Adaptive output dynamic feedback control for nonaffine pure-feedback time delay system with unknown backlash-like hysteresis

In this paper, an extreme learning machine (ELM)-based adaptive output feedback command filtered control method is investigated for nonlinear nonaffine pure-feedback system with unknown time delay and backlash-like hysteresis. Firstly, the considered nonaffine pure-feedback system is transformed into affine form on account of the implicit function theorem and mean value theorem. Then, an adaptive state observer is constructed to estimate the unmeasured states. ELM is employed to approximate unknown function without prior knowledge, which is a key operation in each step. Secondly, a novel adaptive command filtered controller is developed for the system under consideration. The “explosion of complexity” exists in traditional backstepping design can also be avoided via embedding the command filter in each step of the controller design. Simultaneously, the compensating signals are introduced to eliminate the effect of filtering errors, and the completely unknown backlash-like hysteresis control input that frequently exists in real systems is also taken into account. Design difficulties from unknown time delay terms are surmount employing the Lyapunov-Krasovskii functionals. Based on the stability analysis scheme, this method will guarantee all signals of the system are bounded. Finally, the metal cutting machine system is taken as an example to further verify the effectiveness of the proposed control strategy.