyapunov stability analysis is performed on the evolution along the trajectory axis. The validity of the proposed state-periodic adaptive control method is illustrated through a simulation example.